Disordered Weyl semimetals and their topological family

TL;DR

This paper develops a topological framework for disordered Weyl semimetals, showing their bulk transport robustness via an analytically derived anisotropic theta-term within a non-linear sigma model, connecting various topological phases.

Contribution

It introduces a topological theory for disordered Weyl semimetals using gauge invariance and boundary-bulk correspondence, deriving a novel anisotropic theta-term that guarantees transport robustness.

Findings

Derived an anisotropic topological theta-term for disordered Weyl semimetals.

Established relations among topological terms across different dimensions and phases.

Showed the robustness of bulk transverse transport against disorder.

Abstract

We develop a topological theory for disordered Weyl semimetals in the framework of gauge invariance of replica formalism and boundary-bulk correspondence of Chern insulators. An anisotropic topological $\theta$-term is analytically derived for the effective non-linear sigma model. It is this nontrivial topological term that ensures the bulk transverse transport of Weyl semimetals to be robust against disorders. Moreover, we establish a general diagram that reveals the intrinsic relations among topological terms in the non-linear sigma models and gauge response theories respectively for $(2n + 2)$-dimensional topological insulators, $(2n+1)$-dimensional chiral fermions, $(2n+1)$-dimensional chiral semimetals, and $(2n)$-dimensional topological insulators with $n$ being a positive integer.