Axionic band topology in inversion-symmetric Weyl-charge-density waves

Benjamin J Wieder,Kuan-Sen Lin,Barry Bradlyn

doi:10.1103/physrevresearch.2.042010

Abstract

In recent theoretical and experimental investigations, researchers have linked the low-energy field theory of a Weyl semimetal gapped with a charge-density wave (CDW) to high-energy theories with axion electrodynamics. However, it remains an open question whether a lattice regularization of the dynamical Weyl-CDW is in fact a single-particle axion insulator (AXI). In this Letter, we use analytic and numerical methods to study both lattice-commensurate and incommensurate minimal (magnetic) Weyl-CDW phases in the mean-field state. We observe that, as previously predicted from field theory, the two inversion- ($\mathcal{I}$-) symmetric Weyl-CDWs with $\phi = 0,\pi$ differ by a topological axion angle $\delta\theta_{\phi}=\pi$. However, we crucially discover that $neither$ of the minimal Weyl-CDW phases at $\phi=0,\pi$ is individually an AXI; they are instead quantum anomalous Hall (QAH) and "obstructed" QAH insulators that differ by a fractional translation in the modulated cell, analogous to the two phases of the Su-Schrieffer-Heeger model of polyacetylene. Using symmetry indicators of band topology and non-abelian Berry phase, we demonstrate that our results generalize to multi-band systems with only two Weyl fermions, establishing that minimal Weyl-CDWs unavoidably carry nontrivial Chern numbers that prevent the observation of a static magnetoelectric response. We discuss the experimental implications of our findings, and provide models and analysis generalizing our results to nonmagnetic Weyl- and Dirac-CDWs.

Highlights

In recent theoretical and experimental investigations, researchers have linked the low-energy field theory of a Weyl semimetal gapped with a charge-density wave (CDW) to high-energy theories with axion electrodynamics
Using symmetry indicators of band topology and non-Abelian Berry phase, we demonstrate that our results generalize to multiband systems with only two Weyl fermions, establishing that minimal Weyl-CDWs unavoidably carry nontrivial Chern numbers that prevent the observation of a static magnetoelectric response
To extrapolate from a low-energy field theory to an experimentally observable response, one must carefully complete the theory to short (UV) wavelengths—two field theories that are identical at the k · p level may differ at large momenta, leading to distinct physical interpretations

Summary

Introduction

In recent theoretical and experimental investigations, researchers have linked the low-energy field theory of a Weyl semimetal gapped with a charge-density wave (CDW) to high-energy theories with axion electrodynamics. As previously predicted from field theory, the two inversion (I)-symmetric Weyl-CDWs with φ = 0, π differ by a topological axion angle δθφ = π .

Results

Conclusion