Bulletin of the American Physical Society
APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022; Chicago
Session N56: Twisted Bilayer Graphene: Theory, Transport, Thermodynamics, and OpticsRecordings Available

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Sponsoring Units: DCMP Chair: Xiaomeng Liu, Princeton University Room: Hyatt Regency Hotel Burnham 
Wednesday, March 16, 2022 11:30AM  11:42AM 
N56.00001: Probing strong correlation and discriminating insulating phases in twisted bilayer graphene through scanning tunneling microscopy Dumitru Calugaru, Myungchul Oh, Kevin P Nuckolls, Dillon Wong, Ryan Lee, Kenji Watanabe, Takashi Taniguchi, Ali Yazdani, Oskar Vafek, Nicolas Regnault, Andrei B Bernevig At integer fillings, the quenched kinetic energy in twisted bilayer graphene (TBG) at the magic angle induces a wealth of correlated insulators. For a large manifold of insulating ground states, the exact manybody chargeone excitations can be computed analytically. This gives direct access to the corresponding spectral function (SF)  the key quantity measured in scanning tunneling microscopy. We derive the fullyinteracting TBG SF at ±4 electrons/moiré unit cell (where the nature of the ground state is unambiguous) and experimentally validate our approach, finding evidence of strong correlations. For all other integer fillings, we consider the spatial features of the corresponding SFs and assess the possibility of Kekulé distortion (KD) emerging at the graphene lattice scale. Remarkably, we find that coupling the two graphene valleys in the intervalleycoherent TBG insulators does not always result in KD. For instance, we show that the KIVC state and its nonchiral U(4) rotations do not exhibit any KD. Consequently, we argue that the presence or absence of KD can be used to discriminate the various TBG insulators. 
Wednesday, March 16, 2022 11:42AM  11:54AM 
N56.00002: Detecting symmetry breaking in magic angle graphene using scanning tunneling microscopy Jung Pyo Hong, Tomohiro Soejima, Michael P Zaletel A growing body of experimental work suggests that magic angle twisted bilayer graphene exhibits a "cascade'' of spontaneous symmetry breaking transitions, sparking interest in the potential relationship between symmetrybreaking and superconductivity. However, it has proven difficult to find experimental probes which can unambiguously identify the nature of the symmetry breaking. Here we show how atomicallyresolved scanning tunneling microscopy can be used as a fingerprint of symmetry breaking order. By analyzing the pattern of sublattice polarization and "Kekulé'' distortions in small magnetic fields, order parameters for each of the most competitive symmetrybreaking states can be identified. In particular, we show that the "Kramers intervalley coherent state'', which theoretical work predicts to be the ground state at even integer fillings, shows a Kekulé distortion which emerges only in a magnetic field. 
Wednesday, March 16, 2022 11:54AM  12:06PM 
N56.00003: Probing entropy and magnetization in graphene heterostructures Fangyuan Yang, Yu Saito, Jingyuan Ge, Xiaoxue Liu, Takashi Taniguchi, Kenji Watanabe, Jia Li, Erez Berg, Andrea Young We developed a technique to determine entropy and magnetization by measuring chemical potential in van der Waals heterostructures. In twisted bilayer graphene with near 1.1 degree rotate angle, large entropy – on the order of unity per unit cell in unit of Boltzmann constant – is discovered around filling factor +1. The entropy is suppressed by inplane magnetic field, suggesting a weakly coupled isospinordered phase with strong fluctuations at higher temperatures, while the corresponding low temperature ground state is isospin unpolarized. This is in contrast with the typical scenario that ordered phase are favored at lower temperature, and is an analogue to the Pomerachuk effect discovered in 3He. We also applied this technique to nonMoiré type graphene systems, such as Bernal stack bilayer graphene. 
Wednesday, March 16, 2022 12:06PM  12:18PM 
N56.00004: Correlated Hofstadter Spectrum and Flavor Phase Diagram in Magic Angle Graphene Jiachen Yu, Ben A Foutty, Zhaoyu Han, Mark E Barber, Yoni Schattner, Kenji Watanabe, Takashi Taniguchi, Philip W Phillips, ZhiXun Shen, Steven A Kivelson, Benjamin E Feldman In magic angle twisted bilayer graphene (MATBG), the moiré superlattice potential gives rise to narrow electronic bands which support a multitude of manybody quantum phases. Further richness arises in the presence of a perpendicular magnetic field, where the interplay between moiré and magnetic length scales leads to fractal Hofstadter subbands. In this talk, I will describe local electronic compressibility measurements of this strongly correlated Hofstadter platform conducted with a scanning singleelectron transistor. By probing both gapped phases and the intervening compressible regimes, we simultaneously unveil novel sequences of brokensymmetry Chern insulators and resolve sharp phase transitions between competing states with different topological quantum numbers and spin/valley flavor occupations. Our measurements provide a complete experimental mapping of the energy spectrum and thermodynamic phase diagram of interacting Hofstadter subbands in MATBG. In addition, we observe full lifting of the degeneracy of the zeroth Landau levels together with level crossings, suggesting moiré valley splitting driven by mirror symmetry breaking. I will present a unified flavor polarization mechanism that accounts for the intricate interplay of topology, interactions, and symmetry breaking as a function of density and applied magnetic field in this system. 
Wednesday, March 16, 2022 12:18PM  12:30PM 
N56.00005: Thermodynamic measurements of magic graphene systems using SET Uri Zondiner, Asaf Rozen, Dahlia R Klein, Jeong Min Park, Daniel RodanLegrain, Takashi Taniguchi, Kenji Watanabe, Erez Berg, Yuval Oreg, Ady Stern, Pablo JarilloHerrero, Shahal Ilani In recent years different flatband graphene systems were shown to undergo thermodynamic phase transitions upon electrical charging. In Magic moire systems, such as magic angle bilayer graphene, these phase transitions happen at the vicinity of integer moire filling. However, these transitions are not bound strictly to integer fillings and can follow Clausius–Clapeyron relations. In some cases, The CC relation manifests as an exotic Pomeranchuk like effect where the less compressible phase is more entropic. This lecture will present our latest thermodynamic measurements of these transitions as probed by our scanning singleelectron transistor. 
Wednesday, March 16, 2022 12:30PM  12:42PM 
N56.00006: Efficient simulation of moire materials using the density matrix renormalization group Tomohiro Soejima, Nick Bultinck, Michael P Zaletel, Johannes Hauschild, Daniel E Parker We present an infinite densitymatrix renormalization group (DMRG) study of a model of twisted bilayer graphene (tBLG) near the magic angle. Because of the longrange Coulomb interaction, tBLG is difficult to study with standard DMRG techniques—even constructing and storing the Hamiltonian already poses a major challenge. To overcome these difficulties, we use a recently developed compression procedure to obtain a matrix product operator representation of the interacting tBLG Hamiltonian. We focus mainly on the spinless, singlevalley version of the problem where, at half filling, we find that the ground state is a nematic semimetal. Remarkably, we find that the ground state is essentially a kspace Slater determinant, so that HartreeFock and DMRG give virtually identical results for this problem. Our results show that the effects of longrange interactions in magic angle graphene can be efficiently simulated with DMRG and open up a new route for numerically studying strong correlation physics. 
Wednesday, March 16, 2022 12:42PM  12:54PM 
N56.00007: Quantum critical behaviour in magicangle twisted bilayer graphene Alexandre Jaoui, Ipsita Das, giorgio di battista, Jaime DíezMérida, Xiaobo Lu, Leonid Levitov, Hiroaki Ishizuka, Dmitri K Efetov The flat bands of magicangle twisted bilayer graphene (MATBG) host stronglycorrelated electronic phases such as correlated insulators, superconductors and a strange metal state. [14]. The latter state, believed to hold the key to a deeper understanding of the electronic properties of MATBG, is obscured by the abundance of phase transitions; so far, this state could not be unequivocally differentiated from a metal undergoing frequent electronphonon collisions [5]. We report on transport measurements in superconducting (SC) MATBG in which the correlated insulator states were suppressed by screening [6]. The uninterrupted metallic ground state features a Tlinear resistivity extending over three decades in temperature, from 40 mK to 20 K, spanning a broad range of dopings including those where a correlationdriven Fermi surface reconstruction occurs. This strangemetal behavior is distinguished by Planckian scattering rates and a linear magnetoresistivity ρ∝B. On the contrary, near charge neutrality or a fullyfilled flat band, as well as for devices twisted away from the magic angle, the archetypal Fermi liquid behavior is recovered. Our measurements demonstrate the existence of a quantumcritical point whose fluctuations dominate the metallic ground state. Further, a transition to the strange metal is observed upon suppression of the SC order, which suggests an intimate relationship between quantum fluctuations and superconductivity in MATBG. 
Wednesday, March 16, 2022 12:54PM  1:06PM 
N56.00008: Carrier transport theory for twisted bilayer graphene in the metallic regime Shaffique Adam, Girish Sharma, Indra Yudhistira, Nilotpal Chakraborty, Derek Ho, Mohammed M Al Ezzi, Michael S Fuhrer, Giovanni Vignale Understanding the normalmetal state transport in twisted bilayer graphene near magic angle is of fundamental importance as it provides insights into the mechanisms responsible for the observed strongly correlated insulating and superconducting phases. Here we provide a rigorous theory for phonondominated transport in twisted bilayer graphene describing its unusual signatures in the resistivity (including the variation with electron density, temperature, and twist angle) showing good quantitative agreement with recent experiments. We contrast this with the alternative Planckian dissipation mechanism that we show is incompatible with available experimental data. An accurate treatment of the electronphonon scattering requires us to go well beyond the usual treatment, including both intraband and interband processes, considering the finitetemperature dynamical screening of the electronphonon matrix element, and going beyond the linear Dirac dispersion. In addition to explaining the observations in currently available experimental data, we make concrete predictions that can be tested in ongoing experiments. 
Wednesday, March 16, 2022 1:06PM  1:18PM 
N56.00009: Study of spin and valley properties of magicangle twisted bilayer graphene based on density functional theory YoSep Cho, Young Woo Choi, Hyoung Joon Choi Magicangle twisted bilayer graphene (MATBG) has drawn great attention for its tunable flat bands by the twist angle. Various electronic phases have been observed experimentally at different doping concentrations, so quantitative theoretical study of corresponding electronic structures is required. In this work, we present spinvalley flavorpolarized electronic band structures based on the density functional theory (DFT). For the large number of atoms in the moiré supercell, we developed an efficient method to obtain electronic structures of doped MATBG from selfconsistent DFT results of undoped MATBG. With this method, we studied spinvalley flavorpolarized electronic structures of MATBG as a function of doping. We discuss implication of our results compared with reported experimental observations. 
Wednesday, March 16, 2022 1:18PM  1:30PM 
N56.00010: Fermionic Monte Carlo study of a realistic model of twisted bilayer graphene Johannes S Hofmann, Eslam Khalaf, Ashvin Vishwanath, Erez Berg, Jong Yeon Lee The rich phenomenology of twisted bilayer graphene (TBG) near the magic angle is believed to arise from electron correlations in topological flat bands. An unbiased approach to this problem is highly desirable, but also particularly challenging, given the multiple electron flavors, the topological obstruction to defining tightbinding models and the longranged Coulomb interactions. While numerical simulations of realistic models have thus far been confined to zero temperature, typically excluding some spin or valley species, analytic progress has relied on fixed point models away from the realistic limit. Here we present unbiased Monte Carlo simulations of realistic models of magic angle TBG at chargeneutrality. Our results include (i) the emergence of an insulating Kramers intervalley coherent ground state in competition with a correlated semimetal phase, (ii) detailed temperature evolution of order parameters and electronic spectral functions which reveal a `pseudogap' regime, in which gap features are established at a higher temperature than the onset of order and (iii) predictions for electronic tunneling spectra and their evolution with temperature. 
Wednesday, March 16, 2022 1:30PM  1:42PM 
N56.00011: Fermionic Monte Carlo study of a realistic model of twisted bilayer graphene (part II) Jong Yeon Lee, Eslam Khalaf, Ashvin Vishwanath, Erez Berg, Johannes S Hofmann The rich phenomenology of twisted bilayer graphene (TBG) near the magic angle is believed to arise from electron correlations in topological flat bands. An unbiased approach to this problem is highly desirable, but also particularly challenging, given the multiple electron flavors, the topological obstruction to defining tightbinding models and the longranged Coulomb interactions. While numerical simulations of realistic models have thus far been confined to zero temperature, typically excluding some spin or valley species, analytic progress has relied on fixed point models away from the realistic limit. Here we present unbiased Monte Carlo simulations of realistic models of magic angle TBG at chargeneutrality. Our results include (i) the emergence of an insulating Kramers intervalley coherent ground state in competition with a correlated semimetal phase, (ii) detailed temperature evolution of order parameters and electronic spectral functions which reveal a `pseudogap' regime, in which gap features are established at a higher temperature than the onset of order and (iii) predictions for electronic tunneling spectra and their evolution with temperature. 
Wednesday, March 16, 2022 1:42PM  1:54PM 
N56.00012: Interaction driven giant thermopower in magicangle twisted bilayer graphene Anindya Das, Arup K Paul, AYAN GHOSH, Kenji Watanabe, Takashi Taniguchi, Sumilan Banerjee, Subroto Mukerjee, Adhip Agarwala, Souvik Chakraborty, Ujjal Roy, Ranit Dutta, Animesh Panda Magicangle twisted bilayer graphene (MtBLG) has proven to be an extremely promising new platform 
Wednesday, March 16, 2022 1:54PM  2:06PM 
N56.00013: Heterostrain Induced Giant Injection Current in Twisted Bilayer Graphene Heterostructures Arpit Arora, Jian Feng Kong, Justin Song The moiré superlattices that twisted bilayer graphene (TBG) host exhibits rich phenomenology owing to its geometrically nontrivial bands. Here we predict that stacking and straincontrolled Bloch band geometry gives rise to giant circular injection currents in TBG. The high sensitivity of electronic wavefunctions on details of local atomic configurations allow strain enabled injection currents which sensitively depend on the alignment of graphene layers with hBN in TBGhBN heterostructures that break sublattice symmetry. We argue that the giant injection currents proceed from large and highly peaked interband Berry curvature dipole density, which captures the quantum geometry associated with interband transitions giving rise to these currents. Strikingly, pronounced responses are found in the THz regime, which can be tuned by chemical potential. 
Wednesday, March 16, 2022 2:06PM  2:18PM 
N56.00014: Correlated insulators, density wave states, and their nonlinear optical response in magicangle twisted bilayer graphene Jianpeng Liu, Shihao Zhang, Xin Lu The correlated insulator (CI) states and the recently discovered density wave (DW) states in magicangle twisted bilayer graphene (TBG) have stimulated intense research interest. However, up to date, the nature of these "featureless" correlated states observed at different integer and fractional fillings of the flat bands are still elusive, which are lack of direct experimental characters. Thus an experimental probe to identify the characters of these featureless CI and DW states are urgently needed. In this work, we theoretically study the correlated insulators and density wave states at different integer and fractional fillings of the flat bands in magicangle TBG based on extended unrestricted HartreeFock calculations including the Coulomb screening effects from the remote bands. We further investigate the nonlinear optical responses, such as secondharmonic generations and shiftcurrent responses, of the various correlated states, and find that the different components of the nonlinear optical conductivities can be used to identify the nature of these CI and DW states at most of the fillings. Thus we propose nonlinear optical response as a unique experimental probe to unveil the nature of the peculiar CI and DW states discovered in experiments in magicangle TBG. 
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