Mirror Symmetry Breaking and Lateral Stacking Shifts in Twisted Trilayer Graphene

TL;DR

This paper develops a continuum model for twisted trilayer graphene based on ab initio calculations, analyzing how mirror symmetry breaking and lateral stacking shifts affect electronic properties relevant to experiments and potential superconductivity.

Contribution

It introduces a detailed continuum model that incorporates moiré variations and examines the effects of symmetry breaking and stacking shifts on electronic transport properties.

Findings

Mirror symmetry breaking influences electronic transport.

Lateral stacking shifts affect Drude weight and Hall conductivity.

Accidental stacking shifts may impact superconductivity in twisted trilayers.

Abstract

We construct a continuum model of twisted trilayer graphene using {\it ab initio} density-functional-theory calculations, and apply it to address twisted trilayer electronic structure. Our model accounts for moir\'e variation in site energies, hopping between outside layers and within layers. We focus on the role of a mirror symmetry present in ABA graphene trilayers with a middle layer twist. The mirror symmetry is lost intentionally when a displacement field is applied between layers, and unintentionally when the top layer is shifted laterally relative to the bottom layer. We use two band structure characteristics that are directly relevant to transport measurements, the Drude weight and the weak-field Hall conductivity, and relate them via the Hall density to assess the influence of the accidental lateral stacking shifts currently present in all experimental devices on electronic properties, and comment on the role of the possible importance of accidental lateral stacking shifts for superconductivity in twisted trilayers.