Anderson's Theorem for Correlated Insulating States in Twisted Bilayer Graphene.

The emergence of correlated insulating phases in magic-angle twisted bilayer graphene exhibits strong sample dependence. Here, we derive an Anderson theorem governing the robustness against disorder of the Kramers intervalley coherent (K-IVC) state, a prime candidate for describing the correlated insulators at even fillings of the moiré flat bands. We find that the K-IVC gap is robust against local perturbations, which are odd under PT, where P and T denote particle-hole conjugation and time reversal, respectively. In contrast, PT-even perturbations will in general induce subgap states and reduce or even eliminate the gap. We use this result to classify the stability of the K-IVC state against various experimentally relevant perturbations. The existence of an Anderson theorem singles out the K-IVC state from other possible insulating ground states.

Domain Formation Driven by the Entropy of Topological Edge Modes.

In this Letter we study interacting systems with spontaneous discrete symmetry breaking, where the degenerate symmetry-broken states are topologically distinct gapped phases. Edge modes appear at domain walls between the two topological phases. In the presence of a weak disorder field conjugate to the order parameter, we find that the entropy of the edge modes drives a thermal transition between a gapped uniform phase and a phase with a disorder-induced domain structure. We characterize this transition using a phenomenological Landau functional, and corroborate our conclusions with a concrete microscopic model. Finally, we discuss the possibilities of experimental signatures of this phase transition, and propose graphene-based moiré heterostructures as candidate materials in which such a phase transition can be detected.

Theory of Correlated Insulators and Superconductivity in Twisted Bilayer Graphene.

We introduce and analyze a model that sheds light on the interplay between correlated insulating states, superconductivity, and flavor-symmetry breaking in magic angle twisted bilayer graphene. Using a variational mean-field theory, we determine the normal-state phase diagram of our model as a function of the band filling. The model features robust insulators at even integer fillings, occasional weaker insulators at odd integer fillings, and a pattern of flavor-symmetry breaking at noninteger fillings. Adding a phonon-mediated intervalley retarded attractive interaction, we obtain strong-coupling superconducting domes, whose structure is in qualitative agreement with experiments. Our model elucidates how the intricate form of the interactions and the particle-hole asymmetry of the electronic structure determine the phase diagram. It also explains how subtle differences between devices may lead to the different behaviors observed experimentally. A similar model can be applied with minor modifications to other moiré systems, such as twisted trilayer graphene.

Fractional Conductance in Strongly Interacting 1D Systems.

We study one-dimensional clean systems with few channels and strong electron-electron interactions. We find that in several circumstances, even when time-reversal symmetry holds, they may lead to two-terminal fractional quantized conductance and fractional shot noise. The condition on the commensurability of the Fermi momenta of the different channels and the strength of the interactions resulting in such remarkable phenomena are explored using Abelian bosonization. Finite temperature and length effects are accounted for by a generalization of the Luther-Emery refermionization at specific values of the interaction strength, in the strongly interacting regime. We discuss the connection of our model to recent experiments in a confined two-dimensional electron gas, featuring possible fractional conductance plateaus, including situations with a zero magnetic field, when time-reversal symmetry is conserved. One of the most dominant observed fractions, with two-terminal conductance equal to 2/5(e^{2}/h), is found in several scenarios of our model. Finally, we discuss how at very small energy scales the conductance returns to an integer value and the role of disorder.