Topological charge pumping by sliding moir\'{e} pattern

TL;DR

This paper investigates how adiabatic interlayer sliding in moiré superlattices induces quantized topological charge pumping, with applications to twisted bilayer graphene, revealing non-zero sliding Chern numbers linked to spectral gaps.

Contribution

It demonstrates that sliding a layer in moiré superlattices causes quantized charge pumping characterized by sliding Chern numbers, extending topological concepts to layered materials.

Findings

Quantized charge pumping occurs during interlayer sliding in moiré superlattices.

Sliding Chern numbers are non-zero in energy gaps above and below flat bands.

Topological pumping can occur perpendicular to the sliding direction.

Abstract

We study the adiabatic topological charge pumping driven by interlayer sliding in the moir\'{e} superlattices. We show that, when we slide a single layer of the twisted bilayer system relatively to the other, a moir\'{e} pattern flow and a quantized transport of electrons occurs. When the Fermi energy is in a spectral gap, the number of pumped charges in the interlayer sliding process is quantized to a sliding Chern number, which obeys a Diophantine equation analogous to the quantum Hall effect. We apply the argument to the twisted bilayer graphene, and find that energy gaps above and below the nearly-flat bands has non-zero sliding Chern numbers. When the Fermi energy is in either of those gaps, the slide-driven topological pumping occurs perpendicularly to the sliding direction.