Non-Abelian gauge potentials in graphene bilayers

TL;DR

This paper investigates how spatial modulations in interlayer hopping in graphene bilayers create non-Abelian gauge potentials, leading to zero-energy states and flat bands, with implications for electronic confinement.

Contribution

It demonstrates that non-Abelian gauge potentials govern the low-energy physics of modulated graphene bilayers, revealing new mechanisms for zero-energy state formation and flat band recurrence.

Findings

Charge accumulation and zero-energy bands recur with pattern period L.

Non-Abelian gauge potentials cause spatial confinement of zero-energy states.

Flat zero-energy bands are linked to the non-Abelian nature of the gauge coupling.

Abstract

We study the effect of spatial modulations in the interlayer hopping of graphene bilayers, such as those that arise upon shearing or twisting. We show that their single-particle physics, characterized by charge accumulation and recurrent formation of zero-energy bands as the pattern period L increases, is governed by a non-Abelian gauge potential arising in the low-energy electronic theory due to the coupling between layers. We show that such gauge-type couplings give rise to a potential that, for certain discrete values of L, spatially confines states at zero energy in particular regions of the Moir\'e patterns. We also draw the connection between the recurrence of the flat zero-energy bands and the non-Abelian character of the potential.