Topological properties of Dirac and Weyl semimetals

TL;DR

This paper explores the topological electromagnetic responses of Dirac and Weyl semimetals, linking their transport phenomena to topological terms with non-quantized coefficients and relating these to Fermi surface properties.

Contribution

It provides a novel perspective on the electromagnetic response of topological semimetals, connecting topological terms to observable transport phenomena and Fermi surface characteristics.

Findings

Topological terms with non-integer coefficients describe electromagnetic responses.

Observable transport phenomena are linked to the topological properties of semimetals.

A connection between topological response and Fermi surface size is established.

Abstract

This chapter describes topological (Dirac and Weyl) semimetals from the viewpoint of their observable electromagnetic response. We argue that this response may be represented by topological terms with unquantized (non-integer) coefficients and make a connection with the Luttinger's theorem, which relates the size of the Fermi surface of an ordinary metal to the number of electrons per unit cell. We discuss observable transport phenomena, associated with this topological response.