Axion response in gapless systems

TL;DR

This paper investigates the axion response in gapless topological systems, revealing a non-quantized magneto-electric coupling that persists with bulk Fermi surfaces, extending the concept of topological responses to gapless phases.

Contribution

It demonstrates that non-quantized axion responses and higher-dimensional analogs of the anomalous Hall effect exist in gapless topological materials, broadening the understanding of topological responses beyond gapped insulators.

Findings

Non-quantized magneto-electric coupling persists with bulk Fermi surfaces.

Higher-dimensional analogs of the anomalous Hall effect appear in gapless systems.

3D axion response derives from 4D intrinsic anomalous Hall effect.

Abstract

The strong topological insulator in 3D is expected to realize a quantized magneto-electric response, the so-called axion response. However, many of the materials predicted to be topological insulators have turned out to be metallic, with bulk Fermi surfaces. Following the result of Bergman et al. (Phys. Rev. B 82, 195417 (2010)) that the helical surface states of the topological insulator persist even when the band structure gap is closed, we explore the fate of the magneto-electric response in such systems. We find a non-quantized magneto-electric coupling remains once a bulk Fermi surface opens - a non-universal axion response. More generally we find that higher dimensional analogs of the intrinsic anomalous Hall effect appear for \emph{every} Chern form - non-quantized response coefficients for gapless systems, as opposed to quantized transport coefficients in gapped systems, both with a topological origin. In particular, the non-quantized magneto-electric response in 3D descends from the intrinsic anomalous Hall effect analog in 4D.