TY - JOUR

T1 - Correlation-Induced Insulating Topological Phases at Charge Neutrality in Twisted Bilayer Graphene

AU - Liao, Yuan Da

AU - Kang, Jian

AU - Breio, Clara N.

AU - Xu, Xiao Yan

AU - Wu, Han-Qing

AU - Andersen, Brian M.

AU - Fernandes, Rafael M.

AU - Meng, Zi Yang

PY - 2021/1/22

Y1 - 2021/1/22

N2 - Twisted bilayer graphene (TBG) provides a unique framework to elucidate the interplay between strong correlations and topological phenomena in two-dimensional systems. The existence of multiple electronic degrees of freedom-charge, spin, and valley-gives rise to a plethora of possible ordered states and instabilities. Identifying which of them are realized in the regime of strong correlations is fundamental to shed light on the nature of the superconducting and correlated insulating states observed in the TBG experiments. Here, we use unbiased, sign-problem-free quantum Monte Carlo simulations to solve an effective interacting lattice model for TBG at charge neutrality. Besides the usual cluster Hubbard-like repulsion, this model also contains an assisted-hopping interaction that emerges due to the nontrivial topological properties of TBG. Such a nonlocal interaction fundamentally alters the phase diagram at charge neutrality, gapping the Dirac cones even for infinitesimally small interactions. As the interaction strength increases, a sequence of different correlated insulating phases emerge, including a quantum valley Hall state with topological edge states, an intervalley-coherent insulator, and a valence bond solid. The charge-neutrality correlated insulating phases discovered here provide the sought-after reference states needed for a comprehensive understanding of the insulating states at integer fillings and the proximate superconducting states of TBG.

AB - Twisted bilayer graphene (TBG) provides a unique framework to elucidate the interplay between strong correlations and topological phenomena in two-dimensional systems. The existence of multiple electronic degrees of freedom-charge, spin, and valley-gives rise to a plethora of possible ordered states and instabilities. Identifying which of them are realized in the regime of strong correlations is fundamental to shed light on the nature of the superconducting and correlated insulating states observed in the TBG experiments. Here, we use unbiased, sign-problem-free quantum Monte Carlo simulations to solve an effective interacting lattice model for TBG at charge neutrality. Besides the usual cluster Hubbard-like repulsion, this model also contains an assisted-hopping interaction that emerges due to the nontrivial topological properties of TBG. Such a nonlocal interaction fundamentally alters the phase diagram at charge neutrality, gapping the Dirac cones even for infinitesimally small interactions. As the interaction strength increases, a sequence of different correlated insulating phases emerge, including a quantum valley Hall state with topological edge states, an intervalley-coherent insulator, and a valence bond solid. The charge-neutrality correlated insulating phases discovered here provide the sought-after reference states needed for a comprehensive understanding of the insulating states at integer fillings and the proximate superconducting states of TBG.

KW - MAGIC-ANGLE

KW - TRANSITIONS

KW - CASCADE

KW - STATES

U2 - 10.1103/PhysRevX.11.011014

DO - 10.1103/PhysRevX.11.011014

M3 - Journal article

VL - 11

JO - Physical Review X

JF - Physical Review X

SN - 2160-3308

IS - 1

M1 - 011014

ER -