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

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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 the spectral gap, which defines frequency thresholds related to transitions to and from a flat band.
Funding Information
  • Nederlandse Organisatie voor Wetenschappelijk Onderzoek
  • Ministerie van Onderwijs, Cultuur en Wetenschap
  • European Research Council
  • Horizon 2020
  • National Academy of Sciences of Ukraine (0122U002313)

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