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Di Huang, Kevin Sampson, Yue Ni, Zhida Liu, Danfu Liang, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Hebin Li, Eric Martin, Jesper Levinsen, Meera M. Parish, Emanuel Tutuc, Dmitry K. Efimkin, Xiaoqin Li

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[Quantum Dynamics of Attractive and Repulsive Polarons in a Doped <math display="inline">  <mrow>    <msub>      <mrow>        <mi>MoSe</mi>      </mrow>      <mrow>        <mn>2</mn>      </mrow>    </msub>  </mrow></math> Monolayer](https://mdr.nims.go.jp/datasets/e7b27749-5f5d-46d4-a150-8cb5e9fcb8cb)

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Quantum Dynamics of Attractive and Repulsive Polarons in a Doped MoSe2 MonolayerQuantum Dynamics of Attractive and Repulsive Polarons in a Doped MoSe2 MonolayerDi Huang ,1 Kevin Sampson,1 Yue Ni,1 Zhida Liu,1 Danfu Liang,3 Kenji Watanabe ,6 Takashi Taniguchi,7 Hebin Li ,3Eric Martin,5 Jesper Levinsen ,2 Meera M. Parish ,2 Emanuel Tutuc,4 Dmitry K. Efimkin ,2 and Xiaoqin Li 1,*1Department of Physics and Center for Complex Quantum Systems,The University of Texas at Austin, Austin, Texas 78712, USA2School of Physics and Astronomy and ARC Centre of Excellence in Future Low-Energy ElectronicsTechnologies, Monash University, Victoria 3800, Australia3Department of Physics, Florida International University, Miami, Florida 33199, USA4Microelectronics Research Center, Department of Electrical and Computer Engineering,The University of Texas at Austin, Austin, Texas 78712, USA5MONSTR Sense Technologies, LLC, Ann Arbor, Michigan, 48104, USA6Research Center for Functional Materials, National Institute for Materials Science,1-1 Namiki, Tsukuba 305-0044, Japan7International Center for Materials Nanoarchitectonics, National Institute for Materials Science,1-1 Namiki, Tsukuba 305-0044, Japan(Received 17 July 2022; revised 12 November 2022; accepted 23 January 2023; published 2 March 2023)When mobile impurities are introduced and coupled to a Fermi sea, new quasiparticles known as Fermipolarons are formed. There are two interesting, yet drastically different regimes of the Fermi polaronproblem: (i) the attractive polaron (AP) branch connected to pairing phenomena spanning the crossoverfrom BCS superfluidity to the Bose-Einstein condensation of molecules and (ii) the repulsive branch (RP),which underlies the physics responsible for Stoner’s itinerant ferromagnetism. Here, we study Fermipolarons in two-dimensional systems, where many questions and debates regarding their nature persist. Themodel system we investigate is a doped MoSe2 monolayer. We find the observed AP-RP energy splittingand the quantum dynamics of attractive polarons agree with the predictions of polaron theory. As thedoping density increases, the quantum dephasing of the attractive polarons remains constant, indicativeof stable quasiparticles, while the repulsive polaron dephasing rate increases nearly quadratically. Thedynamics of Fermi polarons are of critical importance for understanding the pairing and magneticinstabilities that lead to the formation of rich quantum phases found in a wide range of physical systemsincluding nuclei, cold atomic gases, and solids.DOI: 10.1103/PhysRevX.13.011029 Subject Areas: Condensed Matter Physics, Optics,Semiconductor PhysicsI. INTRODUCTIONFermi-polaron quasiparticles are mobile impurities(e.g., excitons) that are coherently dressed by density fluc-tuations (particle-hole excitations) of a surrounding Fermisea [1,2]. As illustrated in Fig. 1(a), the attractive interactionbetween the exciton and Fermi sea leads to an energeticallyfavorable state—the attractive polaron—as well as a higher-energy repulsive polaron, a metastable state that eventuallydecays into attractive polarons. The behavior of Fermipolarons has been extensively studied in the context ofultracold atomic gases, where experiments have probed theformation of polarons [3] as well as their quasiparticleproperties, such as the polaron energy [4], lifetime [5], andthe effective mass [6]. However, cold-atom experiments havefocused on three-dimensional systems. Intriguing and openquestions remain, e.g., how the Fermi polarons evolve as thedimensionality is lowered and low-energy density fluctua-tions of the Fermi sea are enhanced. In one-dimensionalsystems, the impurity problem becomes exactly solvable [7],and polaronic quasiparticles are destroyed by quantumfluctuations. Thus, the intermediate case of two-dimensional(2D) systems represents a particularly interesting yet unre-solved case, where quantum fluctuations are enhanced butquasiparticles can still exist.Atomically thin transition-metal dichalcogenides(TMDCs) represent exemplary 2D systems to study therich properties of Fermi polarons, where an exciton isdressed by Fermi seas with a unique valley degree of*elaineli@physics.utexas.eduPublished 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 13, 011029 (2023)2160-3308=23=13(1)=011029(8) 011029-1 Published by the American Physical Societyhttps://orcid.org/0000-0003-3698-5158https://orcid.org/0000-0003-3701-8119https://orcid.org/0000-0002-2126-4086https://orcid.org/0000-0002-2010-3512https://orcid.org/0000-0001-8705-0171https://orcid.org/0000-0002-3929-5753https://orcid.org/0000-0002-2279-3078https://crossmark.crossref.org/dialog/?doi=10.1103/PhysRevX.13.011029&domain=pdf&date_stamp=2023-03-02https://doi.org/10.1103/PhysRevX.13.011029https://doi.org/10.1103/PhysRevX.13.011029https://doi.org/10.1103/PhysRevX.13.011029https://doi.org/10.1103/PhysRevX.13.011029https://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/freedom [8,9]. A variety of exciton resonances (neutral orcharged states, biexcitons, spatial and momentum-spaceindirect excitons) have been identified and investigated inTMDC monolayers [10,11]. The trion, a three-body boundstate consisting of an exciton bound to an extra electron orhole, has been used widely in the literature to describe anoptical resonance appearing at an energy of approximately20–30 meV below the neutral excitons [12]. The trionpicture is difficult to distinguish from the polaron picture atlow doping densities, where the Fermi energy is smallerthan the intrinsic exciton linewidth [13–16]. However, asdoping increases, a continuous energy shift suggests thatthe three-body bound-state picture is insufficient [17–19].Attractive and repulsive polarons (APs and RPs), asillustrated in Fig. 1(b), have been proposed to explainthe evolution of reflectivity spectra of doped TMDCmonolayers and bilayers with doping [8,20]. This polaronpicture is anticipated to be relevant up to moderate doping,where the interelectron distance is sufficiently large com-pared to the radii of photoexcited excitons such that theirformation is not disturbed. A critical question remains:Does polaron theory predict different properties of APs andRPs? Quantum decoherence associated with APs and RPs,for example, has never been investigated experimentally,and a comparison between experiments and theory has notbeen possible so far.Here, we study the emergence and evolution of APs andRPs in a MoSe2 monolayer as the electron doping densityincreases. Using two-dimensional coherent electronic spec-troscopy (2DCES), we follow the changes in resonantenergy, oscillator strength, and quantum decoherence ofthe AP and RP branches. The observed redshift of the APresonance suggest that these new quasiparticles are ener-getically stable. The redshift increases until a criticaldoping density is reached, and a more pronounced blueshiftoccurs. Intriguingly, the quantum decoherence rate of APs(measured via the homogeneous linewidth) remains nearlyconstant up to a critical density, which suggests thatthe excitons are coherently dressed by the Fermi sea.The quantum decoherence rate of RPs, however, increasesmonotonically and rapidly with doping density. Our studyhighlights that optically excited TMDCs represent a novelFIG. 1. Illustration of the MoSe2 device and physical concept. (a) Schematic of Fermi polarons. When excitons are attractivelycoupled to a Fermi sea of electrons, the spectrum of the whole system splits into two branches: APs and RPs. In the limit of vanishingFermi energy εF, the APs and RPs recover the energies of trions (ET) and excitons (EX), respectively. (b) Evolution from an exciton-trionpicture to a Fermi-polaron picture as the doping density increases in a monolayer. Spheres in red refer to electrons (−) and holes (þ) inone valley, while spheres in green color indicate the opposite valley. The displacement of electrons around the exciton in the moderate-doping regime represents the polaronic cloud of density fluctuations (particle-hole excitations). (c) Reflectance spectra from a dopedMoSe2 monolayer at different top-gate voltages (VTG). The dashed lines are guidelines for the evolution of APs (bright) and RPs (dark).(d) Schematics of a collinear 2DCES experiment performed on a monolayer MoSe2 device. A train of three pulses (A, B, C) is focusedonto the monolayer MoSe2, and the photon-echo (PE) signal is collected via the same microscope objective. The pulses are incidentperpendicular to the sample but are illustrated here at an angle for clarity.DI HUANG et al. PHYS. REV. X 13, 011029 (2023)011029-2playground to study the rich phenomenology of stronglyimbalanced quantum mixtures.II. RESULTSWe control the doping density in a MoSe2 monolayerencapsulated between hexagonal boron nitride (h-BN) layersusing a device with a few-layer graphite top gate (TG) and asilicon back gate (BG) (details in Supplemental Material[21]). All optical measurements are taken at 16 K unlessstated otherwise. We first measure reflectance spectra atdifferent doping levels, as shown in Fig. 1(c). When theMoSe2 monolayer is charge neutral or in the regime of dilutedoping density (between the two orange dashed lines), tworesonances at 1635 and 1605 meV are attributed to excitonsand trions, respectively. We focus on the electron dopingregimes with positive TG voltages. The exciton resonanceevolves into the RP branch, which exhibits a blueshift atVTG > 0.5 V. The lower-energy resonance exhibits a smallredshift for VTG ¼ 0.5–1.5 V before a pronounced blueshiftstarts to occur at VTG > 1.5 V.In the following, we analyze the spectral shift, oscillatorstrength changes, and quantum dephasing of these reso-nances using 2DCES. As illustrated in Fig. 1(d), threecollinearly polarized ultrafast pulses derived from the samelaser are focused onto the sample by a microscopeobjective. The third-order optical nonlinear response leadsto a coherent photon-echo signal, which is collected by theFIG. 2. One-quantum rephasing amplitude spectra of the MoSe2 monolayer at different gate voltages. (a) Schematic of the one-quantum rephasing pulse sequence. Details are further discussed in the Supplemental Material [21]. (b)–(e) 2D spectra taken at differenttop-gate voltages at 0, 0.7, 1.3, and 2.5 V, respectively. These gate voltages correspond to estimated electron doping densities ofne− ¼ 0; 6.6 × 1011; 2.6 × 1012, and 6.6 × 1012 e−=cm2. IB, inhomogeneous broadening; HCP and LCP, higher and lower off-diagonalcross peak. Homogeneous (inhomogeneous) linewidth of exciton, AP, and RP could be extracted by fitting the cross-diagonal (diagonal)slices of the spectra, as illustrated by the arrows in blue (exciton and RP) and red (AP) color.QUANTUM DYNAMICS OF ATTRACTIVE AND REPULSIVE … PHYS. REV. X 13, 011029 (2023)011029-3same objective, isolated, and detected using a frequency-modulation scheme after the heterodyne detection with areference pulse (details in Supplemental Material [21]).The laser spectrum covers both the AP and RP resonancesidentified in the reflectance spectrum, and resonantlyexcites them.We perform one-quantum rephasing measurements inwhich the time delays between the first two excitationpulses (τ) and that between the third pulse and a referencepulse (t) are scanned, as illustrated in Fig. 2(a). These twotime delays (τ and t) are then Fourier transformed to yieldthe absorption energy (ℏωτ) and emission energy (ℏωt),respectively. The waiting time T between the second andthird pulses is kept at 100 fs to avoid artifacts that occurduring the temporal overlap between the excitation pulses.The amplitude of the photon-echo signal as a correlationbetween absorption and emission frequencies is shown inFigs. 2(b)–2(e). The elongation along the diagonal direc-tion indicated by the dashed line is determined by theinhomogeneous linewidth, while the full width at halfmaximum along the cross diagonal direction indicated bytwo arrows reveals the homogeneous linewidth 2γ [22],where γ is the decoherence rate and inversely proportionalto the quantum dephasing time 1=T2 ¼ γ=ℏ.We further investigate the one-quantum spectra of mono-layer MoSe2 at several doping levels in Figs. 2(b)–2(e). Inthe charge-neutral regime up to VTG ¼ 0.5 V, the spectrumis dominated by the exciton resonance at approximately1633 meV [23,24]. At the carrier density of n ¼ 6.6 ×1011 e−=cm2 (or VTG ¼ 0.7 V), both AP and RP areobserved as two diagonal peaks appearing at approximately1605 and 1637 meV, respectively. Moreover, two off-diagonal cross peaks emerge, which are labeled as the lowerand higher cross peak (i.e., LCP and HCP). These crosspeaks result from electronic coupling between the APs andRPs as previously studied in the nominally doped MoSe2monolayers [25]. The unbalanced LCP and HCP intensitiesoriginate from both coherent quantum beats and decays fromRP to AP. Upon further increasing the doping density ton ¼ 2.6 × 1012 e−=cm2 (VTG ¼ 1.3 V), the spectral weighthas nearly completely shifted to APs. A weak LCP peakremains in the spectrum, suggesting that the metastable RPsstill absorb light but quickly decay to APs. At the highestdoping density n ¼ 6.6 × 1012 e−=cm2 (VTG ¼ 2.5 V)where a nonlinear signal is still detectable, the AP resonancebecomes much broader and shifts to higher energy.We carefully analyze the energy shifts and quantumdecoherence rates of APs and RPs extracted from 2Dspectra as shown in Fig. 3. The slices along the cross-diagonal direction for the RPs and APs peak at a fewselected TG voltages are displayed in Figs. 3(a) and 3(b),respectively. The homogeneous linewidth of the RP rapidlyincreases with electron doping density (γ ¼ 1.03� 0.09and 2.50� 0.30 meV with VTG ¼ 0 and 0.7 V, respec-tively) corresponding to a higher decoherence rate assummarized in Fig. 3(c) (blue curve). By contrast, theFIG. 3. Homogeneous linewidths and resonant energies of APs and RPs extracted from 2D spectra. Cross-diagonal line cuts of 2Dspectra used to extract homogeneous linewidths for (a) RPs and (b) APs at a few selected top-gate voltages. The data points are fittedby a modified Voigt function as discussed in the Supplemental Material [21]. (c) Homogeneous linewidths and (d) resonant energy ofRPs (blue) and APs (red) as a function of the top-gate voltage (bottom x axis) and corresponding Fermi levels (top x axis). The shadedgray area indicates the doping density range over which the polaron theory applies.DI HUANG et al. PHYS. REV. X 13, 011029 (2023)011029-4decoherence rate of APs remains largely constant until thedoping density exceeds a critical density at VTG ¼ 1.5 Vas shown in Fig. 3(c) (red curve) (γ ¼ 1.87� 1.06,2.08� 0.41, and 5.77� 1.14 meV with VTG ¼ 0.7, 1.3and 2.5 V, respectively). Figure 3(d) displays the centralenergies of the APs (red points) and RPs (blue points) whichare extracted from fitting to the inhomogeneous slicesalong the diagonal direction of the 2D spectra (details inSupplemental Material Figs. S5 and S6 [21]). In the range ofgate voltages that correspond to a modest doping density,a continuous redshift of the AP resonance is observed,suggesting the coherent dressing of the quasiparticle canlower its energy. The redshift of the APs against the dopinglevel is often overlooked or left unexplained in previousstudies [26]. By contrast, the energy of the RP exhibits ablueshift over the whole doping range in which thisresonance is observable in the 2DCES spectra.Interestingly, the energy of the APs begins to blueshift ata critical density that approximately coincides with wherethe quantum dephasing rate starts to increase.III. DISCUSSION AND CONCLUSIONRemarkably, most of the key experimental observations(doping-dependent energy, oscillator strength, and quantumdecoherence rate) can be well captured by a microscopictheory based on the simple Chevy ansatz [27] of Fermipolarons. The excess electrons have two main effects:exciton renormalization and polaronic dressing [8]. Theformer modifies the resonance frequency and oscillatorstrength of excitons, but it does not lead to polaron formationor two separate branches. These excitons interact with excesselectrons, and the polaronic dressing splits them into AP andRP branches. The polaronic physics is solely responsible forthe relative behavior of the two branches (i.e., the relativefrequency, broadening, and the oscillator strength), which isthe focus of the present paper. As illustrated in Fig. 4(a), anexciton polaron (P†q) represents the coherent superposition ofthe undressed exciton (X†q with weight ϕq) and the polaroncloud, which is approximated as a single-electron-holeexcitation of the opposite valley to that in which the excitonresides (f†kfk0 in the Fermi sea with weight χqkk0 andmomenta k > kF and k0 < kF):P†q ¼ ϕqX†q þXkk0χqkk0X†qþk0−kf†kfk0 : ð1ÞAs sketched in Figs. 1(b) and 4(b), the exciton andthe unbound electron-hole excitation responsible for thepolaronic dressing reside in different valleys in ourmicroscopic theory, since same-valley correlations are sup-pressed by exchange effects due to the indistinguishabilityFIG. 4. Polaron theory and comparison with experiments. (a) The exciton polaron is the coherent superposition of a bare exciton andan exciton dressed by a polaron cloud approximated by a single Fermi sea (FS) unbound electron-hole pair in momentum space.(b) Exciton and the FS pair are assumed to reside in different valleys. In panels (a) and (b), red spheres refer to electrons (−) and holes(þ) in one valley, while green spheres indicate those in the opposite valley. Comparisons between measurements and calculations for(c) energy splitting between APs and RPs, (d) relative oscillator strengths, and (e) homogeneous linewidths of APs and RPs as a functionof the Fermi level. In panels (c)–(e), the dashed lines indicate calculations, while solid points are extracted from 2D spectra.QUANTUM DYNAMICS OF ATTRACTIVE AND REPULSIVE … PHYS. REV. X 13, 011029 (2023)011029-5between the electron bound in the exciton and those in theFermi sea [28].The comparisons between experimental observationsand predictions from the Fermi-polaron theory are sum-marized in Figs. 4(c)–4(e). A hallmark of the Fermi-polaron theory in 2D is a linear increase of the energysplitting between APs and RPs (ΔERP−AP) as a function ofthe Fermi energy as ΔERP−AP ¼ εT þ 3εF=2 where εT isthe binding energy of the exciton-electron bound state(i.e., the trion) and is treated as a fitting parameter.The prefactor 3=2 originates from the inverse reducedexciton-electron mass 2me=3 in TMDCs [29], and is asignature of a mobile impurity. The experimentallyextracted energy splitting matches the prediction remark-ably well [Fig. 4(d)] including the slope of the lineardependence [30]. The parameters used in the analysis ofexperimental data are discussed in detail in SupplementalMaterial [21], in particular, εT is estimated to be approx-imately 26.9 meV in our fitting. We further analyze therelative oscillator strength transfer between the APs (fAP)and RPs (fRP) as a function of the Fermi level. Theoscillator strength of both APs and RPs is evaluated byintegrating the amplitude over the area (labeled as SAP andSRP) around the resonances in the 2DCES spectra (details inSupplemental Material [21]). An excellent agreement isfound between our measurements and the prediction of thepolaron theory in Fig. 4(e). Note that the oscillator strengthof the AP peak vanishes as the Fermi energy goes to zero,while the energy splitting between branches remains finiteand reduces to the trion binding energy. Moreover, for lowdoping εF ≲ 2 meV, the trion and polaron pictures giveequivalent results for the oscillator strength [13].Another key prediction of the Fermi-polaron theoryis that the AP linewidth is almost doping independent,which agrees well with the experimental observation up toεF ∼ 15 meV [Fig. 4(d)]. This behavior cannot be cap-tured within the trion picture, which instead predicts thatthe AP linewidth increases approximately linearly with εF[13,31]. However, the polaron theory substantially under-estimates the observed RP broadening as doping densityincreases. This observation is in sharp contrast to thesituation in ultracold atomic gases, where the Chevyansatz accurately describes the RP linewidth [32]. Theobserved RP linewidth is very well fitted by adding anextra quadratic term to the linear dependence on εFpredicted by the polaron theory [blue solid line inFig. 4(e)]. This discrepancy suggests the existence of aqualitatively new contribution to RP decay. The quadraticdependence of the additional broadening hints at theinvolvement of electron-electron interactions. In particu-lar, the additional RP decay can originate from non-radiative transitions from the RP to the AP. Althoughwe cannot rule out phonons and charge fluctuations aspossible contributing factors to dephasing, they areanticipated to affect both polaronic branches in similarways, making them unlikely reasons for different doping-dependent dephasing. The decay due to electron-electroninteractions involves an extra particle-hole pair that carriesaway the energy difference between the branches, leadingto a six-particle final state that is not included in the Chevyansatz. This decay process is enhanced when the Fermi-sea pair is in the same valley as the exciton since thisavoids Pauli blocking effects with the dressing cloud.We estimate the nonradiative decay from RPs to APsusing Fermi’s golden rule:γee ¼ πXqk0jhfjĤe−ejiij2× δðΔERP−AP − ϵXq − ϵek0−q þ ϵek0 Þ: ð2ÞHere, jii ¼ P†0;Rjgi is the initial RP state, while the finalstate jfi ¼ P†q;Af̃†k0−qf̃k0 jgi includes an electron-hole exci-tation (jk0 − qj > kF and jk0j < kF) that is distinguishablefrom that participating in the polaron state described byEq. (1). We neglect short-range exciton-exciton and exci-ton-electron interactions and keep only the dominant long-range electron-electron Coulomb interactions in Ĥe−e. Theenergy conservation is determined by the energy differenceΔERP−AP between the zero-momentum RP and AP states,the dispersion of the AP in the final state which can beapproximated by the bare exciton dispersion ϵXk , andthe energy associated with an electron-hole excitation interms of the electron dispersion ϵek. As presented in theSupplemental Material [21], the additional broadening canbe written asγee ≈3πM24ε2FεXε2T: ð3ÞHere, εX is the binding energy for excitons. The dimension-less constant M describes the overlap between polaronicclouds in the initial and final states (details in SupplementalMaterial [21]). M is largely independent of doping densityand is used as a fitting parameter. Most importantly, thisextra contribution is proportional to ε2F. When it is combinedwith the linear doping dependence from the Chevy ansatz,the experimental data can be fitted well.Examples of accurate theory for strongly interactingmany-body systems are rare. In this work, we demonstratehow the Fermi-polaron theory can be used to describe thequantum dynamics of an imbalanced quantum mixtureof excitons and an electron gas in a MoSe2 monolayer.While Fermi polarons in the cold-atom systems and 2Dsemiconductors share similar properties, e.g., the linearRP-AP energy splitting and stable quantum dynamics ofAPs as a function of the Fermi level [2], there are alsoimportant differences. The quantum dephasing rate of RPsincreases quadratically with the doping density in TMDCmonolayers in contrast to the linear dependence found inDI HUANG et al. PHYS. REV. X 13, 011029 (2023)011029-6cold-atom systems [33]. The additional broadening isintricately connected with the rich and complicated inter-play of two valleys that is present not only in MoSe2,but in all TMDC monolayer semiconductors. Our studydemonstrates another fruitful playground to study theFermi-polaron problem complementary to cold atomswhere this problem has been investigated intensely inrecent years [5,33–35]. The understanding of Fermipolarons in monolayers also provides a foundation forexploring the coupling between excitons and other corre-lated electronic ground states such as Wigner crystals,Mott insulating states, and superconductivitylike states indoped TMDC twisted bilayers [36].ACKNOWLEDGMENTSThe spectroscopic experiments performed by D. H.and K. S. at UT Austin were primarily supported by theDepartment of Energy, Basic Energy Science program viaGrant No. DE-SC0019398, and N. Y. is partially supportedby NSF Grant No. DMR-1808042. The work was partlydone at the Texas Nanofabrication Facility supported byNSF Grant No. NNCI-2025227. K. S. acknowledges afellowship via NSF Grant No. DMR-1747426 and partialsupport from the NSF MRSEC Program No. DMR-1720595, which also supports the facility for preparingthe sample. X. L. gratefully acknowledges sample prepa-ration support by the Welch Foundation via Grant No.F-1662. H. L. acknowledges support by NSF via GrantNo. DMR-2122078. J. L., D. K. E., and M.M. P. acknowl-edge support from the Australian Research CouncilCentre of Excellence in Future Low-Energy ElectronicsTechnologies (Grant No. CE170100039). J. L. andM.M. P.are also supported through the ARC Future FellowshipGrants No. FT160100244 and No. FT200100619, respec-tively, and J. L. furthermore acknowledges support fromthe ARC Discovery Project No. DP210101652. E. T.acknowledges support from the Army Research OfficeGrant No. W911NF-17-1-0312, and the NSF MRSECProgram No. DMR-1720595. K.W. and T. T. acknowledgesupport from JSPS KAKENHI (Grants No. 19H05790,No. 20H00354, and No. 21H05233).D. H., K. S., and Y. 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