Adiabatic Pumping of Chern-Simons Axion Coupling

TL;DR

This paper investigates the adiabatic pumping of the Chern-Simons axion coupling in topological materials, revealing how non-zero second Chern numbers induce quantized charge transfer through Berry curvature dynamics.

Contribution

It introduces a new formula for the CSA coupling using hybrid Wannier functions and elucidates the mechanism of quantized pumping via sheet-touching events in the Wannier charge center representation.

Findings

Quantized CSA coupling is pumped during adiabatic cycles with non-zero second Chern number.

Sheet-touching events transfer Berry curvature quanta between Wannier charge sheets.

Explicit tight-binding models demonstrate the theoretical predictions.

Abstract

We study the adiabatic pumping of the Chern-Simons axion (CSA) coupling along a parametric loop characterized by a non-zero second Chern number $C^{(2)}$ from the viewpoint of the hybrid Wannier representation, in which the Wannier charge centers (WCCs) are visualized as sheets defined over a projected 2D Brillouin zone. We derive a new formula for the CSA coupling, expressing it as an integral involving Berry curvatures and potentials defined on the WCC sheets. We show that a loop characterized by a non-zero $C^{(2)}$ requires a series of sheet-touching events at which $2\pi$ quanta of Berry curvature are passed from sheet to sheet, in such a way that $e^2/h$ units of CSA coupling are pumped by a lattice vector by the end of the cycle. We illustrate these behaviors via explicit calculations on a model tight-binding Hamiltonian and discuss their implications.