Optical conductivity of semi-Dirac and pseudospin-1 models: Zitterbewegung approach

TL;DR

This paper introduces a quasiparticle velocity correlator method based on zitterbewegung to analytically compute optical conductivities in semi-Dirac and pseudospin models, revealing effects of spectrum anisotropy, topological transitions, and flat bands.

Contribution

It presents a novel analytical approach using velocity correlators to evaluate optical conductivity in complex lattice models, including semi-Dirac and pseudospin systems.

Findings

Exact expressions for optical conductivities in semi-Dirac and lattice models.

Identification of topological transition signatures in dc transport.

Role of spectral gaps and flat bands in optical response.

Abstract

We present a method to calculate the optical conductivity of semi-Dirac and pseudospin models based on the evaluation of quasiparticle velocity correlators which also describe the phenomenon of zitterbewegung. Applying this method to the semi-Dirac model with merging Dirac cones and gapped dice and Lieb lattice models we find exact analytical expressions for optical longitudinal and Hall conductivities. For the semi-Dirac model the obtained expressions allow us to analyze the role of spectrum anisotropy, van Hove singularities and Dirac cones in longitudinal conductivity. In addition, we predict signatures of topological phase transition with changing gap parameter in such a system that are manifested in dc transport at low temperatures. For the dice and Lieb lattices we emphasize the role of spectral gap, which defines frequency thresholds related to transitions to and from flat band.