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

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.

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• Synthetic non-Abelian gauge fields and gravitomagnetic effects in tilted Dirac cone systems
• Signatures of Lifshitz transition in the optical conductivity of two-dimensional tilted Dirac materials
• Floquet spectrum for anisotropic and tilted Dirac materials under linearly polarized light at all field intensities
• Highly anisotropic optical conductivities in two-dimensional tilted semi-Dirac bands
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• Dirac materials under linear polarized light: quantum wave function evolution and topological Berry phases as classical charged particles trajectories under electromagnetic fields
• Excitonic instability in transition metal dichalcogenides