Nematic insulator at charge neutrality in twisted bilayer graphene

TL;DR

This paper explores the emergence of a nematic insulator state in twisted bilayer graphene near magic angles, using advanced theoretical models and renormalization group analysis to understand the interplay of interactions and symmetry.

Contribution

It introduces a comprehensive symmetry-based framework and RG analysis to identify and characterize nematic insulating phases in twisted bilayer graphene.

Findings

Proximity to magic angle favors nematic insulator formation.

Identification of interaction classes leading to gap opening or nematic order.

Layer-polarized, gapped state with spatial modulation near magic angles.

Abstract

We investigate twisted bilayer graphene near charge neutrality using a generalized Bistritzer-MacDonald continuum model, accounting for corrugation effects. The Fermi velocity vanishes for particular twist angles properly reproducing the physics of the celebrated magic angles. Using group representation theory, we identify all contact interaction potentials compatible with the symmetries of the model. This enables us to identify two classes of quartic interactions leading to either the opening of a gap or to nematic ordering. We then implement a renormalization group analysis to study the competition between these interactions for a twist angle approaching the first magic value. This combined group theory-renormalization study reveals that the proximity to the first magic angle favors the occurrence of a layer-polarized, gapped state with a spatial modulation of interlayer correlations, which we call nematic insulator.