Disordered Weyl semimetals and their topological family

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 ?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.