Quantum anomalies in nodal line semimetals

TL;DR

This paper investigates quantum anomalies in nodal line semimetals, revealing a 3D parity anomaly and linking drumhead surface states to this anomaly, expanding understanding of topological semimetals.

Contribution

It introduces the concept of a three-dimensional parity anomaly in nodal line semimetals and connects it to their unique surface states and responses.

Findings

Identification of a 3D parity anomaly in nodal line semimetals

Relation of drumhead surface states to the parity anomaly

Derivation of a field theory describing the anomalous response

Abstract

Topological semimetals is a new class of condensed matter systems with nontrivial electronic structure topology. Their unusual observable properties may often be understood in terms of quantum anomalies. In particular, Weyl and Dirac semimetals, which have point band touching nodes, are characterized by the chiral anomaly, which leads to the Fermi arc surface states, anomalous Hall effect, negative longitudinal magnetoresistance and planar Hall effect. In this paper we explore analogous phenomena in nodal line semimetals. We demonstrate that such semimetals realize a three dimensional analog of the parity anomaly, which is a known property of two dimensional Dirac semimetals arising, for example, on the surface of a three dimensional topological insulator. We relate one of the characteristic properties of nodal line semimetals, namely the drumhead surface states, to this anomaly, and derive the field theory, which encodes the corresponding anomalous response.