Change of Corner Charge and Adiabatic Current Distribution in Two Dimensional Insulators with Inversion Symmetry

TL;DR

This paper investigates how corner charge and adiabatic current distribution change in 2D insulators with inversion symmetry during adiabatic processes, revealing a mixed bulk-edge effect and confirming findings with numerical models.

Contribution

It provides an analytical expression for adiabatic current in 2D insulators with inversion symmetry, linking corner charge changes to edge currents and validating with numerical simulations.

Findings

Corner charge change is linked to adiabatic edge currents.

Derived adiabatic current matches numerical simulations.

Change of corner charge is a mixed bulk and edge effect.

Abstract

We discuss the change of the corner charge for noninteracting two dimensional insulators with inversion symmetry undergoing adiabatic evolution. We show that the change of the corner charge is accounted for by the adiabatic current flowing along the edges of the system. The study of systems with quasi-1D geometry is necessary to derive the analytical expression for the adiabatic current. This fact suggests that the change of the corner charge is neither a purely bulk nor edge effect, but rather a mixed one. The derived adiabatic current was examined and shows good agreement with the numerical calculation of Benalcazar-Bernevig-Hughes model.