Abstract 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.
A topological Mott insulator (TMI) with spontaneous time-reversal symmetry breaking and nonzero Chern number has been discovered in a real-space effective model for twisted bilayer graphene (TBG) at 3/4 filling in the strong coupling limit [1]. However, the finite temperature properties of such a TMI state remain illusive. In this work, employing the state-of-the-art thermal tensor network and the perturbative field-theoretical approaches, we obtain the finite-T phase diagram and the dynamical properties of the TBG model. The phase diagram includes the quantum anomalous Hall and charge density wave phases at low T, and an Ising transition separating them from the high-T symmetric phases. Because of the proliferation of excitons-particle-hole bound states-the transitions take place at a significantly reduced temperature than the mean-field estimation. The exciton phase is accompanied with distinctive experimental signatures in such as in charge compressibilities and optical conductivities close to the transition. Our work explains the smearing of the many-electron state topology by proliferating excitons and opens an avenue for controlled many-body investigations on finite-temperature states in the TBG and other quantum moiré systems.
Mott physics in topological bands has recently attracted considerable attention, particularly in the context of twisted bilayer graphene (TBG). However, the essential ingredients for stabilizing this physics remain unclear. Here, we demonstrate a quantum Mott semimetal phase as the ground state within a one-dimensional spinful Hubbard model featuring only one orbital per unit cell, protected by inversion and particle-hole symmetries. We start from a two-orbital model where a localized
f orbital on the A sublattice hybridizes with a delocalized
c orbital on the B sublattice. Projecting the
f-orbital Hubbard
U onto the active flat band yields a lattice model with Wannier orbitals centered on the B sublattice. Similar to TBG, a momentum-space scale
k∗ emerges, setting the interaction range in the projected model to
1/k∗. While the ground state is ferromagnetic with only the Hubbard
U, introducing an inter-site antiferromagnetic spin coupling
J stabilizes a Mott semimetal
∗ phase with a central charge
c=3. Using exact diagonalization (ED) and density matrix renormalization group (DMRG) methods, we show that this phase hosts a spinful Dirac fermion coexisting with a neutral spin mode -- analogous to the fractionalized Fermi liquid (FL
∗) phase in higher dimensions. Furthermore, breaking particle-hole (PH) symmetry via dispersion transforms the Mott semimetal into a Mott insulator, which is separated from a distinct Mott insulating phase by a continuous transition with a polarization jump of
1/2. Our work provides the first unbiased evidence of a Mott semimetal ground state and demonstrates that this 1D model captures some essential aspects of TBG physics, despite lacking a Wannier obstruction.
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.
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.
Motivated by recent experimental studies that have found signatures of a correlated insulator phase and tuning superconductivity in twisted bilayer graphene, we study the temperature-dependent conductivity, the spin correlation and the superconducting pairing correlation within a two-orbital Hubbard model on an emergent honeycomb lattice. Evaluation of the temperature dependence of the conductivity demonstrates that there is a metal-insulator transition, and the Mott phase at strong coupling is accompanied by antiferromagnetic order. The electronic correlation drives a
d+id superconducting pairing to be dominant over a wide filling region. All of the dc conductivity, the spin correlation and the superconductivity are suppressed as the interlayer coupling strength increases, and the critical
Uc for metal-insulator transition is also reduced. Our intensive numerical results reveal that the TBG should be a uniquely tunable platform for exploring correlated states.