Patterns of Electro-magnetic Response in Topological Semi-metals

Abstract

Topological semimetals are gapless states of matter which have robust and unique electromagnetic responses and surface states. In this paper, we consider semimetals which have point like Fermi surfaces in various spatial dimensions $D=1,2,3$ which naturally occur in the transition between a weak topological insulator and a trivial insulating phase. These semimetals include those of Dirac and Weyl type. We construct these phases by layering strong topological insulator phases in one dimension lower. This perspective helps us understand their effective response field theory that is generally characterized by a 1-form $b$ which represents a source of Lorentz violation and can be read off from the location of the nodes in momentum space and the helicities/chiralities of the nodes. We derive effective response actions for the 2D and 3D Dirac semi-metals, and extensively discuss the response of the Weyl semimetal. We also show how our work can be used to describe semi-metals with Fermi-surfaces with lower co-dimension as well as to describe the topological response of 3D topological crystalline insulators.

arXiv comment42 pages, 19 figures

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• Chiral Separation Effect in lattice regularization
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• Topological Electromagnetic Responses of Bosonic Quantum Hall, Topological Insulator, and Chiral Semi-Metal phases in All Dimensions
• Stripe melting, a transition between weak and strong symmetry protected topological phases
• Anatomy of the chiral vortical effect
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• Unified Topological Response Theory for Gapped and Gapless Free Fermions
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