Session N56: Twisted Bilayer Graphene: Theory, Transport, Thermodynamics, and Optics

Probing strong correlation and discriminating insulating phases in twisted bilayer graphene through scanning tunneling microscopy

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 many-body charge-one 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 fully-interacting 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 intervalley-coherent TBG insulators does not always result in KD. For instance, we show that the K-IVC 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.   

Detecting symmetry breaking in magic angle graphene using scanning tunneling microscopy

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 symmetry-breaking 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 atomically-resolved 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 symmetry-breaking 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.   

Probing entropy and magnetization in graphene heterostructures

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 in-plane magnetic field, suggesting a weakly coupled isospin-ordered 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  non-Moiré type graphene systems, such as Bernal stack bilayer graphene.   

Correlated Hofstadter Spectrum and Flavor Phase Diagram in Magic Angle Graphene

In magic angle twisted bilayer graphene (MATBG), the moiré superlattice potential gives rise to narrow electronic bands which support a multitude of many-body 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 single-electron transistor.  By probing both gapped phases and the intervening compressible regimes, we simultaneously unveil novel sequences of broken-symmetry 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.    

Thermodynamic measurements of magic graphene systems using SET

In recent years different flat-band 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 single-electron transistor.   

Efficient simulation of moire materials using the density matrix renormalization group

We present an infinite density-matrix renormalization group (DMRG) study of a model of twisted bilayer graphene (tBLG) near the magic angle. Because of the long-range 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, single-valley 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 k-space Slater determinant, so that Hartree-Fock and DMRG give virtually identical results for this problem. Our results show that the effects of long-range interactions in magic angle graphene can be efficiently simulated with DMRG and open up a new route for numerically studying strong correlation physics.   

Quantum critical behaviour in magic-angle twisted bilayer graphene

The flat bands of magic-angle twisted bilayer graphene (MATBG) host strongly-correlated electronic phases such as correlated insulators, superconductors and a strange metal state. [1-4]. 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 electron-phonon 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 T-linear resistivity extending over three decades in temperature, from 40 mK to 20 K, spanning a broad range of dopings including those where a correlation-driven Fermi surface reconstruction occurs. This strange-metal behavior is distinguished by Planckian scattering rates and a linear magneto-resistivity ρ∝B. On the contrary, near charge neutrality or a fully-filled 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 quantum-critical 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.

[1] Y. Cao, et al., Nature 556, 43-50 (2018).

[2] Y. Cao et al., Nature 556, 80-84 (2018).

[3] X. Lu et al., Nature 574, 653-657 (2019).

[4] Y. Cao et al., Physical Review Letters 124, 076801 (2020).

[5] H. Polshyn et al., Nature Physics 15, 1011-1016 (2019).

[6] P. Stepanov et al., Nature 583, 375-378 (2020).   

Carrier transport theory for twisted bilayer graphene in the metallic regime

Understanding the normal-metal 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 phonon-dominated 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 electron-phonon scattering requires us to go well beyond the usual treatment, including both intraband and interband processes, considering the finite-temperature dynamical screening of the electron-phonon 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.   

Study of spin and valley properties of magic-angle twisted bilayer graphene based on density functional theory

Magic-angle twisted bilayer graphene (MA-TBG) 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 spin-valley flavor-polarized 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 MA-TBG from self-consistent DFT results of undoped MA-TBG. With this method, we studied spin-valley flavor-polarized electronic structures of MA-TBG as a function of doping. We discuss implication of our results compared with reported experimental observations.   

Fermionic Monte Carlo study of a realistic model of twisted bilayer graphene

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 tight-binding models and the long-ranged 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 charge-neutrality. Our results include (i) the emergence of an insulating Kramers inter-valley coherent ground state in competition with a correlated semi-metal 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.   

Fermionic Monte Carlo study of a realistic model of twisted bilayer graphene (part II)

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 tight-binding models and the long-ranged 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 charge-neutrality. Our results include (i) the emergence of an insulating Kramers inter-valley coherent ground state in competition with a correlated semi-metal 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.   

Interaction driven giant thermopower in magic-angle twisted bilayer graphene

Magic-angle twisted bilayer graphene (MtBLG) has proven to be an extremely promising new platform

to realize and study a host of emergent quantum phases arising from the strong correlations in

its narrow bandwidth flat band. In this regard, thermal transport phenomena like thermopower, in

addition to being coveted technologically, is also sensitive to the particle-hole (PH) asymmetry, making

it a crucial tool to probe the underlying electronic structure of this material. We have carried

out thermopower measurements of MtBLG as a function of carrier density, temperature and magnetic

field, and report the observation of an unusually large thermopower reaching up to a value as

high as ~100μV/K at a low temperature of 1K. Surprisingly, our observed thermopower exhibits

peak-like features in close correspondence to the resistance peaks around the integer Moire fillings,

including the Dirac Point, violates the Mott formula. We show that the large thermopower peaks and

their associated behaviour arise from the emergent highly PH asymmetric electronic structure due to

the cascade of Dirac revivals. Furthermore, the thermopower shows an anomalous peak around the

superconducting transition on the hole side and points towards the possible role of enhanced superconducting

fluctuations in MtBLG.   

Hetero-strain Induced Giant Injection Current in Twisted Bilayer Graphene Heterostructures

The moiré superlattices that twisted bilayer graphene (TBG) host exhibits rich phenomenology owing to its geometrically non-trivial bands. Here we predict that stacking and strain-controlled 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 TBG-hBN 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.   

Correlated insulators, density wave states, and their nonlinear optical response in magic-angle twisted bilayer graphene

The correlated insulator (CI) states and the recently discovered density wave (DW) states in magic-angle 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 magic-angle TBG based on extended unrestricted Hartree-Fock calculations including the Coulomb screening effects from the remote bands. We further investigate the nonlinear optical responses, such as second-harmonic generations and shift-current 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 magic-angle TBG.