Patterns of Electro-magnetic Response in Topological Semi-metals

TL;DR

This paper investigates the electromagnetic responses of topological semimetals with point-like Fermi surfaces across various dimensions, providing effective response theories and exploring their relation to topological phases and crystalline insulators.

Contribution

It introduces a unified framework for understanding the electromagnetic response of Dirac and Weyl semimetals through effective field theories derived from layered topological insulators.

Findings

Derived response actions for 2D and 3D Dirac semimetals.

Analyzed the electromagnetic response of Weyl semimetals.

Extended the framework to Fermi-surfaces with lower co-dimension.

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.