Parity Anomaly in the non-linear response of Nodal-Line Semimetals

TL;DR

This paper explores the parity anomaly in the non-linear optical response of nodal-line semimetals, revealing potential experimental signatures of topological effects linked to symmetry properties.

Contribution

It demonstrates that the parity anomaly manifests in the non-linear response of nodal-line semimetals, extending understanding beyond linear transport phenomena.

Findings

Parity anomaly appears in non-linear optical response

Tilting term preserves combined symmetry but breaks individual symmetries

Potential for experimental observation of Hall conductivities

Abstract

Nodal-line semimetals are topological semimetals characterized by one-dimensional band-touching loops protected by the combined symmetry of inversion $\mathcal{P}$ and time-reversal $\mathcal{T}$ in absence of spin-orbit coupling. These nodal loops can be understood as a one-parameter family of Dirac points exhibiting the parity anomaly associated to $\mathcal{P}*\mathcal{T}$ symmetry. We find that the parity anomaly also appears in the non-linear optical response of these systems in an analogous way to the linear response transport. We analyze the presence of a tilting term in the Hamiltonian as an element that does not spoil $\mathcal{P}*\mathcal{T}$ symmetry: while it is $\mathcal{P}*\mathcal{T}$-symmetric, it breaks separately both $\mathcal{P}$ and $\mathcal{T}$ symmetries, allowing for the potential experimental observability of the linear and non-linear Hall conductivities in appropriate nodal-line semimetals.