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 $\theta$-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.

5 pages and 2 figures. Accepted by PRL

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• Exploring topological double-Weyl semimetals with cold atoms in optical lattices
• Novel ${\mathbb{Z}}_2$-topological metals and semimetals
• A smeared quantum phase transition in disordered holography
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• Nonlinearity and Topology
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• Exotic Haldane Superfluid Phase of Soft-Core Bosons in Optical Lattices
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• General response theory of topologically stable Fermi points and its implications for disordered cases
• Robust Weyl points in a 1D superlattice with transverse spin-orbit coupling
• Absence of localization in Weyl semimetals
• A domain-specific language and matrix-free stencil code for investigating electronic properties of Dirac and topological materials
• Transport scaling and critical tilt effects in disordered two-dimensional Dirac fermions