Confining and repulsive potentials from effective non-Abelian gauge fields in graphene bilayers

TL;DR

This paper explores how shear and strain in graphene bilayers create effective non-Abelian gauge fields that significantly alter electronic properties, leading to phenomena like electron localization and flat band formation.

Contribution

It demonstrates how smooth lattice modulations induce non-Abelian gauge fields that produce confining or repulsive effects on electrons in graphene bilayers, revealing new electronic behaviors.

Findings

Strain acts as a repulsive gauge field expelling electrons from domain walls.

Shear induces a confining gauge field leading to localized electronic states.

Flat low-energy bands resemble zeroth Landau levels of Dirac fermions.

Abstract

We investigate the effect of shear and strain in graphene bilayers, under conditions where the distortion of the lattice gives rise to a smooth one-dimensional modulation in the stacking sequence of the bilayer. We show that strain and shear produce characteristic Moir\'e patterns which can have the same visual appearance on a large scale, but representing graphene bilayers with quite different electronic properties. The different features in the low-energy electronic bands can be ascribed to the effect of a fictitious non-Abelian gauge field mimicking the smooth modulation of the stacking order. Strained and sheared bilayers show a complementary behavior, which can be understood from the fact that the non-Abelian gauge field acts as a repulsive interaction in the former, expelling the electron density away from the stacking domain walls, while behaving as a confining interaction leading to localization of the electronic states in the sheared bilayers. In this latter case, the presence of the effective gauge field explains the development of almost flat low-energy bands, resembling the form of the zeroth Landau level characteristic of a Dirac fermion field. The estimate of the gauge field strength in those systems gives a magnitude of the order of several tens of Tesla, implying a robust phenomenology that should be susceptible of being observed in suitably distorted bilayer samples.