Kubo conductivity for anisotropic tilted Dirac semimetals and its application to 8-Pmmn borophene: The role of different frequency, temperature and scattering limits

TL;DR

This paper calculates the anisotropic conductivity of tilted Dirac semimetals using the Kubo formula, revealing how frequency, temperature, and scattering influence minimal conductivity and optical responses, with applications to borophene.

Contribution

It provides a detailed analysis of the frequency, temperature, and scattering effects on conductivity in anisotropic tilted Dirac semimetals, including application to 8-Pmmn borophene.

Findings

Minimal conductivity is sensitive to the order of limits taken.

Conductivities are direction-dependent and follow a geometric mean relation at high frequency and low temperature.

A temperature-dependent minimum in interband scattering is observed due to tilt and chemical potential effects.

Abstract

The electronic and optical conductivities for anisotropic tilted Dirac semimetals are calculated using the Kubo formula. As in graphene, it is shown that the minimal conductivity is sensitive to the order in which the temperature, frequency and scattering limits are taken. Both intraband and interband scattering are found to be direction dependent. In the high frequency and low temperature limit, the conductivities do not depend on frequency and are weighted by the anisotropy in such a way that the geometrical mean $\sqrt{\sigma_{xx}\sigma_{yy}}$ of the conductivity is the same as in graphene. This results from the fact that in the zero temperature limit, interband transitions are not affected by the tilt in the dispersion, a result that is physically interpreted as a global tilting of the allowed transitions. Such result is verified by an independent and direct calculation of the absorption coefficient using the Fermi golden rule. However, as temperature is raised, an interesting minimum is observed in the interband scattering, interpreted here as a result of the interplay between the tilt and the chemical potential increasing with temperature.