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Sébastien Roux, Christophe Arnold, Etienne Carré, Alexandre Plaud, Lei Ren, Frédéric Fossard, Nicolas Horezan, Eli Janzen, James H. Edgar, Camille Maestre, Bérangère Toury, Catherine Journet, Vincent Garnier, Philippe Steyer, [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), Cédric Robert, Xavier Marie, François Ducastelle, Annick Loiseau, Julien Barjon

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[Exciton Self-Trapping in Twisted Hexagonal Boron Nitride homostructures](https://mdr.nims.go.jp/datasets/3bf8a123-41ca-45f2-ab3c-b5f318ac6f9a)

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Exciton Self-Trapping in Twisted Hexagonal Boron Nitride homostructuresExciton Self-Trapping in Twisted Hexagonal Boron Nitride homostructuresSébastien Roux ,1,2,† Christophe Arnold ,2 Etienne Carré,1,2 Alexandre Plaud,1,2 Lei Ren,3 Frédéric Fossard,1Nicolas Horezan,4 Eli Janzen,5 James H. Edgar ,5 Camille Maestre ,6 Bérangère Toury,6 Catherine Journet ,6Vincent Garnier ,7 Philippe Steyer,7 Takashi Taniguchi ,8 Kenji Watanabe ,9 Cédric Robert,3 Xavier Marie ,3François Ducastelle,1,* Annick Loiseau ,1,‡ and Julien Barjon2,§1Université Paris-Saclay, ONERA, CNRS, LEM, 92320 Châtillon, France2Université Paris-Saclay, UVSQ, CNRS, GEMaC, 78000, Versailles, France3Université de Toulouse, INSA-CNRS-UPS, LPCNO, 135 Av. Rangueil, 31077 Toulouse, France4Université Paris-Saclay, ONERA, DMAS, F-92322 Châtillon, France5Tim Taylor Department of Chemical Engineering, Kansas State University Manhattan,Kansas 66506, USA6Laboratoire des Multimatériaux et Interfaces, UMR CNRS 5615, Univ Lyon Université Claude BernardLyon 1, F-69622 Villeurbanne, France7Laboratoire MATEIS, UMR CNRS 5510, Univ Lyon, INSA Lyon, F-69621 Villeurbanne, France8Research Center for Materials Nanoarchitectonics, National Institute for Materials Science,1-1 Namiki, Tsukuba 305-0044, Japan9Research Center for Electronic and Optical Materials, National Institute for Materials Science,1-1 Namiki, Tsukuba 305-0044, Japan(Received 19 May 2024; revised 14 December 2024; accepted 12 February 2025; published 27 May 2025)One of the main interests of 2D materials is their ability to be assembled with many degrees offreedom for tuning and manipulating excitonic properties. There is a need to understand how thestructure of the interfaces between atomic layers influences exciton properties. Here we usecathodoluminescence and time-resolved cathodoluminescence experiments to study how excitonsinteract with the interface between two twisted hexagonal boron nitride (h-BN) crystals with variousangles. An efficient capture of free excitons by the interface is demonstrated, which leads to apopulation of long-lived and interface-localized (2D) excitons. Temperature-dependent experimentsindicate that for high twist angles, these excitons localized at the interface further undergo a self-trapping. It consists in a distortion of the lattice around the exciton on which the exciton traps itself. Ourresults suggest that this exciton-interface interaction causes the broad 4-eV optical emission of highlytwisted h-BN–h-BN structures. Exciton self-trapping is finally discussed as a common feature of sp2hybridized boron nitride polytypes and nanostructures due to the ionic nature of the B—N bond and thesmall size of their excitons.DOI: 10.1103/PhysRevX.15.021067 Subject Areas: Condensed Matter Physics,Materials Science,Semiconductor PhysicsI. INTRODUCTIONThe conception of 2D material heterostructures (h-2Ds)benefits from a large number of degrees of freedom in thechoice of atomic layers and the way they are stacked,creating structural singularities at the interfaces between thelayers [1–4]. Taking advantage of these capabilities allowsone to control and manipulate the properties of excitons:the efficiency of their radiative recombination [5–10], theproperties of their emission [11], their diffusion length,their valley and/or spin coherence [12,13], and the dielec-tric screening between the electron and the hole [14–17].Finally, excitons can interact with moiré superpotentials,which tune their properties and motion [18–24]. Thus,h-2Ds offer an ideal platform for creating novel electronicdevices using exciton fluxes (excitronics) [25] or usingtheir spin or valley indices (valleytronics and spintronics)[26]. Hexagonal boron nitride (h-BN) is present in most*Deceased.†Contact author: sroux@insa-toulouse.fr‡Contact author: annick.loiseau@onera.fr§Contact author: julien.barjon@uvsq.frPublished by the American Physical Society under the terms ofthe Creative Commons Attribution 4.0 International license.Further distribution of this work must maintain attribution tothe author(s) and the published article’s title, journal citation,and DOI.PHYSICAL REVIEW X 15, 021067 (2025)2160-3308=25=15(2)=021067(17) 021067-1 Published by the American Physical Societyhttps://orcid.org/0000-0001-6493-744Xhttps://orcid.org/0000-0001-5540-8589https://orcid.org/0000-0003-0918-5964https://orcid.org/0000-0002-7911-3758https://orcid.org/0000-0002-3328-317Xhttps://orcid.org/0000-0003-0607-4409https://orcid.org/0000-0002-1467-3105https://orcid.org/0000-0003-3701-8119https://orcid.org/0000-0002-7772-2517https://orcid.org/0000-0002-1042-5876https://ror.org/03xjwb503https://ror.org/03xjwb503https://ror.org/03xjwb503https://ror.org/03xjwb503https://ror.org/03mkjjy25https://ror.org/004raaa70https://ror.org/004raaa70https://ror.org/03xjwb503https://ror.org/03xjwb503https://ror.org/05p1j8758https://ror.org/029brtt94https://ror.org/029brtt94https://ror.org/029brtt94https://ror.org/026v1ze26https://ror.org/026v1ze26https://crossmark.crossref.org/dialog/?doi=10.1103/PhysRevX.15.021067&domain=pdf&date_stamp=2025-05-27https://doi.org/10.1103/PhysRevX.15.021067https://doi.org/10.1103/PhysRevX.15.021067https://doi.org/10.1103/PhysRevX.15.021067https://doi.org/10.1103/PhysRevX.15.021067https://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/h-2Ds since it is the best insulating material for use as asubstrate or as a capping layer for other 2Dmaterials such astransition-metal dichalcogenides (TMDs), 2D magnets[27], and graphene [11,14,28–32]. Because h-BN plays sucha key role in h-2D-based devices, it is crucial to understandthe surface and interface effects associated with it.The simplest h-BN-based h-2D is the twisted h-BN–h-BN homostructure, which consists of two h-BN crystalswith different in-plane crystal orientations. These structuresexhibit many properties that are not present in single h-BNcrystals. At small twist angles, triangular ferroelectricdomains appear at the interface [33,34], as well as drasticchanges in the electronic properties, such as, in some cases,a spatial separation of the electron and hole wave functionswithin the moiré supercell [35,36]. At high twist angles,h-BN–h-BN homostructure exhibits intense second-harmonic generation, which could be modulated by thetwist angle [37]. Finally, a new 4-eV luminescence signalhas recently been discovered in cathodoluminescence (CL)on twisted h-BN–h-BN structures.Twisted h-BN–h-BN structures are composed of twostacked multilayer h-BN flakes, as shown in Fig. 1(a).On the one hand, the single flakes are arranged in theAA0 stacking configuration [Fig. 1(b)], with high symmetryand exclusively out-of-plane hetero πB─N bonds. On theother hand, the twisted interface presents a variety ofout-of-plane bonds, including homo πB─B and πN─N bonds[Figs. 1(c) and 1(d)]. For small twist angles, a macroscopicmoiré superstructure appears with πB─B and πN─N localizedat specific positions of the interface. For large twist angles,close to the 30° twist quasicrystal limit, atomic orbitalsvary locally from site to site, and homo πB─B and πN─Nbonds are densely distributed all over the interface. Theluminescence of single flakes is dominated by thefree-exciton emission, while highly twisted h-BN–h-BNstructures exhibit a new emission shown in Fig. 1(e)characterized by a large linewidth (2 eV) and a maximumintensity at 4 eV, i.e., 2 eV below the h-BN gap [38,39].The origin of this optical emission, its 2-eV redshift, and itsrelation to the structure of the interface are debated in theliterature. First, a giant exciton trapping at the interfacemoiré was proposed [39,40]. However, this is not consistentwith theoretical studies, which estimate the depth of theinterface energy well to be only a few hundreds of meV forexcitons [41,42]. Therefore, another group has discarded itsexcitonic nature and rather attributed this emission to deepdefects near the interface [41].In this paper, we propose an alternative explanation withthe occurrence of exciton self-trapping at the interface ofthe homostructure. The phenomenon of self-trapping of anelectron, hole, or exciton was predicted theoretically in the1930s [43,44] and demonstrated experimentally in alkalihalide crystals as early as the 1960s [45–49]. Self-trappingresults from a local deformation of the crystal lattice arounda charged particle (or dipole) where the particle (or dipole)is trapped. The particle (or dipole) induces the latticedeformation, hence the term “self-trapped state.” This stateis a kind of polaron: a charge associated with the defor-mation cloud it induces around itself. If the coupling withthe deformation mode is strong enough, the self-trappedstate is more energetically stable than the Bloch state of thefree particle in the undeformed lattice [43]. h-BN is a goodcandidate for exciton self-trapping since it is a highly ionicmaterial with a very compact exciton [50]. It makesexcitons and atomic B—N bonds dipoles of similar size,which is expected to favor exciton-lattice interactions.Today, the puzzle for understanding the nature and theorigin of this new optical emission is incomplete. In thiswork, we present a deterministic approach to elucidatethe interplay between twist angles, defects, and excitonsusing CL and time-resolved CL (TRCL). To this end,16 h-BN–h-BN structures with different twist angles andfabricated from different h-BN crystal sources are studiedin CL and TRCL at room temperature and as a function ofthe temperature. We show how the whole set of exper-imental data supports an exciton self-trapping mechanismoccurring at the interface of h-BN–h-BN homostructures.II. EXPERIMENTSAll CL experiments are performed using a JEOL7001Fscanning electron microscope (SEM) equipped with ah-BN–h-BNSingle h-BN(a) (e)BNh-BN - AA’ stacking(b)(d)h-BN–h-BN 3° twist h-BN–h-BN 23° twist (c)FIG. 1. (a) Sketch of an h-BN–h-BN structure. Top views of(b) the AA0 stacking arrangement of h-BN, (c) a 3°-twistedh-BN–h-BN interface, and (d) a 23°-twisted h-BN–h-BN inter-face. (e) CL spectra measured on a single bulk h-BN crystal (thebottom part alone), in black, and on the 23° h-BN–h-BN stack, inred. The luminescence is modulated by Fabry-Perot interferencesrelated to the thinness of the crystals.SÉBASTIEN ROUX et al. PHYS. REV. X 15, 021067 (2025)021067-2Horiba Jobin-Yvon CL system optimized for UV detection,as described in detail in Ref. [51]. Secondary electrons aredetected by an Everhart-Thornley detector (SE detector).The SEM image corresponds to the intensity of the signalcollected by the SE detector as a function of the position ofthe focused electron beam, with an ultimate spatial reso-lution of 1.2 nm. CL images are measured by a photo-multiplier (Hamamatsu HJY model, cooled to −30° C bythe Peltier effect) as the electron beam scans the selectedarea of the sample. The signal from the SE detector and theintensity collected by the photomultiplier are recorded atthe same time. In this way, SEM and CL images of the samearea are generated simultaneously, which allows us tocorrelate the emission of a CL signal with the topographyof the sample. The CL image can be panchromatic (totalintensity, unfiltered) or monochromatic, filtered in energyby a monochromator equipped with diffraction gratings.CL spectra are recorded with a CCD camera.Thanks to a careful calibration of the detection system, theCL signal provides the absolute intensity of light emissionfrom the sample [51]. As a result, the internal quantumefficiency (IQE) of a luminescence signal can be evaluatedfrom a CL experiment. The IQE corresponds to the ratiobetween the rate of photons emitted inside the sample andthe rate of electron-hole pairs generated by the electronbombardment. Details of the IQE measurements for theconsidered signal are given in Appendix A. Finally, TRCLexperiments are performed using a custom-built beam-blanking device mounted on the SEM column. The overalltime resolution of the TRCL setup is measured equal to100 ps (details of the setup are presented in Ref. [50]).To study the emission of twisted h-BN–h-BN structures,we decided to vary a large number of parameters in thefabrication of the homostructures: the twist angle, thethickness of the crystal flakes in stack, but also the qualityof the starting h-BN crystals and the way the two crystalflakes are assembled. h-BN crystals with natural boronisotope content were grown by three different processes:an atmospheric pressure high-temperature (APHT) process[52–55] from Ni=Cr solvent, a high-pressure high temper-ature (HPHT) route [56,57], and a polymer-derived-ceramic (PDC) method [58,59]. h-BN from the HPHTmethod is recognized in the 2D materials scientific com-munity as the reference h-BN crystals. In a previous study,a quantitative benchmarking of the respective quality, interms of defect density, of these different h-BN sources wasperformed based on the measured free-exciton lifetimesand correlated to the electron mobility in h-BN encapsu-lated graphene [50,60]. The values of the lifetime and IQEof the free exciton measured on bulk crystals from thedifferent h-BN sources are given in Table I.To fabricate twisted homostructures made of HPHTcrystals, the bottom h-BN layer is exfoliated with a PDMSstamp and deposited onto an Si=SiO2 substrate [61]. Thesecond h-BN flake is similarly exfoliated and depositedover the bottom h-BN under a microscope. The samples arethen annealed at 150° C for 1.5 hours. With this method,one atomic layer of the twisted interface was in contactwith the PDMS.For twisted homostructures of APHT and PDC crystals,the bottom layer is peeled off using Scotch tape on aTABLE I. Presentation of the 16 h-BN–h-BN samples of thepresent study and the respective thickness of top and bottomflakes. The IQE and the lifetime (τ) of the free exciton measuredon bulk crystals from the same sources [50] are indicated toquantitatively compare the quality of the samples.SampleFree excitonIQE (%) [50]τ (ns)[50]Toph-BN (nm)Bottomh-BN (nm)HPHT-11° 18 4.2 260 730HPHT-14° 15 290HPHT-15° 17 990HPHT-23° 9 220HPHT-27° 13 990APHT-3° 4.2 1.0 60 40APHT-4° 67 37APHT-10° 84 38APHT-13° 100 60APHT-29° 20 50PDC-2° 1.7 0.43 27 46PDC-13° 68 46PDC-16° 310 125PDC-18° 310 370PDC-19° 44 46PDC-26° 102 460°10°20°30°Top h-BN n°2 Top h-BN n°327° 14°Bottom h-BNReference : 0°(c)100 µm(b)100 µm12 3(a)12 3FIG. 2. (a) SEM image of three h-BN–h-BN homostructuresfabricated from an HPHT bulk crystal. The lower h-BN flake isindicated by red dotted lines. The upper h-BN flakes arenumbered from 1 to 3 and surrounded by solid black lines.(b) EBSD mapping of the in-plane crystal orientation of the h-BNflakes. The orientation of the bottom h-BN crystal is taken as thereference for evaluating the twist angle of the top h-BN. (c) ECPrecorded on the lower h-BN crystal and upper h-BN crystalsNo. 2 and No. 3.EXCITON SELF-TRAPPING IN TWISTED HEXAGONAL BORON … PHYS. REV. X 15, 021067 (2025)021067-3Si=SiO2 substrate [62], while the top layer is peeled offusing PDMS [61] and deposited over the bottom h-BNflake under the microscope. This method ensures that thetwo atomic layers of the h-BN–h-BN interface have neverbeen in contact with either the PDMS or the Scotch tapeand does not involve annealing. All procedures for theHPHT, APHT, and PDC samples were performed in acontrolled atmosphere glove box.The twist angle between the two h-BN flakes ismeasured with diffraction by electron-backscatter diffrac-tion (EBSD) or by electron-channeling patterns (ECPs)as shown in Fig. 2. Details of the twist angle measurementare presented in Appendix B. The samples are namedaccording to the crystal synthesis method from which theyare issued (HPHT, APHT, or PDC) and the twist angle.Table I lists the different samples and the respectivethickness of the top and bottom parts measured by atomicforce microscopy.III. EVIDENCE OF THE EXCITONIC ORIGINOF THE BROAD 4-EV OPTICAL EMISSIONAll h-BN–h-BN samples were first analyzed usingcontinuous excitation CL at room temperature. The firstobservation is that the 4-eV luminescence mainly appearsin homostructures with high twist angles (Fig. 3). For lowtwist angles, such as in the PDC-2°, APHT-3°, and APHT-4° samples, no clear luminescence signal could be detectedin the (3–5)-eV range, confirming a recent study [39].We conclude that the 4-eV luminescence becomes trulysignificant at angles larger than 5°. A spectrum measuredon a low-angle h-BN–h-BN structure is presented inAppendix C. Spectra measured on three highly twistedh-BN–h-BN homostructures (purple) and on a single h-BNcrystal as a reference (black) are shown in Fig. 3(b). The4-eV emission is modulated by Fabry-Perot interferenceswhose periodicity is consistent with the thickness of theflakes (see Table I). CL images filtered at 4 eVare shown inFig. 3(c). They clearly demonstrate that the 4-eV cath-odoluminescence component is due to the presence of thetwisted h-BN–h-BN interface.The full set of spectra and CL images recorded for the 16structures investigated in this work are provided in theSupplemental Material [63]. The signals are comparable forall samples regardless of h-BN source and flake thickness.They show common features in line with previous obser-vations [39–41]: intense, 2-eV broadening and 2-eV red-shift with respect to the 6.25-eV h-BN band gap [51].To summarize these first observations, the emissionphenomenon is very robust and appears unconditionallyas soon as the twist angle is large, as already reported inRef. [39], for instance. As it does not depend on thedifferences in nature and density of defects that present thethree h-BN sources used to fabricate our homostructures,the emission seems to be intrinsic to the presence of theinterface itself rather than related to extrinsic defects. Thisraises the question of its origin, and more specifically,(a) SEM image (c) 4-eV CL imageTHPA-29THPH-11PDC-18  Single h-BNh-BN–h-BN3 4 5 6Energy (eV)(b) CL spectraFIG. 3. (a) SEM images of the twisted homostructures outlinedwith a dotted line. (b) CL spectra measured on the bottom crystalalone (in black) and on the homostructure (in purple) at 300 K.(c) CL images filtered at 4.1� 0.1 eV at 300 K, on HPHT-11°(5 kV, 27 pA), APHT-29° (3 kV, 280 pA), and PDC-18° (5 kV,340 pA) samples. Scale bars are 10 μm.0.0 0.5 1.0 1.50.010.110 1 2 3104105106107108HPHT-11° at 5.75 eVSingle h-BN at 5.75 eVFitsTRCLintensity(norm.)Time (µs)� = 3 ns� = 0.46 µs� = 0.46 µs� = 0.47 µs(b)HPHT-11° at 4.1 eVHPHT-11° at 5.75 eVFitsTRCLintensity(photonss-1)Time (µs)(a)FIG. 4. (a) Decay of the free-exciton luminescence filtered at5.75� 0.2 eV, on the bottom h-BN alone (gray) and on theh-BN–h-BN twisted structure HPHT-11° (orange) after interrupt-ing the TRCL excitation at initial time (5 kV, 27 pA, spot size of10 μm). Biexponential decay functions are used for the fits.(b) Decay of the free-exciton luminescence (black) and of the4-eV emission (purple) filtered at 4.1� 0.1 eV after interruptionof steady excitation at t ¼ 0 on HPHT-11° homostructure (5 kV,27 pA, 10-μm excitation spot diameter). Intensities during steady-state excitation (t < 0) are normalized to the integrated intensityrecorded independently in continuous CL spectra. Experimentsdone at 300 K.SÉBASTIEN ROUX et al. PHYS. REV. X 15, 021067 (2025)021067-4the interplay between the exciton and the twisted-interfacestructure, which we will explore next using TRCL.The goal of the TRCL study is to identify the role of bulkfree excitons in the process leading to the 4-eV lumines-cence. Figure 4(a) compares the decay of the free-excitonluminescence at 5.75 eV in the HPHT-11° homostructurewith the decay obtained on the bottom h-BN crystal alone.A drastic change is observed. For the crystal alone, thedecay is dominated by a short 3-ns component, typical ofthe TRCL decay of the free exciton in a single bulkHPHT–h-BN crystal [50]. For the homostructure, the fastinitial component is similar, but a long component of0.46 μs appears with a significant intensity (30% on theHPHT-11° sample). This long time constant is muchlarger than the radiative lifetime of the free excitonmeasured at 27 ns [50], which requires an incomingflux of free excitons that persists after the primaryexcitation has stopped. We conclude that the long-lastingfree-exciton emission is fed by the detrapping of excitonsfrom the interface, revealing a balance between a pop-ulation of interface excitons and the population offree excitons in the h-BN volume based on a trapping-detrapping process.As shown in Appendix D, the temporal decay of the4-eV luminescence is energy-independent in the (3–5)-eVenergy range. Figure 4(b) further illustrates that its decaytime matches the long-lived component of the free-excitonemission. Without going into the quantitative analysis(presented later), it demonstrates that the broad 4-eVluminescence is excited by the long-lived and interface-localized excitons. This implies that the 2-eV broadeninglikely does not arise from energy dispersion of an ensembleof localized quantum emitters. Instead, it appears to resultfrom the radiative recombination process of interfaceexcitons. Still, the radiative process has to be identified,which is the subject of the next parts.IV. POWER DEPENDENCE AND INTERNALQUANTUM EFFICIENCY OF THE 4-EV EMISSIONDuring CL experiments, the electron-beam excitationis spread in depth, so that the h-BN–h-BN interface isindirectly excited by the diffusion of free excitons gen-erated in the volume of the h-BN crystals toward theinterface between them [64]. The efficiency of the interfaceexciton luminescence, therefore, depends on two factors:the efficiency of free-exciton transport from the bulk to theinterface, and the efficiency of radiative recombination atthe interface.The luminescence from the twisted h-BN–h-BN homo-structures is analyzed here as a function of the areal densityof the excitation power (W=cm2). Low-power-density datawere recorded with an acceleration voltage of 5 kV with aconstant current of 27 pA and spot diameters ranging from1.6 to 26 μm. High-power densities were obtained with afixed-spot diameter of 1.6 μm and excitation currentsranging from 27 to 5600 pA. This dual approach madeit possible to vary the excitation power density over 5orders of magnitude.Figure 5(a) shows the CL spectra normalized by theexcitation power for different excitation densities on theHPHT-11° sample. In Fig. 5(b), it is observed that above0.1 W=cm2, the efficiency of the 4-eV luminescencedecreases significantly with IQE ∝ power−0.38. This cor-responds to a sublinear regime in CL intensity withICL ∝ power0.62, suggesting a bimolecular recombinationof excitons at high-power densities. Figure 5(c) indicatesthat this saturation effect appears in all HPHT homostruc-tures with little effect of the twist angle on the 0.1-W=cm2saturation threshold. In contrast, under similar excitationconditions, bulk h-BN luminescence saturates only above50 W=cm2 due to exciton-exciton annihilation (EEA) offree excitons [65,66]. The much lower threshold in twistedh-BN–h-BN structures suggests that saturation is ratherdriven by the EEA of interface excitons. This interpretationis consistent with the much higher exciton density at theinterface than in the volume, which results from theefficient capture of excitons at the interface, as shownlater in this section.3 4 5 610310410510-1 100 101 102 10311010-2 10-1 10010100Power denstity(W cm-2) :0.0250.0400.0800.651.215951400CLintensity(photonss-1µW-1)Energy (eV)4-eVbandIQE(%)Power density(W cm-2)y = a × x -0.38HPHT:27°23°14°15°11°4-eVbandIQE(%)Power density(W cm-2)(a)(b) (c)FIG. 5. (a) CL spectra normalized by the excitation power fordifferent excitation densities (5 kV, 300 K) measured on theHPHT-11° sample (b) IQE of the 4-eV emission, deduced from(a), as a function of the excitation power density. The black arrowindicates the transition point between the two methods forvarying the excitation density, as indicated in the text. (c) IQEof the 4-eVemission as a function of the excitation density for thefive HPHT samples.EXCITON SELF-TRAPPING IN TWISTED HEXAGONAL BORON … PHYS. REV. X 15, 021067 (2025)021067-5Interestingly, at low-power densities (below 0.1 W=cm2),the IQE of the 4-eV luminescence can reach very highvalues, as overviewed in Table II. We observe that the IQEincreases with the twist angle, reaching nearly 100% ata 30° twist. This suggests that, for 30° twist angles, the vastmajority of excitons are trapped at the interface andrecombine via photon emission in the 4-eV band. Such ahighly efficient emission is rare at 300 K and may bepromising for light-emitting devices. A unity IQE of theinterface luminescence implies that (i) the transport offree excitons from the bulk to the interface is withoutlosses, and (ii) that the exciton recombinations at theinterface are fully radiative. Previous results on excitondiffusion in bulk h-BN monocrystals suggest that theconversion of 3D excitons into 2D interface or surfaceexcitons is extremely efficient even for dark interfaces(with low twist angles) and for the nonradiative freesurface [64]. This study further shows that the recombi-nation of the 2D interface excitons is mostly radiativenear the 30° twist angle quasicrystal limit.Note that between 10−2 and 10−1 W=cm2, the averageenergy of the photons emitted within the 4-eV bandis slightly redshifted by about 15 meV as the excitationpower is increased. In contrast, a hypothetical donor-acceptor pair (DAP) recombination, which would havebeen a candidate for such a broad emission, shouldexhibit a blueshift when increasing the excitation power[67,68]. Our observations then discard a DAP origin forthe 4-eV emission.As a summary of this section, power-dependent experi-ments reveal a strong decrease in the efficiency of the 4-eVemission at moderate excitation power, probably caused bya bimolecular annihilation process between excitons accu-mulated at the h-BN–h-BN interface. At low excitationpower, in the most favorable cases, i.e., at twist angles closeto 30° with HPHT crystals presenting a long-range excitondiffusion, most excitons recombine radiatively at the inter-face with a 4-eV photon emission.V. EXCITON SELF-TRAPPING AT THE TWISTEDh-BN–h-BN INTERFACEThe characteristics of the 4-eV emission (2-eV energyshift and the 2-eV broadening) support a self-trappingmechanism of excitons at the interface that we develop inthis section.Figure 6(a) illustrates the difference between simpleexciton trapping in the potential well formed by theinterface between the two twisted h-BN flakes (X2D) andself-trapping of this exciton at the interface (XST). A self-trapped exciton is an exciton that induces a lattice distortionaround it, and that is trapped in this distorted area.The configuration diagram drawn in Fig. 6(b) displaysthe exciton energy as a function of the lattice deformationaround it represented by the configuration coordinate. Inthis diagram, we define the trapping energy potential of thetwisted interface at zero deformation denoted ET . Its valuefor the twisted interface in h-BN is a priori estimated tobe of the order of 100 meV following recent theoreticalcalculations [41,42].The energy barrier for the self-trapping phenomenon isdenoted EST in Fig. 6(b). Its existence was predicted byLandau [43] and Toyozawa [69] for electrons and byRashba [70,71] and Sumi and Toyozawa [72] for excitons.The presence of an energy barrier for self-trapping wasevidenced experimentally in the 1960s and 1970s in alkaliTABLE II. IQE of the 4-eV emission measured below0.1 W=cm2 on twisted h-BN homostructures made of HPHTcrystals.Sample 4-eV IQE (%)HPHT-11° 20HPHT-14° 50HPHT-15° 30HPHT-23° 80HPHT-27° 90Interface trapped exciton (X2D)Bottom h-BNeh e hTop h-BN N B e-h+ ExcitonInterface self-trapped exciton (XST) (a)(b)X2DXSTX3DGSEnergyConfiguration coordinateEST0ETFIG. 6. (a) Schematics of a trapped exciton at the interface(X2D) in red and of a self-trapped exciton at the interface (XST) inpurple, with a self-induced lattice deformation on which theexciton is trapped. (b) Configuration diagram representing thethree exciton populations in h-BN–h-BN structures: X3D, X2D,and XST. The exciton trapping potential of the interface at zerodistortion appears as ET between X3D and X2D. The energybarrier for the formation of the self-trapped exciton is indicated(EST). The long straight arrows represent the photons resultingfrom the radiative recombination of free excitons (in black), ofthermalized self-trapped excitons (purple, solid lines), and ofnonthermalized self-trapped excitons or “hot” self-trapped ex-citons (purple, dashed line). The small curved arrows representthe phonons required for the lattice to return to the ground stateduring the recombination of a self-trapped exciton.SÉBASTIEN ROUX et al. PHYS. REV. X 15, 021067 (2025)021067-6halides [73–75]. The energy barrier disappears only forself-trapping of a localized exciton on a 0D site [71,76],while here the h-BN–h-BN interface is a 2D defect.The presence of the energy barrier EST implies thecoexistence of excitons simply trapped at the 2D interface(X2D) and excitons self-trapped at the interface (XST).Considering the free excitons in the 3D bulk h-BN(X3D), there are thus three coupled exciton populationsduring the CL experiments: X3D, X2D, and XST.Note that, though EST ≠ 0, the energy barrier for self-trapping is necessarily low unless an efficient tunnelingoccurs, since luminescence of XST is still observed closeto the liquid helium temperature (see Appendix E).However, its presence basically limits the formation ofXST and reduces the intensity of their luminescence as thetemperature is lowered [73–75].The general features of self-trapped excitons are wellconsistent with our observations. Indeed, the radiativerecombination of a self-trapped exciton is accompaniedby the emission of a set of phonons to restore the crystallattice to its undistorted form as sketched in Fig. 6(b). Thisdrastically reduces the energy of the emitted photon withrespect to the band gap of the interface and explains thelarge energy shift (approximately 2 eV) between theexcitonic band gap and the luminescence at the interface.Furthermore, the luminescence of self-trapped excitons isinherently broad for several reasons. First, due to localdisorder at the interface [which is likely to be high at largetwist angles; see Fig. 1(d)], the variation of the localpotential landscape might cause self-trapped excitons toexhibit a variety of energies and distortions. Second, therecombination of self-trapped excitons requires multiplephonon emissions, which further increase the broadeningof their luminescence. This is illustrated in Fig. 6(b), wherethe three purple arrows (solid lines) represent photons ofdifferent energies resulting from the recombination ofdifferent self-trapped excitons at the band edge.Experimentally in this study, the emission related toexcitons simply trapped at the interface (X2D) has not beendetected in CL. Two possible scenarios can be consideredto account for an almost zero-luminescence intensity: either(1) the X2D population is empty, or (2) the X2D excitons aredark, i.e., have an infinite radiative lifetime. In the firstscenario, excitons would accumulate at the interface in theself-trapped form as an XST state. This requires their self-trapping to be almost instantaneous, which contradicts thepresence of an energy barrier to self-trapping limitingthe formation of XST. Scenario (1) also implies that thedetrapping of excitons from the interface into the volumeoccurs from the XST states, which would be energeticallytoo costly. The first scenario clearly appears inconsistentwith the significant release of free excitons in the bulkh-BN volume from the interface observed by TRCL.Therefore, we have ruled out scenario (1), and in thefollowing we will consider only scenario (2).In this scenario, X2D excitons have a negligible prob-ability of radiative recombination (dark excitons). This isin good qualitative agreement with (i) recent investigations[64] which show that the free surface of h-BN singlecrystals acts as a non radiative trap for excitons, (ii) thelong-lasting release of the interface excitons in the volume,and (iii) the IQE close to 100% observed for XST at hightwist angles (Table II), implying that the recombination rateof X2D is very low compared to that of XST. Since the IQEreaches almost unity at high angles (see Table II), thelocalized self-trapped excitons then recombine radiativelywith an almost instantaneous rate compared to the otherprocesses that have been considered. For this reason, wewill further neglect the eventual nonradiative recombina-tions of X2D. Figure 8 further summarizes theseconclusions.VI. TEMPERATURE-DEPENDENT EXPERIMENTSTo strengthen the attribution of the 4-eV emission to aself-trapping process and to characterize the differentexciton populations in more detail, we have performed aseries of experiments as a function of the temperature.The intermediate twist angle samples HPHT-11°and HPHT-15° are studied at a very low-power den-sity (5 kV, 27 pA, 60-μm spot diameter; approximately0.005 W=cm2), which prevents saturation effects down to100 K. Since saturation effects appears to be stronger atlow temperature and could not be avoided below 100 K,we limited the data analysis to the (100–300)-K range.We first studied the influence of the temperature onthe spectral features of the 4-eV luminescence withFigs. 7(a) and 7(b).Nonthermalized (hot) self-trapped excitons are known tobe favored at high temperatures, where their recombination,shown in Fig. 6(b), occurs at a higher energy than whenthermalized. We therefore expect an increase in theemission energy of self-trapped excitons as the temperatureincreases [77,78]. Between 200 and 300 K, Figs. 7(a)and 7(b) indeed depict an increase of the XST excitonluminescence in the (4–5)-eV region with respect to the(3–4)-eV region, consistent with a contribution from non-thermalized XST. The broadening of the 4-eV emission onthe high-energy side indicated by black arrows in Figs. 7(a)and 7(b) is quantitatively characterized by the standarddeviation of the emission energy [Fig. 7(c)] and by theaverage energy of the XST emission [Fig. 7(d)]. Bothslightly increase at high temperature. Note that the spectralwidth of the h-BN–h-BN 4-eV luminescence still remainsaround 2 eV at cryogenic temperatures, as shown inAppendix E. This rules out the possibility of color centeremission which would exhibit narrow linewidths at5 K [79,80].Figure 7(e) shows that the IQE of the XST luminescencedrops below 200 K and is only a few percent at 100 K.The activation of XST emission with the temperature isEXCITON SELF-TRAPPING IN TWISTED HEXAGONAL BORON … PHYS. REV. X 15, 021067 (2025)021067-7consistent with the presence of an energy barrier for self-trapping, as discussed in the previous section [named ESTin Fig. 6(b)]. With an Arrhenius plot fit, we find ESTvalues of 32 and 41 meV for the HPHT-11° and HPHT-15°samples, respectively. These values are probably over-estimated due to the saturation effects evidenced inSec. IV, which are not completely avoided near 100 K.They are also subject to a high uncertainty due to the smalltemperature range investigated. It is therefore reasonableto estimate the activation energy of the self-trapping to bea few tens of meV in these samples. This corresponds wellto the order of magnitude found in the literature for theself-trapping of excitons in other materials such as alkalihalides [73,75,77,81,82].As a summary, the various effects revealed by thetemperature-dependent experiments appear to be wellconsistent with a 4-eV emission band resulting from therecombination of excitons that are self-trapped at thetwisted h-BN–h-BN interface.VII. PHENOMENOLOGICAL MODEL FOREXCITON RECOMBINATION DYNAMICSWe now explain the recombination dynamics of thethree exciton populations in h-BN–h-BN homostructures(X3D, X2D, and XST), considering the interactions thatbind them, in order to ascribe a physical meaning to thedecay times measured in TRCL. Different transitionsbetween these exciton populations are shown in Fig. 8 asa summary of Sec. V conclusions. X2D accumulate at theinterface after their capture at a rate C from free excitonsof the h-BN bulk crystals generated by the primaryexcitation. They are then either released to the volumeas X3D, with a detrapping rate D, or self-trapped in theXST states with a rate ST.100 200 3004.04.14.2100 200 3000.400.440.480.003 0.006 0.0095503 4 5 61031041051063 4 5 6103104105106Meanenergy(eV)Temperature (K)(a)Std.deviation(eV)Temperature (K)HPHT-11°HPHT-15°IQEofXST(%)1/T (K-1)32 meV41 meV293 K250 K200 K150 K125 K100 KCLintensity(photonss-1nm-1)Energy (eV)(b)HPHT-11° HPHT-15°XSTX3D(c) (d) (e)CLintensity(photonss-1nm-1)Energy (eV)300 200 100Temperature (K)FIG. 7. CL spectra recorded on the HPHT-11° (a) and HPHT-15° (b) samples between 100 and 293 K. (c) Standard deviation of the4-eV emission energy, (d) average emission energy, and (e) IQE of the self-trapped exciton XST luminescence as a function of thetemperature extracted from the spectra in (a) and (b). Arrhenius laws are shown in full lines in (e), from which activation energies areextracted.GTrapping (C)Self-trapping (ST)Detrapping (D)X3DX2DXSTXST  recombinationX3D  recombinationSTFIG. 8. Energy levels and transitions between the three excitonpopulations within the twisted h-BN–h-BN homostructures. Inthis scenario, excitons from volume (X3D) are trapped at theinterface, where they accumulate in the dark and long-living form(X2D). Once self-trapped (XST), they recombine instantaneouslywith a photon emission, leading to the intense light emissionaround 4 eV.SÉBASTIEN ROUX et al. PHYS. REV. X 15, 021067 (2025)021067-8According to this scenario, the long decay time of X3Dand XST measured in TRCL (τl) after the interruption ofthe continuous excitation (see Fig. 4) corresponds to thelifetime of the X2D excitons decaying either by detrappingor self-trapping. Considering the associated rates, τl isgiven by 1=τl ≈Dþ ST (details given in Appendix F). Inthe following, we discuss the temperature dependence ofthe long decay time common to X3D and XST. Since thesedecay times are found equal for the X3D and XST pop-ulations when decreasing the temperature, we present onlythe TRCL measurements of X3D. Figure 9(a) shows thedecays for two samples with intermediate twist angles:HPHT-11° and HPHT-15°. The decays are normalized bythe absolute integrated intensity of the X3D band obtainedby independent CL measurements under continuous exci-tation [spectra in Figs. 7(a) and 7(b)]. The characteristictime of the long component τl is extracted from biexpo-nential function fits.Figure 9(b) shows a plot of 1=τl ≈Dþ ST as a functionof 1=T (K). The data are fitted with Arrhenius functions,yielding activation energies of 100 and 110 meV for theHPHT-11° and HPHT-15° samples, respectively. Given thelow activation energy estimated for the formation of self-trapped excitons (EST ≃ 10 meV), 1=τl ≈Dþ ST is likelylimited instead by the thermal activation of the detrappingrate D, with an activation energy corresponding to ET .The self-trapping of an exciton requires the assistance ofmany phonons for the distortion to occur. Despite arelatively low activation energy, the self-trapping may beextremely slow at room temperature, in good agreementwith the next results in this section. It indicates thatD ≫ ST between 150 and 300 K, consistent with therelatively low efficiency of the 4-eV luminescenceobserved in these samples at 300 K (see Table II). Weconclude that the extracted activation energies corre-spond to the depth of the potential well experienced bybulk excitons at the twisted h-BN interface ET , which isfound to be around 100 meV for twist angles between 10°and 15°. This value is in good agreement with the firsttheoretical estimates of ET [41,42].Coming back to the high twist angles, we remind that theefficiency of the 4-eV emission is close to 100% near 30°twist angles at 300 K (see Table II). This efficiencyrequires an almost full conversion of X2D into XST statesvia self-trapping. To achieve this, the detrapping rate isnecessarily negligible compared to the self-trapping rateD ≪ ST, and the lifetime of the interface excitons is thenlimited by the self-trapping 1=τl ≈ ST. The situation isopposite to the 10°–15° twisted h-BN crystals, where1=τl ≈D. This comparison highlights that the interpre-tation of the long decay time observed in TRCL iscautious depending on twist angles.We further analyze and compare the TRCL resultsbetween 15° and 27° twists at 300 K in Fig. 10. At a15° twist angle, we then attribute the long decay time to thedetrapping rate D found equal to 2.5 × 106 s−1 at 300 K,while the self-trapping rate ST is much lower but unknown.At 27° twist angle, we access the self-trapping rateST = 2.5 × 105 s−1, while the detrapping rate D is muchlower but unknown. These limit cases are very interestingcompared to intermediate twist angles where both shouldcontribute to the long decay time with 1=τl ≈Dþ ST.0 1 21041051061070 1 20.003 0.004 0.005 0.006 0.0070.11293 K275 K250 K225 K200 K175 K150 KFitsTRCLofX3D(photonss-1)Time (µs)HPHT-11° HPHT-15°(a)(b)Time (µs)1/ �l(µs-1)1/T (K-1)HPHT-11°HPHT-15°100 meV110 meV300 250 200 150Temperature (K)FIG. 9. (a) TRCL decays of the free-exciton luminescence fortemperatures in the range 150–293 K on the HPHT-11° andHPHT-15 samples. Biexponential decay fits are used to extractthe characteristic time of the long component τl. (b) 1=τl as afunction of 1=T in the HPHT-11° and HPHT-15° samples.Arrhenius laws appear as solid lines.0 1 2 3103104105106107108 XSTX3DTRCLintensity(photonss-1)Time (µs)�l �= 0.40 µs�l �= 0.39 µs�l�= 3.1 µs�l��= 3.2 µsHPHT-15° HPHT-27°0 1 2 3Time (µs)FIG. 10. (a) TRCL decays of the free-exciton luminescence(in black) as compared to the self-trapped exciton luminescence(in purple) for an intermediate twist angle sample HPHT-15°and a high twist angle sample HPHT-27°. Experiments doneat 300 K.EXCITON SELF-TRAPPING IN TWISTED HEXAGONAL BORON … PHYS. REV. X 15, 021067 (2025)021067-9The self-trapping process is found to be particularly slowaround 30° twist (3.2 μs on HPHT-27°, 4 μs on HPHT-24°)though giving high efficiency of the 4-eVemission. Around15° twist, the dominant detrapping is about 10 times faster(0.40 μs on HPHT-15° and 0.46 μs on HPHT-11°) with atypical efficiency decrease of the 4-eVemission by a factorof 2 (see Table II). This suggests that the detrapping ofexcitons from the interface is decreasing at high angle,giving enough time for exciton trapped at the interface toslowly deform the crystal locally around it for self-trapping.This means that the depth of the potential well formed bythe twisted h-BN interface ET found equal to 100 meV at15°, increases near 30° so that detrapping becomes negli-gible in front of self-trapping. Theoretical calculations ofET for twist angles between 15° and 30° would be welcometo confirm that point.In summary, we interpret our experimental data withexcitons accumulating at the interface in a nonradiativeand long-lived form (X2D) followed by their subsequentconversion into X3D and XST via their detrapping or self-trapping. Our results suggest that the depth of the inter-face trapping potential for free excitons in h-BN increaseswith the twist angle. For low angles, the detrapping isbelieved to be dominant and limits the efficiency of theinterface luminescence, while close to 30°, the detrappingis negligible, and the efficiency of the interface emissionreaches almost 100%. Our phenomenological modelprovides a good description of the full experimentaldataset, including the long-lasting luminescence andthe high IQE.VIII. DISCUSSION: SELF-TRAPPING IN sp2 BNWe finally discuss the origin of the exciton self-trappingin h-BN. Exciton self-trapping is favored by the ability ofthe lattice to deform around the exciton. Given the highionicity of the covalent B—N bonds, a strong exciton-lattice interaction is expected in h-BN. In the excitons ofbulk h-BN, the electron and the hole are distant fromapproximately 7 Å [50], which makes the h-BN excitonsparticularly small. Still, an exciton dipole of this size isprobably too large to interact with the atomic bonds in bulkh-BN and to give rise to self-trapped excitons.The exciton behavior at the h-BN–h-BN interface stillneeds further investigation, but we can already drawgeneral lines. When an exciton is spatially confined, it isa general trend that its binding energy increases and its sizedecreases. Theoretical calculations have been reported forthe free surface of h-BN [83] and for the BN monolayer. Inthe latter, the exciton size is calculated at approximately2 Å [84]. A similar trend is expected for 2D excitonsconfined at the h-BN–h-BN interface. We then suggest thatthe exciton size decreases when confined at the interfacewith respect to the bulk, sufficiently to match the order ofthe lattice parameter (2.5 Å in plane, 3.3 Å out of plane),then promoting the exciton-lattice coupling at the interfaceby dipole-dipole interactions.For small twist angles of a few degrees, the interfacesare known to be energetically stabilized by moiré for-mation and are probably weakly deformable after that.Indeed, at low angles, intense atomic reconstructionoccurs and mechanically stabilizes the structure byexpanding the region with stable stacking configurationsand condensing all the strain and the unstable stackingconfigurations into 1D lines [33,34]. On the contrary,near 30° of twist where self-trapping is better observed, atransition from a commensurable to an incommensurableinterface occurs, as studied in quasicrystals, leading to adrastic change in the structure and the physical phenom-ena it can host. While at low angles the perturbation of thecharge distribution induced by the appearance of the πB─Band πN─N homobonds is weak and confined to certainzones of the moiré structure, at high angles a very largefraction of the π bonds are perturbed and denselydistributed throughout the interface. As a consequence,the potential perturbations increase in locality and densitywith increasing twist angle, which could promote a higherbarrier for exciton detrapping and favor the slow self-trapping process.These elements address the role of the twist angle onexciton interactions with the interface, but also highlightthe need for theoretical studies to better understand theorigin of exciton self-trapping by exploring (i) what kind ofh-BN lattice distortions are involved and (ii) how thepotential well seen by h-BN excitons does evolve between5° and 30° twisted interface.This work on self-trapped excitons at twistedh-BN–h-BN interfaces might cast a new light on similarluminescence signal reported in defective h-BN samples[85] as well as in other sp2-hydridized BN samples thatexhibit interface disorder, such as turbostratic BN, pyrolyticBN, or BN multiwall nanotubes [86,87]. Also typically2-eV broad, centered at 4 eV, and with long decaydynamics, this emission is excited only above 6-eVexcitation, i.e., above the excitonic band gap, suggestingan excitonic origin. This similar emission observed indisordered BN materials could also be related to excitonself-trapping, which would then appear to be a fairlycommon phenomenon in the BN material family.Recent studies report unusual exciton-lattice inter-actions at other h-2D interfaces [88–91], which in somecases could lead to the formation of self-trapped excitons[91]. Our results added to these studies show that theproperties of these self-trapped states are easily modu-lated by the structural properties of h-2Ds, such as thetwist angle, the choice of stacking, or the thickness of thecrystals. h-2Ds appear to be an ideal platform for study-ing and manipulating self-trapped states, opening up newfields of application for these materials. In particular,the high efficiency and the large broadening of the 4-eVSÉBASTIEN ROUX et al. PHYS. REV. X 15, 021067 (2025)021067-10luminescence of self-trapped excitons at twistedh-BN–h-BN interfaces could be exploited for broadbandUV light sources [92–95].Finally, the formation of interlayer excitons at theinterfaces between two TMDs (with hole and electronspatially separated in the two layers) has been shown toincrease the exciton lifetime by more than 3 orders ofmagnitude [7–10]. With their long lifetime and darkcharacter, X2D excitons at the h-BN–h-BN interface mighthave common features with interlayer excitons.IX. CONCLUSIONSixteen twisted h-BN–h-BN homostructures have beenstudied using CL and TRCL as function of the temperaturewith the aim of understanding the broad 4-eV luminescencein h-BN–h-BN homostructures. Our study shows that thisluminescence is indirectly excited by the transport of freeexcitons from the upper and lower h-BN flakes to theinterface between them via their diffusion and capture.Accumulated at the interface, excitons probably undergoexciton-exciton annihilation which manifests by thedecrease of the light emission efficiency at moderateexcitation powers. In the low-excitation regime, it wasfound that the efficiency of the 4-eV emission reachesalmost 100% at angles close to 30°. This intense lightemission is attributed to the radiative recombination of self-trapped excitons at the interface. A reduction of theexcitons size after their capture at the interface is believedto favor a local deformation of the crystal around them inwhich they self-trap.TRCL luminescence decays could be analyzed byconsidering a trapping-detrapping phenomenologicalmodel where three exciton populations are coupled: freeexcitons in the volume (X3D), excitons trapped at the 2Dinterface (X2D, not self-trapped), and excitons self-trappedat the interface (XST). In this scenario consistent with ourset of experimental data, excitons accumulate at the inter-face in the nonradiative (dark) and long-living X2D form.Our analysis of temperature-dependant experiments fortwist angles of approximately 15° reveals a self-trappingenergy barrier of a few 10 meV and an interface trappingpotential measured around 100 meV. The quantitativeanalysis of TRCL data further provides an estimation ofthe detrapping rate near 15° and of the self-trapping ratenear 30°. They suggest a deeper interface potential near 30°twist angles, limiting exciton detrapping from the interfaceand thus favoring self-trapping. This is consistent with theremarkably high luminescence efficiency of the XSTluminescence at high twist angles. These values agree withthe literature and theoretical calculations available to date.For highly twisted h-BN–h-BN structures, the crystallattice appears to be locally and densely perturbed acrossthe entire interface. Beyond these qualitative elements,it remains to be understood in detail what are the keyelements that cause self-trapping. The physical phenomenaoccurring in h-2Ds at high angles appear very differentfrom those at small angles with moiré superstructures. Toexplore them, one avenue would be to apply the quasi-crystal physics to h-2Ds with high twist angles.ACKNOWLEDGMENTSThe authors gratefully acknowledge their co-authorFrançois Ducastelle (now deceased) for his involvementin this study from the outset. He provided essential insightsinto the phenomena investigated. The research leading tothese results has received funding European Union’sHorizon 2020 research and innovation program underGrant Agreements No. 785219 (Graphene Core 2) andNo. 881603 (Graphene Core 3). Support for the APHTh-BN crystal growth comes from the Office of NavalResearch, Grant No. N00014-20-1-2474. K.W. and T. T.acknowledge support from the JSPS KAKENHI (GrantsNo. 21H05233 and No. 23H02052) and World PremierInternational Research Center Initiative, MEXT, Japan.This work was also supported by Agence Nationale dela Recherche funding under the program ESR/EquipEx+(Grant No. ANR-21-ESRE-0025) and ANR ATOEMS.APPENDIX A: MEASUREMENT OF THEINTERNAL QUANTUM EFFICIENCYOF THE 4-EV LUMINESCENCEThe procedure to measure the IQE of a luminescenceband during CL experiment under continuous excitation isdescribed in Ref. [51]. In this reference, it is applied tomeasure the IQE of the free-exciton luminescence of h-BNsingle crystals that appears at 5.75 eV. To apply the sameprocedure to the 4-eV band, one should consider thesignificative change of the refractive index of the topsurface between 5.75 and 4 eV.In our case, the CL intensity is integrated between 3.1and 5.2 eV as shown in Fig. 11. The reflection index n of3 4 5 6CLintensity(a.u.)Energy (eV)FIG. 11. Corrected CL spectrum of an h-BN–h-BN homo-structure at 300 K. The integrated intensity of the free-excitonband of h-BN appears in red, and the integrated intensity of the4-eV luminescence characteristic of twisted h-BN–h-BN homo-structures, appears in blue.EXCITON SELF-TRAPPING IN TWISTED HEXAGONAL BORON … PHYS. REV. X 15, 021067 (2025)021067-11the surface is increased from n ¼ 2.37 to n ¼ 3 over the(3.1–5.2)-eV range [96] corresponding to a light extractionthat varies from 3.9% to 2.1%. To simply measure themagnitude of the IQE of this band, we approximate aconstant index n ¼ 2.56 measured at the band maximum(3.2% extraction). This approximation is reasonable giventhe uncertainty of the IQE measurement, which is of theorder of 50% [51].APPENDIX B: MEASUREMENT OF THE TWISTANGLE BY ELECTRON DIFFRACTIONThe twist angle of the h-BN–h-BN homostructure wasdetermined by EBSD and ECP.In EBSD, the surface crystal orientations of a sample inthe SEM are determined for each diffraction pattern usingthe OIM Analysis software from EDAX. For h-BN–h-BNhomostructures, the crystal orientation of the top crystal isexpressed in the reference frame of the bottom crystal. Notsurprisingly, the out-of-plane z axis of the two h-BNcrystals is identical. On the other hand, different in-planeorientations are measured as shown in Fig. 2(b) in the maintext. The twist angle between the two crystals correspondsto this difference in orientation. It is equivalent to thesmallest angle that can be found between the atomic B—Nbonds of the two crystal lattices, regardless of theirorientation (B to N or N to B). Between two h-BN crystals,this angle varies between 0° and 30°. EBSD mapping canquickly measure the orientation of several crystals sepa-rated by a few millimeters with an accuracy of the orderof 1° [Fig. 2(b)].In ECP, mapping is not possible, but the diffractionpattern on a selected zone of a 2D crystal gives its in-planecrystal orientation directly, without the need for complexprocessing. By comparing the ECP images of two 2Dcrystals placed on top of each other, we can measure thetwist angle between the two crystals with an accuracyof the order of 1°. Its absolute value varies between 0° and30° and corresponds to the angle measured by EBSD, asshown in Fig. 2(c).APPENDIX C: CL SIGNAL ON LOW-ANGLEh-BN–h-BN STRUCTURESFigure 12 shows spectra measured on a slightly twistedPDC sample in green and a highly twisted PDC sample inred, compared to a spectrum measured on a single PDCcrystal in black. The single crystal shows emission frompoint defects (labeled α, β, γ) that occur locally in somecrystals. As shown in Fig. 5(c) of the main text, the CLintensity of the h-BN–h-BN interface decreases withdecreasing twist angle. For the PDC-2° sample, the intensityof the interface luminescence is lower than the intensity ofthe native color center emission. To avoid confusion betweennative defects and interface emission, only highly twistedsingle-crystal structures without significant native defectemission in the (3–6)-eV range have been investigated.APPENDIX D: LUMINESCENCE DECAY ASFUNCTION OF THE ENERGY WITHIN THEBROAD 4-EV LUMINESCENCEGiven the linewidth of the emission at 4-eV, whichextends between 3 and 5 eV, the question arises whether itis the result of a population of emitters of different energiesor whether the signal is intrinsically broad. To check this,the decay of the luminescence is studied at differentenergies of the broad emission.Figure 13(a) shows the spectrum of the APHT-29°sample dominated by the luminescence of interest withlittle Fabry-Perot interference contrast. Figure 13(b) showsthe TRCL decays of the luminescence filtered at differentenergies (�0.15 eV). The decay dynamics are perfectlyidentical for all investigated energies. This result suggests aunique recombination mechanism for this particularlybroad band. The large spectral width of the 4-eV bandthus appears to be an intrinsic feature of the luminescenceprocess of twisted h-BN–h-BN homostructures.3 4 5 6Single PDC with defectsPDC-2°PDC-16°CLintensity(a.u.)Energy (eV)���FIG. 12. CL spectra measured at 300 K on PDC-2°, PDC-16°,and on a single PDC crystal under the same excitation conditions(3 kV, 280 pA).0 1 2 3 40.010.113 4 5 6TRCLintensity(a.u.)Time (µs)CLintensity(a.u.)Energy (eV)5 eV4.5 eV4 eV3.5 eV(a) (b)3.1 eVFIG. 13. CL spectrum (3 kV, 280 pA) measured on the APHT-29° homostructure at 300 K. (b) Decay of the luminescenceintensity filtered at different energies recorded in TRCL after theexcitation was stopped at t ¼ 0. The energies corresponding toeach color are indicated by arrows in (a).SÉBASTIEN ROUX et al. PHYS. REV. X 15, 021067 (2025)021067-12APPENDIX E: LOW-TEMPERATURE SPECTRUMOF A TWISTED h-BN–h-BN HOMOSTRUCTUREFigure 14 shows spectra obtained on a 23° twistedh-BN–h-BN structure and on an h-BN single crystal atroom temperature and at cryogenic temperature. On thesingle crystal, the luminescence is dominated by the free-exciton luminescence occurring at 5.75 eV, while on theh-BN–h-BN structure the emission is dominated bythe broad luminescence occurring between 3 and 5 eV.The band is modulated by Fabry-Perot interference. Weobserve that the band remains extremely broad even atcryogenic temperatures. A color center emission alsoappears on the h-BN–h-BN structure and on the singleh-BN crystals, with a zero-phonon band at 4.06 eV (α) andits phonon replica (β and γ). This emission shows a largethermal broadening typical of color centers, indicating thatits nature is different from that of the h-BN–h-BN interfaceemission, whose broadening remains around 2 eV evenwhen the sample holder temperature reaches 5 K.APPENDIX F: SIMULATION OF TRCL DECAYSWITH RATE EQUATIONSThe TRCL decay of the luminescence intensity is relatedto the evolution of the exciton populations and thus totheir interactions. The scenario of exciton populationinteractions discussed in the main text is the following:The free-exciton population N3D generated in the crystalvolume by the primary excitation are trapped (rate C) at theinterface. The excitons accumulate at the 2D interfaceunder a dark and long-living form (N2D population). Theyare finally converted into NST by their self-trapping (rateST) and intoN3D by their detrapping (rateD). This scenarioillustrated in Fig. 8 of the main text leads to the followingdifferential equations:dN3Ddt¼ −N3Dτ0− CN3D þDN2D þGðtÞ;dN2Ddt¼ −ðDþ STÞN2D þ CN3D;dNSTdt¼ −NSTτSTþ STN2D; ðF1Þwhere τ0 is the lifetime of the free exciton in the volume(without interface), and τST is the lifetime of the XSTexcitons. G denotes the generation rate of free excitons,which is constant during continuous excitation and thenzero when the excitation stops. A priori, C varies slightlywith the temperature due to the weak evolution of theexciton diffusion length with the temperature [64], whilethe rates of D and ST are thermally activated.The first two equations of the system are not coupled toNST; they could be considered independently. We find asuperposition of two exponential decays for both N3DandN2D exciton populations: one short with a characteristictime τs and the other long with a characteristic time τl > τs.These times can be written with A ¼ 1=τ0 þ C, andB ¼ Dþ ST:1τs¼ Aþ BþffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðA − BÞ2 þ 4CDp2; ðF2Þ1τl¼ Aþ B −ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðA − BÞ2 þ 4CDp2: ðF3ÞThe interruption of the steady excitation at the initial timeresults in GðtÞ ¼ 0 for t > 0. The previously establishedsteady equilibrium imposes the initial conditionsN2Dð0ÞN3Dð0Þ¼ CB; ðF4Þand the N3D population is written asN3DðtÞN3Dð0Þ¼ Ale− tτl þ ð1 − AlÞe−tτs ðF5Þwith the weight of the long exponential Al given byAl ¼τlτl − τs�1 −1Bτl�≈ 1 −1Bτl: ðF6Þ3 4 5 6300 Kh-BN–h-BNh-BN5 KCLintensity(a.u.)Energy (eV)�������FIG. 14. CL spectra measured at room and cryogenic temper-ature on a single h-BN flake, in black, and on an h-BN–h-BNhomostructure with a 23° twist, in red, both fabricated from thesame HPHT crystal.EXCITON SELF-TRAPPING IN TWISTED HEXAGONAL BORON … PHYS. REV. X 15, 021067 (2025)021067-13This givesB ¼ 1τl11 − Al: ðF7ÞThe parameter B ¼ Dþ ST can therefore be extractedfrom the TRCL decays of the free-exciton luminescencefrom the previous equation or from the simplified formwhen Al ≪ 1:1τl≃Dþ ST: ðF8ÞThe calculations show that all three populations follow thesame decay time, as can be seen in Fig. 15(a), which isconsistent with the experimentally observed decays of theNST andN3D populations in Fig. 15(b) [see also Fig. 4(b) inthe main text]. The long component of the TRCL decay isgoverned by the detrapping and self-trapping rates of theN2D population that occurs in the long term.[1] A. K. Geim and I. V. Grigorieva, van der Waals hetero-structures, Nature (London) 499, 419 (2013).[2] J. F. Sierra, J. Fabian, R. K. Kawakami, S. Roche, and S. O.Valenzuela, van der Waals heterostructures for spintronicsand opto-spintronics, Nat. Nanotechnol. 16, 856 (2021).[3] C. N. Lau, M.W. Bockrath, K. F. Mak, and F. Zhang,Reproducibility in the fabrication and physics of moirématerials, Nature (London) 602, 41 (2022).[4] M. Gibertini, M. Koperski, A. F. Morpurgo, and K. S.Novoselov, Magnetic 2D materials and heterostructures,Nat. Nanotechnol. 14, 408 (2019).[5] H. H. Fang, B. Han, C. Robert, M. A. Semina, D. Lagarde,E. Courtade, T. Taniguchi, K. Watanabe, T. Amand, B.Urbaszek, M. M. Glazov, and X. Marie, Control of theexciton radiative lifetime in van der Waals heterostructures,Phys. Rev. Lett. 123, 067401 (2019).[6] J. Choi, M. Florian, A. Steinhoff, D. Erben, K. Tran, D. S.Kim, L. Sun, J. Quan, R. Claassen, S. Majumder et al., Twistangle-dependent interlayer exciton lifetimes in van der Waalsheterostructures, Phys. Rev. Lett. 126, 047401 (2021).[7] P. Rivera, J. R. Schaibley, A. M. Jones, J. S. Ross, S. Wu, G.Aivazian, P. Klement, K. Seyler, G. Clark, N. J. Ghimireet al., Observation of long-lived interlayer excitons inmonolayer MoSe2-WSe2 heterostructures, Nat. Commun.6, 6242 (2015).[8] S. Ovesen, S. Brem, C. Linderälv, M. Kuisma, T. Korn, P.Erhart, M. Selig, and E. Malic, Interlayer exciton dynamicsin van der Waals heterostructures, Commun. Phys. 2, 23(2019).[9] B. Miller, A. Steinhoff, B. Pano, J. Klein, F. Jahnke,A. Holleitner, and U. Wurstbauer, Long-lived direct andindirect interlayer excitons in van der Waals heterostruc-tures, Nano Lett. 17, 5229 (2017).[10] L. Yuan, B. Zheng, J. Kunstmann, T. Brumme, A. B. Kuc,C. Ma, S. Deng, D. Blach, A. Pan, and L. Huang, Twist-angle-dependent interlayer exciton diffusion in WS2-WSe2heterobilayers, Nat. Mater. 19, 617 (2020).[11] F. Cadiz, E. Courtade, C. Robert, G. Wang, Y. Shen, H. Cai,T. Taniguchi, K. Watanabe, H. Carrere, D. Lagarde et al.,Excitonic linewidth approaching the homogeneous limit inMoS2-based van der Waals heterostructures, Phys. Rev. X7, 021026 (2017).[12] P. Rivera, K. L. Seyler, H. Yu, J. R. Schaibley, J. Yan, D. G.Mandrus, W. Yao, and X. Xu, Valley-polarized excitondynamics in a 2D semiconductor heterostructure, Science351, 688 (2016).[13] J. Kim, C. Jin, B. Chen, H. Cai, T. Zhao, P. Lee, S. Kahn, K.Watanabe, T. Taniguchi, S. Tongay et al., Observation ofultralong valley lifetime in WSe2=MoS2 heterostructures,Sci. Adv. 3, e1700518 (2017).[14] E. Carré, Propriétés optiques du phosphore noir: Du cristalmassif aux couches atomiques, Ph.D. thesis, UniversitéParis Saclay, 2022.[15] S. Latini, T. Olsen, and K. S. Thygesen, Excitons in van derWaals heterostructures: The important role of dielectricscreening, Phys. Rev. B 92, 245123 (2015).[16] Y. Lin, X. Ling, L. Yu, S. Huang, A. L. Hsu, Y.-H. Lee, J.Kong, M. S. Dresselhaus, and T. Palacios,Dielectric screen-ing of excitons and trions in single-layer MoS2, Nano Lett.14, 5569 (2014).[17] W.-T. Hsu, J. Quan, C.-Y. Wang, L.-S. Lu, M. Campbell,W.-H. Chang, L.-J. Li, X. Li, and C.-K. Shih, Dielectricimpact on exciton binding energy and quasiparticlebandgap in monolayer WS2 and WSe2, 2D Mater. 6,025028 (2019).[18] E. M. Alexeev, D. A. Ruiz-Tijerina, M. Danovich, M. J.Hamer, D. J. Terry, P. K. Nayak, S. Ahn, S. Pak, J. Lee, J. I.Sohn et al., Resonantly hybridized excitons in moiré super-lattices in van der Waals heterostructures, Nature (London)567, 81 (2019).[19] C. Jin, E. C. Regan, A. Yan, M. Iqbal Bakti Utama, D.Wang, S. Zhao, Y. Qin, S. Yang, Z. Zheng, S. Shi et al.,Observation of moiré excitons in WSe2=WS2 heterostruc-ture superlattices, Nature (London) 567, 76 (2019).[20] K. L. Seyler, P. Rivera, H. Yu, N. P. Wilson, E. L. Ray,D. G. Mandrus, J. Yan, W. Yao, and X. Xu, Signatures of0 250 5000.0010.010.110 1000 20000.0010.010.11Excitonpopulation(norm.)Time (ns)N2DNSTN3D(a) (b)TRCLintensity(norm.)Time (ns)HPHT-15°:NSTN3DFIG. 15. (a) Simulated decays of the N2D and N3D excitonpopulations for τs ¼ 10 ns, τl ¼ 100 ns, and Al ¼ 0.1, and of theNST self-trapped exciton population for τST ¼ 10 ns. (b) Exper-imental decays for the NST and N3D exciton populations on theHPHT-15° structure measured in TRCL at 5 kV, 27 pA, 300 K.SÉBASTIEN ROUX et al. PHYS. REV. X 15, 021067 (2025)021067-14https://doi.org/10.1038/nature12385https://doi.org/10.1038/s41565-021-00936-xhttps://doi.org/10.1038/s41586-021-04173-zhttps://doi.org/10.1038/s41565-019-0438-6https://doi.org/10.1103/PhysRevLett.123.067401https://doi.org/10.1103/PhysRevLett.126.047401https://doi.org/10.1038/ncomms7242https://doi.org/10.1038/ncomms7242https://doi.org/10.1038/s42005-019-0122-zhttps://doi.org/10.1038/s42005-019-0122-zhttps://doi.org/10.1021/acs.nanolett.7b01304https://doi.org/10.1038/s41563-020-0670-3https://doi.org/10.1103/PhysRevX.7.021026https://doi.org/10.1103/PhysRevX.7.021026https://doi.org/10.1126/science.aac7820https://doi.org/10.1126/science.aac7820https://doi.org/10.1126/sciadv.1700518https://doi.org/10.1103/PhysRevB.92.245123https://doi.org/10.1021/nl501988yhttps://doi.org/10.1021/nl501988yhttps://doi.org/10.1088/2053-1583/ab072ahttps://doi.org/10.1088/2053-1583/ab072ahttps://doi.org/10.1038/s41586-019-0986-9https://doi.org/10.1038/s41586-019-0986-9https://doi.org/10.1038/s41586-019-0976-ymoiré-trapped valley excitons in MoSe2=WSe2 heterobi-layers, Nature (London) 567, 66 (2019).[21] K. Tran, G. Moody, F. Wu, X. Lu, J. Choi, K. Kim, A. Rai,D. A. Sanchez, J. Quan, A. Singh et al., Evidence for moiréexcitons in van der Waals heterostructures, Nature(London) 567, 71 (2019).[22] H. Baek, M. Brotons-Gisbert, Z. X. Koong, A. Campbell,M. Rambach, K. Watanabe, T. Taniguchi, and B. D.Gerardot, Highly energy-tunable quantum light frommoiré-trapped excitons, Sci. Adv. 6, eaba8526 (2020).[23] S. Brem, C. Linderalv, P. Erhart, and E. Malic, Tunablephases of moiré excitons in van der Waals heterostructures,Nano Lett. 20, 8534 (2020).[24] M. Brotons-Gisbert, H. Baek, A. Molina-Sánchez,A. Campbell, E. Scerri, D. White, K. Watanabe, T.Taniguchi, C. Bonato, and B. D. Gerardot, Spin–layerlocking of interlayer excitons trapped in moiré potentials,Nat. Mater. 19, 630 (2020).[25] D. Unuchek, A. Ciarrocchi, A. Avsar, K. Watanabe, T.Taniguchi, and A. Kis, Room-temperature electrical controlof exciton flux in a van der Waals heterostructure, Nature(London) 560, 340 (2018).[26] D. Unuchek, A. Ciarrocchi, A. Avsar, Z. Sun, K. Watanabe,T. Taniguchi, and A. Kis, Valley-polarized exciton currentsin a van der Waals heterostructure, Nat. Nanotechnol. 14,1104 (2019).[27] C. Gong and X. Zhang, Two-dimensional magnetic crystalsand emergent heterostructure devices, Science 363,eaav4450 (2019).[28] Y. Wang, Y. Shao, D. W. Matson, J. Li, and Y. Lin,Nitrogen-doped graphene and its application in electro-chemical biosensing, ACS Nano 4, 1790 (2010).[29] C. R. Dean, A. F. Young, I. Meric, C. Lee, L. Wang, S.Sorgenfrei, K. Watanabe, T. Taniguchi, P. Kim, K. L.Shepard et al., Boron nitride substrates for high-qualitygraphene electronics, Nat. Nanotechnol. 5, 722 (2010).[30] H. Arora, Y. Jung, T. Venanzi, K. Watanabe, T. Taniguchi,R. Hubner, H. Schneider, M. Helm, J. C. Hone, and A. Erbe,Effective hexagonal boron nitride passivation of few-layered InSe and GaSe to enhance their electronic andoptical properties, ACS Appl. Mater. Interfaces 11, 43480(2019).[31] B. Huang, G. Clark, D. R. Klein, D. MacNeill, E. Navarro-Moratalla, K. L. Seyler, N. Wilson, M. A. McGuire, D. H.Cobden, D. Xiao et al., Electrical control of 2D magnetismin bilayer CrI3, Nat. Nanotechnol. 13, 544 (2018).[32] H. H. Kim, B. Yang, S. Li, S. Jiang, C. Jin, Z. Tao, G.Nichols, F. Sfigakis, S. Zhong, C. Li et al., Evolution ofinterlayer and intralayer magnetism in three atomically thinchromium trihalides, Proc. Natl. Acad. Sci. U.S.A. 116,11131 (2019).[33] K. Yasuda, X. Wang, K. Watanabe, T. Taniguchi, andP. Jarillo-Herrero, Stacking-engineered ferroelectricity inbilayer boron nitride, Science 372, 1458 (2021).[34] C. Woods, P. Ares, H. Nevison-Andrews, M. Holwill, R.Fabregas, F. Guinea, A. Geim, K. Novoselov, N. Walet, andL. Fumagalli, Charge-polarized interfacial superlattices inmarginally twisted hexagonal boron nitride, Nat. Commun.12, 347 (2021).[35] X.-J. Zhao, Y. Yang, D.-B. Zhang, and S.-H. Wei, For-mation of Bloch flat bands in polar twisted bilayers withoutmagic angles, Phys. Rev. Lett. 124, 086401 (2020).[36] X.-J. Zhao, Y. Yang, D.-B. Zhang, and S.-H. Wei, Flatbands in twisted bilayers of polar two-dimensional semi-conductors, Phys. Rev. Mater. 5, 014007 (2021).[37] K. Yao et al., Enhanced tunable second harmonic gener-ation from twistable interfaces and vertical superlatticesin boron nitride homostructures, Sci. Adv. 7, eabe8691(2021).[38] A. Plaud, Excitons dans le nitrure de bore lamellaire: Étudedes phases hexagonale, rhomboédrique et d’hétérostruc-tures 2D, Ph.D. thesis, Université Paris Saclay, 2020.[39] H. J. Lee, M.M. Al Ezzi, N. Raghuvanshi, J. Y. Chung,K. Watanabe, T. Taniguchi, S. Garaj, S. Adam, and S.Gradecak, Tunable optical properties of thin films con-trolled by the interface twist angle, Nano Lett. 21, 2832(2021).[40] Y. Li, X. Xie, H. Zeng, B. Li, Z. Zhang, S. Wang, J. Liu, andD. Shen, Giant moiré trapping of excitons in twisted hBN,Opt. Express 30, 10596 (2022).[41] C. Su, F. Zhang, S. Kahn, B. Shevitski, J. Jiang, C. Dai, A.Ungar, J.-H. Park, K. Watanabe, T. Taniguchi, J. Kong, Z.Tang,W.Zhang, F.Wang,M.Crommie, S. G.Louie, S.Aloni,and A. Zettl, Tuning colour centres at a twisted hexagonalboron nitride interface, Nat. Mater. 21, 896 (2022).[42] S. Latil, H. Amara, and L. Sponza, Structural classificationof boron nitride twisted bilayers and ab initio investigationof their stacking-dependent electronic structure, SciPostPhys. 14, 053 (2023).[43] L. D. Landau, The movement of electrons in the crystallattice, Phys. Z. Sowjetunion 3, 644 (1933).[44] J. Frenkel,On the solid body model of heavy nuclei, Phys. Z.Sowjetunion 9, 158 (1936).[45] T. G. Castner and W. Känzig, The electronic structure ofv-centers, J. Phys. Chem. Solids 3, 178 (1957).[46] M. N. Kabler, Low-temperature recombination lumines-cence in alkali halide crystals, Phys. Rev. 136, A1296(1964).[47] R. B. Murray and F. J. Keller, Recombination luminescencefrom vK centers in potassium iodide, Phys. Rev. 137, A942(1965).[48] J. Ramamurti and K. Teegarden, Intrinsic luminescence ofRbI and KI at 10°K, Phys. Rev. 145, 698 (1966).[49] R. A. Kink, G. G. Liidja, C. B. Lushchik, and T. A. Soovik,Self-trapping of excitons and optical phenomena in ioniccrystals, Bull. Russ. Acad. Sci.: Phys. 31, 1982 (1967).[50] S. Roux, C. Arnold, F. Paleari, L. Sponza, E. Janzen, J. H.Edgar, B. Toury, C. Journet, V. Garnier, P. Steyer, T.Taniguchi, K. Watanabe, F. Ducastelle, A. Loiseau, and J.Barjon, Radiative lifetime of free excitons in hexagonalboron nitride, Phys. Rev. B 104, L161203 (2021).[51] L. Schué, L. Sponza, A. Plaud, H. Bensalah, K. Watanabe,T. Taniguchi, F. Ducastelle, A. Loiseau, and J. Barjon,Bright luminescence from indirect and strongly boundexcitons in h-BN, Phys. Rev. Lett. 122, 067401 (2019).[52] Y. Kubota, K. Watanabe, O. Tsuda, and T. Taniguchi,Deepultraviolet light-emitting hexagonal boron nitride syn-thesized at atmospheric pressure, Science 317, 932 (2007).EXCITON SELF-TRAPPING IN TWISTED HEXAGONAL BORON … PHYS. REV. X 15, 021067 (2025)021067-15https://doi.org/10.1038/s41586-019-0957-1https://doi.org/10.1038/s41586-019-0975-zhttps://doi.org/10.1038/s41586-019-0975-zhttps://doi.org/10.1126/sciadv.aba8526https://doi.org/10.1021/acs.nanolett.0c03019https://doi.org/10.1038/s41563-020-0687-7https://doi.org/10.1038/s41586-018-0357-yhttps://doi.org/10.1038/s41586-018-0357-yhttps://doi.org/10.1038/s41565-019-0559-yhttps://doi.org/10.1038/s41565-019-0559-yhttps://doi.org/10.1126/science.aav4450https://doi.org/10.1126/science.aav4450https://doi.org/10.1021/nn100315shttps://doi.org/10.1038/nnano.2010.172https://doi.org/10.1021/acsami.9b13442https://doi.org/10.1021/acsami.9b13442https://doi.org/10.1038/s41565-018-0121-3https://doi.org/10.1073/pnas.1902100116https://doi.org/10.1073/pnas.1902100116https://doi.org/10.1126/science.abd3230https://doi.org/10.1038/s41467-020-20667-2https://doi.org/10.1038/s41467-020-20667-2https://doi.org/10.1103/PhysRevLett.124.086401https://doi.org/10.1103/PhysRevMaterials.5.014007https://doi.org/10.1126/sciadv.abe8691https://doi.org/10.1126/sciadv.abe8691https://doi.org/10.1021/acs.nanolett.0c04924https://doi.org/10.1021/acs.nanolett.0c04924https://doi.org/10.1364/OE.450409https://doi.org/10.1038/s41563-022-01303-4https://doi.org/10.21468/SciPostPhys.14.3.053https://doi.org/10.21468/SciPostPhys.14.3.053https://doi.org/10.1016/0022-3697(57)90023-9https://doi.org/10.1103/PhysRev.136.A1296https://doi.org/10.1103/PhysRev.136.A1296https://doi.org/10.1103/PhysRev.137.A942https://doi.org/10.1103/PhysRev.137.A942https://doi.org/10.1103/PhysRev.145.698https://doi.org/10.1103/PhysRevB.104.L161203https://doi.org/10.1103/PhysRevLett.122.067401https://doi.org/10.1126/science.1144216[53] T. B. Hoffman, B. Clubine, Y. Zhang, K. Snow, and J. H.Edgar, Optimization of Ni-Ccr flux growth for hexagonalboron nitride single crystals, J. Cryst. Growth 393, 114(2014).[54] S. Liu, R. He, L. Xue, J. Li, B. Liu, and J. H. Edgar, Singlecrystal growth of millimeter-sized monoisotopic hexagonalboron nitride, Chem. Mater. 30, 6222 (2018).[55] J. Li, C. Elias, G. Ye, D. Evans, S. Liu, R. He, G. Cassabois,B. Gil, P. Valvin, B. Liu et al., Single crystal growth ofmonoisotopic hexagonal boron nitride from a Fe-Cr flux,J. Mater. Chem. C 8, 9931 (2020).[56] K. Watanabe, T. Taniguchi, and H. Kanda, Direct-bandgapproperties and evidence for ultraviolet lasing of hexagonalboron nitride single crystal, Nat. Mater. 3, 404 (2004).[57] T. Taniguchi and K. Watanabe, Synthesis of high-purityboron nitride single crystals under high pressure by usingBa − Bn solvent, J. Cryst. Growth 303, 525 (2007).[58] Y. Li, V. Garnier, P. Steyer, C. Journet, and B. Toury,Millimeter-scale hexagonal boron nitride single crystals fornanosheet generation, ACS Appl. Nano Mater. 3, 1508(2020).[59] C. Maestre, Y. Li, V. Garnier, P. Steyer, S. Roux, A. Plaud,A. Loiseau, J. Barjon, L. Ren, C. Robert et al., From thesynthesis of hBN crystals to their use as nanosheets in vander Waals heterostructures, 2D Mater. 9, 035008 (2022).[60] T. Ouaj, C. Arnold, J. Azpeitia, S. Baltic, J. Barjon, J.Cascales, H. Cun, D. Esteban, M. Garcia-Hernandez, V.Garnier et al., Benchmarking the integration of hexagonalboron nitride crystals and thin films into graphene-based vander Waals heterostructures, 2D Mater. 12, 015017 (2025).[61] A. Castellanos-Gomez, M. Buscema, R. Molenaar, V.Singh, L. Janssen, H. S. J. van der Zant, and G. A. Steele,Deterministic transfer of two-dimensional materials by all-dry viscoelastic stamping, 2D Mater. 1, 011002 (2014).[62] K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y.Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov,Electric field effect in atomically thin carbon films, Science306, 666 (2004).[63] See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevX.15.021067 for the fullset of CL spectra and CL images recorded on the 16samples.[64] S. Roux, C. Arnold, E. Carré, E. Janzen, J. H. Edgar, C.Maestre, B. Toury, C. Journet, V. Garnier, P. Steyer et al.,Surface recombination and out-of-plane diffusivity of freeexcitons in hexagonal boron nitride, Phys. Rev. B 109,155305 (2024).[65] A. Plaud, L. Schué, K. Watanabe, T. Taniguchi, F. Fossard,F. Ducastelle, A. Loiseau, and J. Barjon, Exciton-excitonannihilation in hBN, Appl. Phys. Lett. 114, 232103 (2019).[66] Experiments are performed at 10 K in Ref. [65], and at300 K in ours. However, since in such samples thediffusivity is temperature independent [64], we do notexpect drastic differences in the probability of exciton-exciton collisions and thus in the EEA rate as the temper-ature is increased.[67] Y. Peter and M. Cardona, Fundamentals of Semiconductors:Physics and Materials Properties (Springer Science &Business Media, New York, 2010).[68] J. I. Pankove,Optical Processes in Semiconductors (CourierCorporation, New York, 1975).[69] Y. Toyozawa, Theory of line-shapes of the exciton absorp-tion bands, Prog. Theor. Phys. 20, 53 (1958).[70] E. I. Rashba, Theory of strong interactions of electronexcitations with lattice vibrations in molecular crystals,Opt. Spectrosc. 2, 75 (1957).[71] E. I. Rashba, Self-trapping of excitons, in Excitons, editedby E. I. Rasha and M. D. Sturge (North Holland PublishingGroup, Amsterdam, 1982).[72] H. Sumi and Y. Toyozawa, Urbach–Martienssen rule andexciton trapped momentarily by lattice vibration, J. Phys.Soc. Jpn. 31, 342 (1971).[73] H. Blume, M. P. Fontana, and W. J. van Sciver, Properties ofexciton states in NaI. II. Excitonic energy transfer to Q andTl centers, Phys. Status Solidi 31, 133 (1969).[74] R. A. Kink and G. G. Liidja, Low temperature luminescenceof pure and activated KI crystals during excitation inexciton band, Sov. Phys. Solid State 11, 1331 (1969).[75] C. Lushchik, Survey of luminescence in alkali halide crystals:(The period 1966–1969), J. Lumin. 1–2, 594 (1970).[76] R. T. Williams and K. S. Song, The self-trapped exciton,J. Phys. Chem. Solids 51, 679 (1990).[77] C. B. Lushchik, Free and self-trapped excitons in alkalihalides: Spectra and dynamics, in Excitons, edited by E. I.Rashba and M. D. Sturge (North Holland Publishing Group,Amsterdam, 1982).[78] I. Y. Tekhver and V. V. Khizhnyakov, Transfer of electronicexcitation during the course of vibrational relaxation, Sov.Phys. JETP 19, 191 (1974).[79] T. Q. P. Vuong, G. Cassabois, P. Valvin, A. Ouerghi, Y.Chassagneux, C. Voisin, and B. Gil, Phonon-photon map-ping in a color center in hexagonal boron nitride, Phys.Rev. Lett. 117, 097402 (2016).[80] C. Fournier, A. Plaud, S. Roux, A. Pierret, M. Rosticher, K.Watanabe, T. Taniguchi, S. Buil, X. Quélin, J. Barjon et al.,Position-controlled quantum emitters with reproducibleemission wavelength in hexagonal boron nitride, Nat.Commun. 12, 3779 (2021).[81] Y. K. Jung, S. Kim, Y. C. Kim, and A. Walsh, Low barrierfor exciton self-trapping enables high photoluminescencequantum yield in Cs3Cu3I5, J. Phys. Chem. Lett. 12, 8447(2021).[82] A. Y. Kobitski, K. S. Zhuravlev, H. P. Wagner, and D. R. T.Zahn, Self-trapped exciton recombination in silicon nano-crystals, Phys. Rev. B 63, 115423 (2001).[83] F. Paleari, T. Galvani, H. Amara, F. Ducastelle, A. Molina-Sánchez, and L. Wirtz, Excitons in few-layer hexagonalboron nitride: Davydov splitting and surface localization,2D Mater. 5, 045017 (2018).[84] T. Galvani, F. Paleari, H. P. C. Miranda, A. Molina-Sánchez,L. Wirtz, S. Latil, H. Amara, and F. Ducastelle, Excitons inboron nitride single layer, Phys. Rev. B 94, 125303 (2016).[85] L. Museur, E. Feldbach, and A. Kanaev, Defect-relatedphotoluminescence of hexagonal boron nitride, Phys. Rev.B 78, 155204 (2008).[86] L. Museur and A. Kanaev, Photoluminescence proper-ties of pyrolytic boron nitride, J. Mater. Sci. 44, 2560(2009).SÉBASTIEN ROUX et al. PHYS. REV. X 15, 021067 (2025)021067-16https://doi.org/10.1016/j.jcrysgro.2013.09.030https://doi.org/10.1016/j.jcrysgro.2013.09.030https://doi.org/10.1021/acs.chemmater.8b02589https://doi.org/10.1039/D0TC02143Ahttps://doi.org/10.1038/nmat1134https://doi.org/10.1016/j.jcrysgro.2006.12.061https://doi.org/10.1021/acsanm.9b02315https://doi.org/10.1021/acsanm.9b02315https://doi.org/10.1088/2053-1583/ac6c31https://doi.org/10.1088/2053-1583/ad96c9https://doi.org/10.1088/2053-1583/1/1/011002https://doi.org/10.1126/science.1102896https://doi.org/10.1126/science.1102896http://link.aps.org/supplemental/10.1103/PhysRevX.15.021067http://link.aps.org/supplemental/10.1103/PhysRevX.15.021067http://link.aps.org/supplemental/10.1103/PhysRevX.15.021067http://link.aps.org/supplemental/10.1103/PhysRevX.15.021067http://link.aps.org/supplemental/10.1103/PhysRevX.15.021067http://link.aps.org/supplemental/10.1103/PhysRevX.15.021067http://link.aps.org/supplemental/10.1103/PhysRevX.15.021067https://doi.org/10.1103/PhysRevB.109.155305https://doi.org/10.1103/PhysRevB.109.155305https://doi.org/10.1063/1.5090218https://doi.org/10.1143/PTP.20.53https://doi.org/10.1143/JPSJ.31.342https://doi.org/10.1143/JPSJ.31.342https://doi.org/10.1002/pssb.19690310116https://doi.org/10.1016/0022-2313(70)90073-6https://doi.org/10.1016/0022-3697(90)90144-5https://doi.org/10.1103/PhysRevLett.117.097402https://doi.org/10.1103/PhysRevLett.117.097402https://doi.org/10.1038/s41467-021-24019-6https://doi.org/10.1038/s41467-021-24019-6https://doi.org/10.1021/acs.jpclett.1c02252https://doi.org/10.1021/acs.jpclett.1c02252https://doi.org/10.1103/PhysRevB.63.115423https://doi.org/10.1088/2053-1583/aad586https://doi.org/10.1103/PhysRevB.94.125303https://doi.org/10.1103/PhysRevB.78.155204https://doi.org/10.1103/PhysRevB.78.155204https://doi.org/10.1007/s10853-009-3334-xhttps://doi.org/10.1007/s10853-009-3334-x[87] P. Jaffrennou, J. Barjon, T. Schmid, L. Museur, A. Kanaev,J.-S. Lauret, C. Y. Zhi, C. Tang, Y. Bando, D. Golberg, B.Attal-Tretout, F. Ducastelle, and A. Loiseau, Near-band-edgerecombinations in multiwalled boron nitride nanotubes:Cathodoluminescence and photoluminescence spectroscopymeasurements, Phys. Rev. B 77, 235422 (2008).[88] P. Merkl, C.-K. Yong, M. Liebich, I. Hofmeister, G.Berghäuser, E. Malic, and R. Huber, Proximity control ofinterlayer exciton-phonon hybridization in van der Waalsheterostructures, Nat. Commun. 12, 1719 (2021).[89] C. M. Chow, H. Yu, A. M. Jones, J. Yan, D. G. Mandrus, T.Taniguchi, K. Watanabe, W. Yao, and X. Xu, Unusualexciton–phonon interactions at van der Waals engineeredinterfaces, Nano Lett. 17, 1194 (2017).[90] Z. Hennighausen, J. Moon, K. M. McCreary, C. H. Li, O. M.van’t Erve, and B. T. Jonker, Interlayer exciton–phononbound state in Bi2Se3=monolayer WS2 van der Waalsheterostructures, ACS Nano 17, 2529 (2023).[91] J.-P. Deng, H.-J. Li, X.-F. Ma, X.-Y. Liu, Y. Cui, X.-J. Ma,Z.-Q. Li, and Z.-W. Wang, Self-trapped interlayer excitonsin van der Waals heterostructures, J. Phys. Chem. Lett. 13,3732 (2022).[92] S. Wang, Y. Yao, J. Kong, S. Zhao, Z. Sun, Z. Wu, L. Li,and J. Luo, Highly efficient white-light emission in a polartwo-dimensional hybrid perovskite, Chem. Commun.(Cambridge) 54, 4053 (2018).[93] T. Jun, T. Handa, K. Sim, S. Iimura, M. Sasase, J. Kim, Y.Kanemitsu, and H. Hosono, One-step solution synthesis ofwhite-light-emitting films via dimensionality control of theCs-Cu-I system, APL Mater. 7, 111113 (2019).[94] X. Li, W. Li, M. Xia, C. Liu, N. Li, Z. Shi, Y. Xu, andX. Zhang, Facile melting-crystallization synthesis ofCs2NaxAg1−xInCl6: Bi double perovskites for white light-emitting diodes, Inorg. Chem. 61, 5040 (2022).[95] L. Lian, P. Zhang, G. Liang, S. Wang, X. Wang, Y. Wang, X.Zhang, J. Gao, D. Zhang, L. Gao et al., Efficient dual-bandwhite-light emission with high color rendering from zero-dimensional organic copper iodide, ACS Appl. Mater.Interfaces 13, 22749 (2021).[96] A. Segura, L. Artús, R. Cuscó, T. Taniguchi, G. Cassabois,and B. Gil, Natural optical anisotropy of h-BN: Highestgiant birefringence in a bulk crystal through the mid-infrared to ultraviolet range, Phys. Rev. Mater. 2,024001 (2018).EXCITON SELF-TRAPPING IN TWISTED HEXAGONAL BORON … PHYS. REV. X 15, 021067 (2025)021067-17https://doi.org/10.1103/PhysRevB.77.235422https://doi.org/10.1038/s41467-021-21780-6https://doi.org/10.1021/acs.nanolett.6b04944https://doi.org/10.1021/acsnano.2c10313https://doi.org/10.1021/acs.jpclett.2c00565https://doi.org/10.1021/acs.jpclett.2c00565https://doi.org/10.1039/C8CC01663Ahttps://doi.org/10.1039/C8CC01663Ahttps://doi.org/10.1063/1.5127300https://doi.org/10.1021/acs.inorgchem.1c03996https://doi.org/10.1021/acsami.1c03881https://doi.org/10.1021/acsami.1c03881https://doi.org/10.1103/PhysRevMaterials.2.024001https://doi.org/10.1103/PhysRevMaterials.2.024001 Exciton Self-Trapping in Twisted Hexagonal Boron Nitride homostructures I. INTRODUCTION II. EXPERIMENTS III. EVIDENCE OF THE EXCITONIC ORIGIN OF THE BROAD 4-EV OPTICAL EMISSION IV. POWER DEPENDENCE AND INTERNAL QUANTUM EFFICIENCY OF THE 4-EV EMISSION V. EXCITON SELF-TRAPPING AT THE TWISTED h-BN-h-BN INTERFACE VI. TEMPERATURE-DEPENDENT EXPERIMENTS VII. PHENOMENOLOGICAL MODEL FOR EXCITON RECOMBINATION DYNAMICS VIII. DISCUSSION: SELF-TRAPPING IN sp2 BN IX. CONCLUSION ACKNOWLEDGMENTS APPENDIX A: MEASUREMENT OF THE INTERNAL QUANTUM EFFICIENCY OF THE 4-EV LUMINESCENCE APPENDIX B: MEASUREMENT OF THE TWIST ANGLE BY ELECTRON DIFFRACTION APPENDIX C: CL SIGNAL ON LOW-ANGLE h-BN-h-BN STRUCTURES APPENDIX D: LUMINESCENCE DECAY AS FUNCTION OF THE ENERGY WITHIN THE BROAD 4-EV LUMINESCENCE APPENDIX E: LOW-TEMPERATURE SPECTRUM OF A TWISTED h-BN-h-BN HOMOSTRUCTURE APPENDIX F: SIMULATION OF TRCL DECAYS WITH RATE EQUATIONS References