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arXiv:2205.09766 · Physical review. B./Physical review. B

Strange metal phase of disordered magic-angle twisted bilayer graphene at low temperatures: From flat bands to weakly coupled Sachdev-Ye-Kitaev bundles

Chenan Wei, Tigran Sedrakyan

Published Aug 2, 2023• 9 citations
arXivHTMLPDF

Abstract

We use stochastic expansion and exact diagonalization to study magic-angle twisted bilayer graphene (TBG) on a disordered substrate. We show that the substrate-induced strong Coulomb disorder in TBG with the chemical potential at the level of the flat bands drives the system to a network of weakly coupled Sachdev-Ye-Kitaev (SYK) bundles, stabilizing an emergent quantum chaotic strange metal (SM) phase of TBG that exhibits the absence of quasiparticles. The Gaussian orthogonal ensemble dominates TBG's long-time chaotic dynamics at strong disorder, whereas fast quantum scrambling appears in the short-time dynamics. In weak disorder, gapped phases of TBG exhibit exponentially decaying specific heat capacity and exponential decay in out-of-time-ordered correlators (OTOCs). This is the system behavior in correlated insulator and superconducting phases, in agreement with the corresponding Larkin-Ovchinnikov result for correlators. The result suggests a low-temperature transition from the superconducting and correlated insulating phases into the strange metal upon increasing the disorder strength. We propose a finite-temperature phase diagram for Coulomb-disordered TBG and discuss the experimental consequences of the emergent SM phase.

DOI
10.1103/physrevb.108.064202

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We use stochastic expansion and exact diagonalization to study magic-angle twisted bilayer graphene (TBG) on a disordered substrate. We show that the substrate-induced strong Coulomb disorder in TBG with the chemical potential at the level of the flat bands drives the system to a network of weakly coupled Sachdev-Ye-Kitaev (SYK) bundles, stabilizing an emergent quantum chaotic strange metal (SM) phase of TBG that exhibits the absence of quasiparticles. The Gaussian orthogonal ensemble dominates TBG's long-time chaotic dynamics at strong disorder, whereas fast quantum scrambling appears in the short-time dynamics. In weak disorder, gapped phases of TBG exhibit exponentially decaying specific heat capacity and exponential decay in out-of-time-ordered correlators (OTOCs). This is the system behavior in correlated insulator and superconducting phases, in agreement with the corresponding Larkin-Ovchinnikov result for correlators. The result suggests a low-temperature transition from the superconducting and correlated insulating phases into the strange metal upon increasing the disorder strength. We propose a finite-temperature phase diagram for Coulomb-disordered TBG and discuss the experimental consequences of the emergent SM phase.
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.We establish the absence of a sign problem for this model in a momentumspace approach and describe a computationally tractable formulation that applies even on breaking chiral symmetry and including band dispersion.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 that 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.Our results pave the way towards uncovering the physics of magic-angle graphene through exact simulations of over a hundred electrons across a wide temperature range.
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We study the single- and many-particle properties of a two-leg ladder model threaded by a flux with the legs coupled by a spatially varying term. Although a priori unrelated to twisted bilayer graphene (TBG), the model is found to have striking similarities: a quasi-flat low-energy band emerges with characteristics similar to that of magic angle TBG. We study the effect of interparticle interaction in our model using the density matrix renormalization group and find that when the band is quasi-flat, the ground state is a ferromagnetic Mott insulator. As the band becomes more dispersive, the system undergoes a ferromagnetic to antiferromagnetic transition. We discuss how our model is relevant not only to magic-angle physics in TBG, but also in the larger context of one-dimensional correlations and magnetism.
Abstract One of the most remarkable theoretical findings in magic angle twisted bilayer graphene (TBG) is the emergence of ferromagnetic Slater determinants as exact ground states for the interacting Hamiltonian at the chiral limit. This discovery provides an explanation for the correlated insulating phase which has been experimentally observed at half filling. This work is the first mathematical study of interacting models in magic angle graphene systems. These include not only TBG but also TBG-like systems featuring four flat bands per valley, and twisted trilayer graphene systems with equal twist angles. We identify symmetries of the chiral limit of the Bistritzer-MacDonald Hamiltonian that are responsible for characterizing the Hartree-Fock ground states as zero energy many-body ground states. Furthermore, for a general class of Hamiltonian, we establish criteria that the ferromagnetic Slater determinants are the unique ground states within the class of uniformly half-filled, translation invariant Slater determinants. We then demonstrate that these criteria can be explicitly verified for TBG and TBG-like systems at the chiral limit, using properties of Jacobi- θ{\theta }θ θ and Weierstrass- ℘{\wp }℘ ℘ functions.
Magic-angle twisted bilayer graphene has recently become a thriving material platform realizing correlated electron phenomena taking place within its topological flat bands. Several numerical and analytical methods have been applied to understand the correlated phases therein, revealing some similarity with the quantum Hall physics. In this work, we provide a Mott-Hubbard perspective for the TBG system. Employing the large-scale density matrix renormalization group on the lattice model containing the projected Coulomb interactions only, we identify a first-order quantum phase transition between the insulating stripe phase and the quantum anomalous Hall state with the Chern number of ±1. Our results not only shed light on the mechanism of the quantum anomalous Hall state discovered at three-quarters filling, but also provide an example of the topological Mott insulator, i.e., the quantum anomalous Hall state in the strong coupling limit.
The dynamics of out-of-time order correlators is studied in strongly correlated electron systems. This certain type of correlation function is a measure for the process of quantum information scrambling which is linked to the fundamental processes of entanglement growth and thermalization in quantum systems. Particularly interesting are quantum chaotic systems where the scrambling rate specifies the exponential growth of out-of-time order correlators. Whereas the scrambling rate is well defined theoretically, its interpretation in a physical context is still under debate. Furthermore, its role for physical effects and quantities which can be measured in experiments is little understood and deserves further investigation. In the first part of this work, scrambling rates are determined analytically and are analyzed for interacting electrons in graphene and electrons in a disordered metal coupled to a dissipative bath of phonons. A resemblance between the scrambling rate and the single-particle scattering rates is observed. In addition, a proposed link between quantum chaotic dynamics of out-of-time order correlators and the dynamics of fluctuations of observables is investigated. This principle could be used to determine scrambling rates in experiments. Subsequently, possible electron orders are investigated in the system of small-angle twisted-bilayer graphene in the second part of this work. Here, the interplay between the moiré interference pattern and the interlayer hybridization due to a finite interlayer tunneling of electrons causes the bandwidth of the so-called moiré bands to depend on the twist-angle. For twist-angles in the vicinity of the magic-angle, interaction effects are strongly enhanced and a series of strong correlation effects is expected. A minimal low-energy model of interacting electrons is derived where relevant electron-electron interaction processes are identified. This model is analyzed with respect to possible electronic ground states as a function of the twist-angle. A tendency towards a formation of nematic states is observed in a weak-coupling regime, whereas various Mott-insulating states are found for strong couplings.