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

The electronic and optical conductivities for anisotropic tilted Dirac semimetals are calculated using the Kubo formula. It is shown that, as in graphene, the minimal conductivity is sensitive to the order in which different temperature, frequency, and scattering limits are taken. Both intraband and interband conductivities are found to be direction dependent. In the high-frequency and low-temperature limit the geometric mean root sigma(xx)sigma(xy) reaches the same constant value 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 tilt in the allowed transitions. Such a result is verified by an independent and direct calculation of the absorption coefficient using Fermi's golden rule. However, as the temperature is raised, an interesting minimum is observed in the interband conductivity, interpreted here as a consequence of the interplay between the tilt in the allowed transitions and the chemical potential increasing with the temperature. This effect is a signature of the global tilt in the allowed optical transitions and can be measured by a suitable optical experiment.