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Yan Sun, Corentin Morice, Damien Garrot, Raphael Weil, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Miguel Monteverde, Alexei D. Chepelianskii

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Quantum Transport and Spectroscopy of 2D Perovskite/Graphene HeterostructuresRESEARCH ARTICLEwww.advelectronicmat.deQuantum Transport and Spectroscopy of 2DPerovskite/Graphene HeterostructuresYan Sun,* Corentin Morice, Damien Garrot, Raphael Weil, Kenji Watanabe,Takashi Taniguchi, Miguel Monteverde, and Alexei D. Chepelianskii*Understanding the quantum transport properties of (Two-dimensional) 2Dperovskite heterostructures is key to interpreting their electronic performanceand promoting optoelectronic devices. Here, it is shown that clear Shubnikov-de Hass oscillation appears in the heterostructure of monocrystalline 2Dperovskites and graphene, thanks to the clean interface. An efficient chargetransfer between perovskite nanosheets and graphene is found, facilitatingthe separation of electrons and holes at the interface. The relation between thecharge transfer efficiency and microscopic interface structures is quantitativelydescribed. The evidence of photo-assisted transport from the photo-responseof magnetoresistance is revealed, which happens between Landaulevels of two graphene layers mediated by hot carriers in the perovskite layer,overcoming the barrier from the organic layers in the Ruddlesden-Popperperovskite phase. These results provide a picture to understand thetransport behavior of 2D perovskite/graphene heterostructure and a referencefor the controlled design of interfaces in perovskite optoelectronic devices.1. IntroductionHalide Perovskite is an attractive new class of promising semi-conductors for optoelectronic devices.[1,2] To improve the powerY. Sun, C. Morice, R. Weil, M. Monteverde, A. D. ChepelianskiiLPSUniversité Paris-SaclayCNRS, UMR 8502, Orsay F-91405, FranceE-mail: yan.sun@universite-paris-saclay.fr;alexei.chepelianskii@universite-paris-saclay.frD. GarrotUniversité Paris-SaclayUVSQ, CNRS, GEMaC, Versailles 78000, FranceK. WatanabeResearch Center for Electronic and Optical MaterialsNational Institute for Materials Science1-1 Namiki, Tsukuba 305-0044, JapanT. TaniguchiInternational Center for Materials NanoarchitectonicsNational Institute for Materials Science1-1 Namiki, Tsukuba 305-0044, JapanThe ORCID identification number(s) for the author(s) of this articlecan be found under https://doi.org/10.1002/aelm.202400211© 2024 The Author(s). Advanced Electronic Materials published byWiley-VCH GmbH. This is an open access article under the terms of theCreative Commons Attribution License, which permits use, distributionand reproduction in any medium, provided the original work is properlycited.DOI: 10.1002/aelm.202400211conversion efficiency and stability, the in-corporation of graphene into perovskite-based optoelectronics has been exploited,in which graphene is introduced intotransport layers or as electrodes to ad-just the optical and electrical propertiesof perovskite devices.[3–9] Graphene isa monolayer structure of carbon atomswith good optical transparency, excellentstability, high mobility, and outstandingthermal and electrical conductivity.[10–12]Moreover, as an ideal 2D system with aDirac electronic spectrum, graphene of-fers a unique platform for discoveringnovel physics.[13,14]Ruddlesden- Popper perovskites(RPPs) have recently become appealingcandidates in optoelectronic devices,thanks to their improved stability andhigher photoluminescence quantumyield, chemical composition and dimensional tunability.[15,16]RPPs have a general formula LA2An−1BnX3n+1, where LA and Arepresent the organic ammonium cations, B is a divalent cation,X is a halide anion, and n is the number of inorganic layers be-tween two planes of LA cations. The large-size organic protec-tive layers in the RPPs enable the natural formation of quantumwell structure,[17,18] the integration with other 2D materials,[18–20]and promising wide-range applications.[21–23] However, the in-terlayer charge transfer hindered by the organic barriers lim-its the performance of the devices. In this context, graphenehas been introduced as a low-resistance contact to form 2D per-ovskite/graphene field effect transistors owing to the atomicallysmooth interface and better energy level alignment.[19,24–26] Nev-ertheless, in graphene-integrated perovskite heterostructures,the microscopic mechanism of electronic properties and inter-facial interactions are poorly understood, which obstructs the de-velopment of design principles of perovskite devices, partly dueto the difficulty of building clear interfaces and keeping phasepurity during processing because of the instability of perovskiteswith humidity and heat.[27] In particular, the perovskite layer’simpact on graphene’s transport properties has not yet been in-vestigated.Here, we study quantum transport properties in the het-erostructure of molecularly thin perovskite (BA)2(MA)3Pb4I13 Bais CH3(CH2)3NH+3 ; Ma is CH3NH+3 and monolayer grapheneby Shubnikov-de Hass (SdH) oscillation and photoresistancespectroscopy. We report that the perovskite efficiently transferscharges to graphene, leading to a high doping level in grapheneAdv. Electron. Mater. 2024, 10, 2400211 2400211 (1 of 9) © 2024 The Author(s). Advanced Electronic Materials published by Wiley-VCH GmbHhttp://www.advelectronicmat.demailto:yan.sun@universite-paris-saclay.frmailto:alexei.chepelianskii@universite-paris-saclay.frhttps://doi.org/10.1002/aelm.202400211http://creativecommons.org/licenses/by/4.0/http://crossmark.crossref.org/dialog/?doi=10.1002%2Faelm.202400211&domain=pdf&date_stamp=2024-09-03www.advancedsciencenews.com www.advelectronicmat.deFigure 1. a) Schematic illustration (top) and micrograph (bottom) of a graphene/BMPI/graphene device, where a vertical region is constructed byintroducing an overlap from top graphene (T-Gra) to bottom graphene (B-Gra). The whole device is encapsulated by two pieces of BN layers and stackedon a SiO2/Si substrate, which also works as a bottom gate. The electrodes used in four-terminal connections are labeled. b) The magneto-resistance ofBMPI/graphene stack at 1.6 K from B-Gra to B-Gra (Rbb) and T-Gra to B-Gra (Rtb) contacts with gate bias Vg = 0 V, both of which have the characteristicof the Shubnikov-de Hass (SdH) oscillations. The resistance of Rbb is multiplied by 5 (the aspect ratio in device geometry). SdH oscillation as a functionof gate bias, c) from Rbb, and d) from Rtb. In both cases, the graphene is heavily hole-doped with carrier density n ≃ 2.78 × 1013 cm−2, deduced fromthe oscillation period. c) The SdH in Rbb shift with bottom gate voltage Vg indicating hole doping, d) while SdH oscillation in Rtb shows a barely visiblegate voltage dependence. This is most likely due to the screening of the gate voltage by the bottom graphene.of up to 2.8 × 1013 cm−2. The clear oscillations indicate locallyuniform hole-doping (to within 1%) in graphene from the chargetransfer at the interface, rather than ion migration or defects. Thedensity functional theory (DFT) simulations show that the chargetransfer efficiency strongly depends on the microscopic struc-tures of the interface, as confirmed by magneto-resistance andmicro-fluorescence (micro-PL) experiments. We find that pho-toresistance in the regime of SdH oscillation provides detailedinformation on the physics of photo excitations at the graphene-BMPI interface, allowing us to estimate the characteristic life-times for photo-gating and heating of the carriers. The photore-sistance spectroscopy provides evidence of direct photo-assistedtransport between the two graphene contacts through the BMPIlayer, indicating that the hot carriers in BMPI interact with bothtop and bottom graphene.2. Results and Discussion2.1. Transport Devices of 2D Perovskite/Graphene(BA)2(MA)3Pb4I13 (BMPI) crystal is prepared by temperature-controlled crystallization. The clean periodic diffraction peaks inthe X-ray diffraction (XRD) pattern in Figure S1 (Supporting In-formation) confirm the phase purity of those 2D perovskite crys-tals. Since generally perovskite is sensitive to heat and humidity,developing a method to avoid degradation during fabrication iscrucial. To minimize heating, the 2D perovskite is assembled byresist-free dry transfer, so that the transfer temperature remainslower than 60 ◦C. To verify the quality of the BMPI layer afterthe exfoliation and dry-transfer process, we performed micro-PL microscopy on a pristine BN/graphene/BMPI/BN sample. Asshown in Figure S2 (Supporting Information, The mean photolu-minescence intensity of BMPI/graphene is almost half as large asthat of BMPI. A quenching of BMPI PL by graphene is expectedsince graphene has no bandgap and is rendered as a collector forboth electrons and holes, which is also proof of a clean interfacebetween BMPI and graphene.[28] All the above characterizationresults show that our crystals and fabrication technique, includ-ing exfoliation and dry transfer, ensure a good sample quality,making transport measurements possible. A schematic and op-tical image of a graphene-BMPI device used in transport experi-ments is shown in Figure 1a. The device containing both horizon-tal and vertical stacking regions is constructed by transferring theBMPI flake (around four layers, thickness about 14 nm) on topof a graphene layer, followed by partly covering the stack with an-other small piece of graphene. The device is encapsulated withtwo h-boron nitride layers. The details of materials and devicefabrication can be found in the methods section.We investigate transport from top to bottom graphene throughBMPI as well as the conductivity of the bottom graphene cov-ered by the BMPI layer. Four-terminal electrical contacts are usedto eliminate the contact resistance and resistance from wires.The resistance of the bottom graphene, Rbb, is normalized bythe geometrical aspect ratio (five squares). The resistance fromtop to bottom graphene, Rtb, is measured from the region T-Gra (top graphene) to B-Gra (bottom graphene) (Figure 1a). Thebottom graphene was measured at room temperature before de-position of the BMPI layers and exhibits a sharp Dirac peakand a small electron doping (Figure S3, Supporting Informa-tion). After stacking with BMPI, the Dirac peak strongly shifted,Adv. Electron. Mater. 2024, 10, 2400211 2400211 (2 of 9) © 2024 The Author(s). Advanced Electronic Materials published by Wiley-VCH GmbH 2199160x, 2024, 11, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/aelm.202400211 by National Institute For, Wiley Online Library on [08/07/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advelectronicmat.dewww.advancedsciencenews.com www.advelectronicmat.depossibly indicating the charge transfer process, which has beenseen in graphene-based Van der Waals heterostructures.[29–31] Toconfirm and quantify the charge transfer in the device, we cooledthe sample to 1.6 K. The resistance of the samples decreased onlyweakly ≈ 15% during cooling (Figure S3, Supporting Informa-tion) for transport from top to bottom graphene. This indicatesthat the BMPI is sufficiently conducting even at low tempera-ture and that transport through BMPI is not thermally activatedconfirming that we prepared clean graphene/BMPI interfaces. Inthe following, we present magneto-transport to elucidate the na-ture of the possible charge transfer process between grapheneand BMPI, and photoresistance spectroscopy to probe the in-teraction between photo-excitations in BMPI and transport ingraphene.2.2. Magneto-Transport at the Graphene-Perovskite InterfaceFigure 1b shows periodic oscillation on the magnetoresistance,with four-terminal contacts on Rbb (blue) and Rtb (red) at 1.6K. The oscillation originates from the SdH effect, which is re-lated to the crossing between the Fermi level and quantized Lan-dau Levels (LL). The appearance of SdH oscillation in this hy-brid graphene/perovskite system under an intermediate field (<8Tesla) implies that the interface between graphene and BMPI isclean. According to Lifshitz-Kosevich theory, the SdH oscillationsin the magnetoresistance of two-dimensional electron gas sys-tems can be described approximately by Equation (1).[32,33] In thelimit of small SdH, their amplitude 𝛿R is given by:𝛿R = R0DT exp(− 𝜋𝜇B)cos(𝜋hn2eB)(1)here n is the carrier density, 𝜇 is the carrier mobility, and R0 is themean longitudinal resistance around which magneto-resistanceoscillates. The phase of the oscillation takes into account theBerry phase 𝜋 for graphene.[34] The temperature damping is de-scribed by the DT:DT =2𝜋2kbT∕ℏ𝜔csinh(2𝜋2kbT∕ℏ𝜔c)(2)where𝜔c = eB∕m∗c is cyclotron frequency, and m∗c = ℏkF∕vF is theeffective mass (cyclotron mass).[35]The resistance versus 1/B measured with gate voltage rangingfrom ‒10 V to 10 V displays a Landau fan diagram (Figure 1c).Applying Equation (1), the oscillation pattern for Rbb (Figure 1c)and Rtb connections (Figure 1d) are simulated (Figure S4, Sup-porting Information). We find that in both cases, the grapheneis heavily hole-doped, with density n ≃ 2.78 × 1013 cm−2 at Vg =0 V. This doping level is so high that the hole density is about1% of the areal density of carbon atoms in graphene (which isabout ≈ 3.8 × 1015 cm−2).The typical distance between two holesis around 2 nm in the graphene, while the carbon-carbon bondlength in graphene is around 0.14 nm, and the lattice constant ofBMPI is around 0.87 nm.[36,37] We notice that similar doping lev-els have been reported in graphene-RuCl3 heterostructures.[38,39]We note that the bottom-gate voltage required to reach this car-rier density is around 400V, which is beyond the breakdown limitof the gate voltage. Considering the non-equivalent fabricationprocess for top and bottom graphenes, the nearly equivalentdoping level in both layers suggests that the high hole densityin graphene is independent of the fabrication process, but anintrinsic property of BMPI/graphene hybrids. The peaks ofSdH oscillations shift and the period slightly increases in Rbbwhen increasing the gate voltage, as expected in quantitativeagreement with the change in hole density. For Rtb, we find thatbottom gate voltage has little infuence on the resistance, thisis probably related to the screen effect by the bottom grapheneand a dominating contribution of the top graphene/BMPIinterface due to the electrode geometry (SupportingInformation).Since graphene becomes hole doped due to charge transferwith the perovskite, the 14nm thick BMPI layer becomes elec-tron doped with the same surface carrier density. The resistancebetween top and bottom graphenes seems largely due to in planegraphene transport as evidenced by the SdH oscillations. This al-lows us to find a lower limit on the electron mobility inside BMPIlayer. We find than for mobility ⩾10−2 cm2 V−1 s−1, the vertialBMPI resistance to becomes much smaller than the resistancefrom in plane graphene transport.Figure 2a shows that the amplitude of SdH oscillations, 𝛿Rbb,gradually decreases with increasing temperature, and tends todisappear under sufficiently high temperature (>54.5 K), where𝛿Rbb is calculated by subtracting the resistance with a liner fitto the background. The temperature-dependent SdH oscillationsare fitted with Equation (1). From the amplitude of the oscil-lation peaks at various temperatures, the only fitting parame-ter m∗c is available from the relation between the amplitude andT/B by Equation (2),[40] which gives m∗c = 0.08 me (Figure 2b).While through m∗c = ℏkF/vF = ℏ√𝜋n/vF,[35] the theoretical ef-fective mass m∗c = 0.12 me, where me is the electron mass, andthe Fermi velocity vF is around 1 × 106 m s−1,[41] as shown inFigure 2b with a broken line for comparison. The detailed dis-cussion on effective mass and mobility in the heterostructure isin Supporting Information.2.3. Interfacial Terminations Affect the Charge Transfer ProcessIn addition to quantum oscillations, the magneto-resistance inFigure 1b shows a global positive magneto-resistance trend,which is not expected in a single carrier Drude model. We simu-lated the potential distribution in the sample by the finite elementmethod (FEM) and modeled the conductivity of our sample as thesum of two conductivities corresponding to the weakly/highlydoped regions. We find that this two-region model can repro-duce the overall magneto-resistance trend (Figure 2c). The high-doped region gives the saturating high field mobility, while thelow-doping region of n1 ≈ 1.26 × 1012 cm−2 with higher mobil-ity of 𝜇1 ≈ 11 000 cm−2 V−1 s−1 explains the low field magnetore-sistance. Evidence of the co-existence of regions with differentcarrier densities is also found in the micro-PL microscopy onthe pristine BN/graphene/BMPI/BN sample, where we see inho-mogeneous photoluminescence with domain size around 2 μm2(Figure S2, Supporting Information).To find out the correlation between the charge transferprocess and the microscopic structure of the BMPI/grapheneAdv. Electron. Mater. 2024, 10, 2400211 2400211 (3 of 9) © 2024 The Author(s). Advanced Electronic Materials published by Wiley-VCH GmbH 2199160x, 2024, 11, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/aelm.202400211 by National Institute For, Wiley Online Library on [08/07/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advelectronicmat.dewww.advancedsciencenews.com www.advelectronicmat.deFigure 2. a) Temperature-dependent SdH oscillations which are fitted with Equation (1). b) The normalized amplitudes of the oscillations as a functionof T/B are collected under several oscillation peaks labeled by the magnetic field, from which the m∗c is available through Equation (2). c) Simulationsof magneto-resistance of Rbb with a model of two types of carriers with different mobility. The mobilities and doping levels are shown in the tables. Thesimulated voltage drop on a model geometry from the finite element method under 12 T is shown in the inset as an example. DFT simulation of theelectron density at the interface between BMPI and graphene for different perovskite terminations. d) BA molecules, e) Pb-I, f) Iodide ions. The bluecurves denote the plane-averaged integral charge density along the stacking direction (y-axis) in the graphene/BMPI heterostructure (𝜌̄hs) with each typeof interface. The charge transfer process mainly happens at the interface and is revealed by calculating the plane-averaged differential charge density(Δ𝜌̄). Positive (negative) values in Δ𝜌̄ indicate charge accumulation (depletion). In (g–i), the Δ𝜌̄ (red line, multiplied by 100) zoomed at the interfaceshows that the electrons are lost on the graphene side while accumulating on the BMPI side. With BA molecular as the termination (g), a slight chargetransfer corresponds to moderate hole doping in graphene. Whereas in the case of the Pb-I section (h) or I ions (i) as termination, a drastic transferhappens on the interface and results in an order of magnitude higher doping in graphene. The doping level of graphene in each case is labeled. Theimage (right-hand side) shows the atomic structure of the interface for each case and the color-coded density contours of Δ𝜌 from the x-y plane, theyellow (cyan) regions correspond to Δ𝜌 > 0 (Δ𝜌 < 0).interface, we considered three structure models of the inter-face, with the following possible terminations of BMPI: BAmolecule (Figure 2d), Pb-I (Figure 2e), and iodine (Figure 2f).The charge densities in graphene are calculated using DFTand compared with the experiment. Because of the chargetransfer process, the charge density in the heterostructure(𝜌hs) is not equal to the charge densities for non-interactinggraphene(𝜌graphene) and BMPI(𝜌BMPI). To show the charge carri-ers distribution, a differential charge density Δ𝜌 is calculatedfrom Δ𝜌 = 𝜌hs − 𝜌graphene − 𝜌BMPI. We introduce the plane-averaged differential charge density Δ𝜌̄, defined as the stack-ing plane-average of Δ𝜌, to estimate the magnitude of chargetransfer,Δ𝜌̄ = 1Sg ∫ Δ𝜌 dxdz (3)The y coordinate is the stacking direction and x, z are the coordi-nates within the graphene plane. The integral runs over slices ofthe unit cell for a fixed y, and Sg is the graphene surface within theunit cell that is used for normalization. The plane-averaged inte-gral charge density of the graphene/BMPI heterostructure (𝜌̄hs)Adv. Electron. Mater. 2024, 10, 2400211 2400211 (4 of 9) © 2024 The Author(s). Advanced Electronic Materials published by Wiley-VCH GmbH 2199160x, 2024, 11, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/aelm.202400211 by National Institute For, Wiley Online Library on [08/07/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advelectronicmat.dewww.advancedsciencenews.com www.advelectronicmat.deis shown along the y-axis (blue line), which corresponds very wellto each crystal structure.The charge transfer primarily arises at the interface betweenBMPI and graphene, as illustrated in Figure 2g,h,i, where Δ𝜌 isconcentrated. Positive values of Δ𝜌̄ indicate electron accumula-tion, while the negative values represent electron depletion. Forall the simulated interfaces, electrons are transferred from thegraphene to BMPI, leading to hole-doped graphene. The ampli-tude of this doping strongly depends on the type of termination.The density contours on the right-hand side visually reflect thedifferential charge density distribution in the x-y plane zoomedon the interface.In Figure 2g, only a small value of Δ𝜌̄ can be seen in the chargetransfer from the BA molecular termination. This mild chargetransfer corresponds to a doping level of around 1.2 × 1012 cm−2in graphene, which is close to the average density in the low dop-ing region as estimated from magnetoresistance in Figure 2c.In contrast, with the Pb-I termination (Figure 2h), the dopinglevel increases by an order of magnitude, reaching up to 1.2 ×1013 cm−3 (see Section S3, Supporting Information for details).For this termination, the separation of charge accumulation anddepletion layers becomes visible from the density contours of Δ𝜌.Finally in the case of I− termination (Figure 2i), a considerableamount of charges accumulate around I−, and results in dopingof 3.9 × 1013 cm−2 in the graphene layer. We note that the den-sity observed from the Shubnikov-de Haas oscillations is betweenthese two high doping values. In the experiment, only a singleSdH oscillation period is visible, which suggests only one typeof high doping interface being realized in the experiment with alow enough disorder to exhibit quantum oscillations. From thedifferential charge density, we estimate that the charge transfercreates an electric field of more than 107 Vcm−1. This large elec-tric field can facilitate the separation of electrons and holes at thegraphene/BMPI interface or be used for avalanche-carrier multi-plication devices.2.4. Photoresistance Spectrum on SdH OscillationFor highly doped graphene in our sample, the mean spacing be-tween holes (around 2 nm) is comparable to the exciton Bohrradius which is estimated to be about 1 nm in 2D RPPs and4.2 nm in 3D perovskites.[42–44] This implies the possibility ofa strong interaction between carriers in graphene and excitonshosted by BMPI.[45,46] To study photo-physics directly at theBMPI-graphene interfaces, we performed photoresistance mea-surements using a home-built cryogenic probe in which the sam-ple was immersed in superfluid helium to ensure good thermal-ization under photo-excitation down to 1.6 K. A sketch of the ex-perimental setup is shown in Figure 3a. The sample was biasedwith both AC and DC currents, and two lock-in amplifiers wereused to measure sample resistance(R, from AC current and withfrequency fac), as well as the photoresistance at the chopper fre-quency (Rp, from DC current and with fp). Since the heterojunc-tions are highly doped, the photo response was always a smallchange in the total sample resistance.We started by illuminating the sample with a 532 nm laser. Thephotoresistance from B-Gra to B-Gra, Rpbb, and from T-Gra to B-Gra, Rptb, are shown in Figure 3b together with the correspondingFigure 3. a)Schematic of the setup for the photo-excitation transport mea-surement, in which the illumination is laser or a Xenon lamp followed bya monochromator. The sample is immersed into superfluid helium fourto accelerate thermal dissipation. The photoresistance is synchronized atchopper frequency (fp) and biased by DC current. b) Photoresistance athigh magnetic field in SdH region for the connection of B-Gra to B-Gra(Rpbb) and T-Gra to B-Gra (Rptb), compared to the corresponding amplitudeof SdH oscillation 𝛿Rbb and 𝛿Rtb. The 𝛿Rtb and Rptbare shifted for clarity.The excitation is from 532 nm laser with the power of 40 Wm−2. The Rptbshows more asymmetrical oscillations, while Rpbbwith weak phase shiftfrom 𝛿Rbb due to the combination of photo-gating and heating.sample resistance 𝛿Rbb and 𝛿Rtb, in which we see photoresistanceoscillations in the SdH region. The strongest photoresistance ap-peared at high magnetic field in the SdH region, which can beattributed to a change in the carrier density (photo-gating) andthe heating of graphene carriers.[47,48] The out-of-phase compo-nent of photoresistance (with respect to SdH) allows us to esti-mate the relative photo-induced change in the carrier density tobe Δn/n ≃ 2.5 × 10−5. The in-phase photoresistance gives a car-rier temperature increase of 0.3 K, which is consistent with theheating expected from our laser excitation intensity. A typical life-time 𝜏 for electrons transferred from BMPI to graphene is around400 ns. Details are given in Section S4 (Supporting Information).In contrast to the simply phase-shifted SdH signal in Rpbb, Rptboscillates very anharmonic with pronounced negative peaks andsome signatures of beating between two periods (Figure 3b).This difference can be related to the difference between pho-tocurrent (extraction of photo-excited electron-hole pairs fromthe BMPI) and photo-assisted transport (transfer of carri-ers between the two graphenes through excitation of BMPI)Adv. Electron. Mater. 2024, 10, 2400211 2400211 (5 of 9) © 2024 The Author(s). Advanced Electronic Materials published by Wiley-VCH GmbH 2199160x, 2024, 11, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/aelm.202400211 by National Institute For, Wiley Online Library on [08/07/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advelectronicmat.dewww.advancedsciencenews.com www.advelectronicmat.deFigure 4. a) The change in resistance under illumination (Rptb) from Rtb is plotted versus excitation wavelength on the vertical axis and magnetic field Bon the horizontal axis. The numbers 1,2,3 label magnetic fields of 9.47 T (B1), 9.41 T (B2), and 9.31 T (B3) respectively in one period. b) Photoresistancespectra show a shift of the absorption peak appearing from B1 to B2. The shift wavelength corresponds to an energy of 16 meV. c) Magnetic fielddependence of the Rptbshow an enhanced amplitude at the maximum of Rtb (the minimum of Rptb) compared to the amplitude expected from harmonicoscillations. d) A sketch of a qualitative model for photoresistance. For B1 the Fermi energy lies inside the LL for both top and bottom graphenes, thisgives maximal photoassisted transport. For B2 the Fermi energy enters the gap between LL in one of the graphene layers, photo-assisted transport nowrequires an extra LL spacing energy ℏ𝜔c to reach the first empty LL. This extra energy blue shifts the photoresistance spectrum at B2 compared to B1and the observed shift of 16 meV is indeed comparable to ℏ𝜔c ≃ 14 meV. Finally, for B3, the Fermi energy lies in the gap between LL for both graphenesleading to a suppressed photoresistance. Panels e) and f) show the comparison of photoresistance peaks under Vg = 0 V and f) Vg = 10 V. The spectralshift disappears with gate voltage. Since both BMPI and the top graphene are screened from Vg by the bottom graphene, the gate voltage only changesthe carrier density in the bottom graphene demonstrating that near alignment of the LL between top to bottom graphene is indeed required.processes, which are allowed in two graphene-contacts geom-etry, but are absent in the single bottom-graphene geometry.Our sample is symmetric between top and bottom grapheneand the applied DC voltages between top/bottom grapheneare small (1 mV), thus strong photocurrent is not expected,leaving photo-assisted transport as the most likely explanationfor the strongly anharmonic photoresistance. We note that incontrol experiments with a pristine graphene device, no mea-surable photoresistance spectrum is found under the sameconditions.To understand the mechanism of photo-assisted transport inthe heterostructure, we focused on Rptb for the photoresistancespectroscopy experiments, in which a monochromator-filteredXe-lamp is used as excitation light. As shown in Figure 4a,b,c, atB1 = 9.47 T, a photoresistance peak is observed around 497 nm,with a weak photoresistance tail at longer wavelengths. The sig-nal at 532 nm is no longer visible because of the much weakerexcitation intensity from the Xenon lamp after filtering of theexcitation wavelength through the monochromator. As the mag-netic field increases to B2 = 9.41 T, a red-shift of the main ab-sorption peak becomes visible at maxima of SdH for Rtb, dis-appearing rapidly away from the maximum. In Figure 4b weshow that this shift in photoresistance spectra appears at fieldB1 = 9.47 T, but disappears already for B2 = 9.41 T. The shiftin wavelength of the photoresistance spectrum corresponds toan energy of around ΔE = 16 meV, with the spacing betweenLL of around 14 meV, and a change of LL energy of aroundℏe(B1 − B2)∕m∗c = 0.09 meV from field B1 to B2. The spectralshift ΔE is thus much closer to the total LL spacing, suggest-ing that it does not come from a single graphene layer but in-stead from photo-induced transport between the top and bottomgraphenes.A sketch of our qualitative model for photoresistance is shownin Figure 4d. When no gate voltage is applied, the density ofthe top and bottom graphene are almost identical. Thus at SdHmaxima, direct photo-assisted transport between the two incom-pletely filled LL is allowed (process 1). The photon energy isthen absorbed within the BMPI layer enabling charge transferbetween the two graphenes. In this situation the magnetic fielddependence of the Rptb starts to show an enhanced amplitude atSdH maxima compared to harmonic SdH oscillations (see Rptb at497 nm in Figure 4c), leading to the more anharmonic magneticfield dependence that was also seen with 532 nm laser excitation.As the magnetic field is changed slightly the LL in one of the twographenes goes below the Fermi energy and an extra energy mustbe provided to transfer carriers to the first empty LL, requiring anincrease in photon energy by the LL spacing ℏ𝜔c (process 2). Fi-nally, when LL on both graphenes are full at SdH minima thephotoassisted transport is suppressed leading to weak photore-sistance (process 3).In this scenario, the LL alignment between the two graphenesis important. We compared the signal at Vg = 0 V (Figure 4e)Adv. Electron. Mater. 2024, 10, 2400211 2400211 (6 of 9) © 2024 The Author(s). Advanced Electronic Materials published by Wiley-VCH GmbH 2199160x, 2024, 11, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/aelm.202400211 by National Institute For, Wiley Online Library on [08/07/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advelectronicmat.dewww.advancedsciencenews.com www.advelectronicmat.deand Vg = 10V (Figure 4f), corresponding to a different positionof the Fermi energy concerning LL in graphenes. The gate volt-age mainly changes the density of the bottom graphene and isscreened in the rest of the device. with Vg = 10V, the shift of thespectrum with the magnetic field disappears completely, whichis in agreement with our model.The anharmonic photoresistance SdH oscillations and theenergy associated with the spectral shift close to ℏ𝜔c confirmour qualitative model for photo-assisted transport relying on thealignment of the LL between the two graphenes. This model im-plicitly assumes hot-carrier transport in BMPI, as the relative en-ergy of the LL in both graphenes would not matter if carriers haveto hop through many sites with random energies on the way. Thismay explain the blue-shifted onset for the main photoresistancespectrum starting at around 500 nm (≈2.48 eV) compared to theexpected position of the optical absorption spectrum for n = 4BMPI, which is reported with bandgap of 2.07 eV.[19] The extraenergy would then correspond to the excitation of higher-energyhot carriers in the BMPI layer.3. ConclusionThrough SdH oscillations in low-temperature magneto-transport, we reveal a strong charge transfer process at theBMPI/graphene interface, leading to a hole doping in graphene.We show that the charge transfer significantly depends on thetermination of the perovskite at its interface by DFT calculation,which is in agreement with magneto-resistance and micro-PLmicroscopy. The photoresistance at a high magnetic field in theregime of SdH oscillations is investigated, where the grapheneLL becomes quantized. A phase shift appears on the photore-sistance under laser excitation, as the combined effects of thephoto-gating effect and slight rise of carrier temperature. Fromthe spectroscopy, the onset of photoresistance shift by an energysimilar to the LL spacing in graphene, suggests photo-assistedtransport between the two graphene contacts through hotcarriers in BMPI.Our results show that perovskite/graphene heterostructure en-ables the exploration of new regimes in photo-assisted transport,and a possible access to new fundamental physics as the interfacehomogeneity improves in future devices. The strong built-in elec-tric field associated with the efficient charge transfer can facilitatethe separation of electrons and holes at the graphene/BMPI inter-face. Combined with the high hole mobility in graphene, this het-erostructure gives the hope of highly efficient optoelectronic de-vices.4. Experimental SectionSynthesis of BMPI Crystals: The synthesis of the BMPI single crystalswas adapted from ref. [18]. Generally, 154mg of PbO (0.69 M), 34mg of BAI(0.17 M), and 82 mg of MAI (0.52 M) precursors were mixed in a vial with0.884 ml HI and 0.116 ml H3PO2 solvent. The PbO can be substituted bythe same molar amount of PbI2. A clear yellow solution is obtained afterheating and stirring at 110 °C for one hour. The stock solution was slowlycooled to room temperature at a rate of 1 ◦Ch−1 in an oven. The precipi-tated black crystals were vacuum filtered and rinsed with toluene severaltimes, followed by drying in a vacuum overnight. The photoluminescencespectrum of the bulk crystal and monolayer BMPI shows a single narrowpeak at around 664 nm (Figure S1, Supporting Information).Fabrication of Graphene/BMPI/Graphene Device: Au(30 nm)/Ti(5 nm)electrodes were deposited on a thin layer of flat hexagonal boron nitride(bottom BN), which had been transferred on a doped silicon substratewith a 300 nm-thick oxide layer. Then a monolayer graphene flake (bottomgraphene) was transferred on top of electrodes and BN, and annealed un-der 200 ◦C at 1 × 10−5 mbar for 2 h. Polydimethylsiloxane (PDMS) is usedduring mechanical exfoliation of BMPI flake (Figure S1). A BMPI flake onthe PDMS surface was transferred to fully cover the bottom graphene. Dur-ing resist-free dry-transfer, 60 ◦C heating was used for a short time (around1 min) to help release the BMPI pieces. Afterward, two top-graphene flakeswere picked up at room temperature with a big top BN flake supported byPDMS. When stamping the top graphene/BN layer, we introduced a smalloverlap region between the top and the bottom graphene through BMPIlayer. The exfoliation and dry-transfer processes were implemented in theair. The stack is encapsulated between two BN layers (Top-BN and Bottom-BN). The electrodes conducting the top and bottom graphene were fab-ricated on top of the bottom-BN layer before transferring graphene andBMPI, to avoid heating of the BMPI and contamination of the graphenesurface during electrode fabrication. The bottom graphene electrodes arewider for better adhesion of the electrodes on the bottom BN layer and toensure continuity across the bottom BN step.The long aspect ratio of thebottom electrodes was chosen to have a well-defined geometry to measurebottom graphene conductivity with a large contact area between grapheneand electrodes. For top graphene contacts that lay flat on the silicon sur-face, thinner electrodes were used and the geometry was adapted to theshape of the top graphene flakes. The device is placed on a highly dopedsilicon wafer with 280 nm SiO2, which also act as a gate electrode.Transport Measurements: Transport measurements are performed us-ing SR830 lock-in amplifiers at an AC bias current of 100 nA, and a low-noise amplifier (LI-75A) with 100x Gain. The frequency for magnetoresis-tance is 17 Hz (fac in Figure 3a), and for photoresistance is 39 Hz (fp) syn-chronized with the chopper frequency. Low-pass 𝜋 filters were added toeach measuring line to protect the sample from noise and abrupt voltagedischarges during connection switching. photoresistance measurementsare performed in a pumped superfluid He4 chamber (temperature around1.6 K). Helium flux into the chamber is fixed by an impedance with a room-temperature flow rate of around 3.5 × 10−2 mbar L s−1.First-Principles Computational Methods: The charge density calcula-tions in this work are based on density functional theory (DFT) con-ducted with plane-wave basis set and projector augmented wave (PAW)pseudopotentials implemented in the Quantum Espresso (QE).[49,50] Theexchange-correlation function is taken as the Perdew–Burke–Ernzerhof(PBE) type of the generalized gradient approximation(GGA).[51] DFT-dcorrection is used for all calculations to describe the van der Waals forcebetween BMPI and graphene.[52] To simulate the 2D system and elimi-nate the interaction effects between the adjacent layers, the calculationswere implemented with a vacuum thickness of 25 Å. The cell parametersand atomic positions are fully relaxed with the k-point mesh of 3 × 1 ×6, generated by using the Monk-horst–Pack scheme. A kinetic energy cut-off of 550 eV is adopted for plane-wave expansion, and the convergencetolerances for the energy and force are set at 10−8 eV. We used a Gaus-sian smearing with a deviation of 0.01 Ha. All the parameters were testedfor convergence.Supporting InformationSupporting Information is available from the Wiley Online Library or fromthe author.AcknowledgementsThe work was financially supported by funding from ANR-20-CE92-0041(MARS), IDF- DIM SIRTEQ, and the European Research Council (ERC)under the European Union’s Horizon 2020 research and innovation pro-gramme (grant Ballistop agreement no. 833350). The authors thank S.Adv. Electron. Mater. 2024, 10, 2400211 2400211 (7 of 9) © 2024 The Author(s). Advanced Electronic Materials published by Wiley-VCH GmbH 2199160x, 2024, 11, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/aelm.202400211 by National Institute For, Wiley Online Library on [08/07/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advelectronicmat.dewww.advancedsciencenews.com www.advelectronicmat.deGuéron, Z.Y.Chen, and E. Delporte for the discussions on the physical pro-cess. The authors also thank M. Entin for the help on modeling.Conflict of InterestThe authors declare no conflict of interest.Author ContributionsY.S., M.M., and A.C. designed the experiments and implemented themagneto-transport measurements. Y.S. fabricated the devices used forthe study and performed calculations of electron charge density underthe guidance of C.M. D.G. carried out micro-PL measurements. R.W con-tributes to the technical assistance. K.W. and T.T. provide boron nitridecrystals used in the experiment. A.C. and Y.S. implemented the Finite el-ement method. 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Comput. Chem. 2009, 30, 934.Adv. Electron. Mater. 2024, 10, 2400211 2400211 (9 of 9) © 2024 The Author(s). Advanced Electronic Materials published by Wiley-VCH GmbH 2199160x, 2024, 11, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/aelm.202400211 by National Institute For, Wiley Online Library on [08/07/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advelectronicmat.de Quantum Transport and Spectroscopy of 2D Perovskite/Graphene Heterostructures 1. Introduction 2. Results and Discussion 2.1. Transport Devices of 2D Perovskite/Graphene 2.2. Magneto-Transport at the Graphene-Perovskite Interface 2.3. Interfacial Terminations Affect the Charge Transfer Process 2.4. Photoresistance Spectrum on SdH Oscillation 3. Conclusion 4. Experimental Section Supporting Information Acknowledgements Conflict of Interest Author Contributions Data Availability Statement Keywords