Parity anomaly in the nonlinear response of nodal-line semimetals*

Nodal-line semimetals (NLSM) are topological semimetals where conduction and valence bands touch each other at one dimensional lines in the Brillouin zone. We will focus on the the PT-symmetric version of NLSM and see how adding and removing a PT symmetry-breaking parameter leaves scars in the electromagnetic response of these systems. Tilting breaks P and T but leaves their product invariant, not modifying the symmetry breaking procedure, but allows the parity anomaly to appear both in the linear and non-linear response. In the case of the linear response, we will show that the tilted NLSM display an axionic electromagnetic response, but with a different origin of the one appearing in Weyl semimetals.