Electrochemical transport in Dirac nodal-line semimetals

Nodal-line semimetals are topological phases where the conduction and the valence bands cross each other along one-dimensional lines in the Brillouin zone, which are symmetry protected by either spatial symmetries or time-reversal symmetry. In particular, nodal lines protected by the combined $\mathcal{PT}$ symmetry exhibits the parity anomaly of 2D Dirac fermions. In this Letter, we study the electrochemical transport in a $\mathcal{PT}$-symmetric Dirac nodal line semimetals by using the semiclassical Boltzmann equation approach. We derive a general formula for the topological current that includes both the Berry curvature and the orbital magnetic moment. We first evaluate the electrochemical current by introducing a small $\mathcal{PT}$-breaking mass term (which could be induced by inversion-breaking uniaxial strain, pressure, or an external electric field) and apply it to the hexagonal pnictide CaAgP. The electrochemical current vanishes in the zero-mass limit. Introducing a tilting term that does not spoil $\mathcal{PT}$ symmetry that protects the nodal ring, we obtain a finite electrochemical current in the zero-mass limit, which can be regarded as a direct consequence of the parity anomaly. We show that the parity anomaly induced electrochemical transport is also present at nonzero temperatures.