Anomalous Hall optical conductivity in tilted topological nodal-line semimetals

Abstract

Nodal-line semimetals are typically characterized by a nodal ring, a closed line of Dirac points in the Brillouin zone, whose topology is characterized by a quantized Berry phase. The nodal loop is protected by the combined inversion and time-reversal ($\mathcal{PT}$) symmetry in the absence of spin-orbit coupling, exhibiting the parity anomaly. Introduction of the $\mathcal{PT}$-break mass term can lead to the transverse Hall response at each point in the nodal ring, but the net Hall current vanishes due to the existence of inversion-symmetry points that contribute to the transverse current with opposite signs. We show that the combination of an inversion-broken tilt term and finite Fermi energy can cause the nonzero anomalous Hall effect. We explore the DC and AC anomalous Hall conductivity in tilted nodal-line semimetals using Kubo formula and focus on the contribution of the free carriers to the Hall conductivity. We find that the interband transition of free carriers dominates the nonvanishing dynamic Hall conductivity over the filled band contribution. The resulting anomalous Hall conductivity exhibits the parity anomaly for the DC case, and rich characteristic frequencies for the AC case which is closely related to the change of the geometry of the Fermi surface. These features may serve as a diagnostic tool to characterize the topological property, tilting parameter, or the radius of the nodal line.