Direct determination of layer anomalous Hall conductivity using uniaxial Wannier functions

TL;DR

This paper introduces a real-space method using hybrid Wannier functions to compute layer-specific anomalous Hall conductivity, validated on topological insulators and antiferromagnets, aiding the design of novel electronic devices.

Contribution

The paper presents a new layer-resolved approach combining Fukui-Hatsugai-Suzuki and Wannier functions to analyze topological transport properties.

Findings

Validated method on MnBi2Te4 showing surface LAHC matches previous surface AHC.

Applied to Mn2Bi2Te5 revealing magnetic structure dependence of LAHC.

Identified cases with and without axion insulating behavior.

Abstract

We propose a method for computing layer anomalous Hall conductivity (LAHC) in real space by integrating the Fukui-Hatsugai-Suzuki method with hybrid Wannier functions localized along a single axis. To validate the method, we calculated the LAHC of axion-insulating MnBi$_2$Te$_4$ and confirmed the agreement between the sum of LAHC on the surface and the surface AHC previously reported. We further applied the method to antiferromagnetic Mn$_2$Bi$_2$Te$_5$ and examined the dependence on the magnetic structure of LAHC, identifying cases with and without axion insulating behavior. This layer-resolved analysis offers a powerful tool for studying topological transport in complex materials, including heterostructures, and may guide the design of future devices based on the anomalous Hall effect with precise layer control.