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Topological semimetals is a new class of condensed matter systems withnontrivial electronic structure topology. Their unusual observable propertiesmay often be understood in terms of quantum anomalies. In particular, Weyl andDirac semimetals, which have point band touching nodes, are characterized bythe chiral anomaly, which leads to the Fermi arc surface states, anomalous Halleffect, negative longitudinal magnetoresistance and planar Hall effect. In thispaper we explore analogous phenomena in nodal line semimetals. We demonstratethat such semimetals realize a three dimensional analog of the parity anomaly,which is a known property of two dimensional Dirac semimetals arising, forexample, on the surface of a three dimensional topological insulator. We relateone of the characteristic properties of nodal line semimetals, namely thedrumhead surface states, to this anomaly, and derive the field theory, whichencodes the corresponding anomalous response.

Quantum anomalies in nodal line semimetals