Linear response of tilted anisotropic two-dimensional Dirac cones

Abstract

We investigate the behavior of the linear-response coefficients, when in-plane electric field (\(\textbf{E}\)) or/and temperature gradient (\(\nabla _{\textbf{r}} T\)) is/are applied on a two-dimensional semimetal harboring anisotropic Dirac cones. The anisotropy is caused by (1) differing Fermi velocities along the two mutually perpendicular momentum axes, and (2) tilting parameters. Using the semiclassical Boltzmann formalism, we derive the forms of the response coefficients, in the absence and presence of a nonquantizing magnetic field \(\textbf{B}\). The magnetic field affects the response only when it is oriented perpendicular to the plane of the material, with the resulting expressions computed with the help of the so-called Lorentz-force operator, appearing in the linearized Boltzmann equation. The solution has to be found in a recursive manner, which produces terms in powers of \(|\textbf{B}|\). We discuss the validity of the Mott relation and the Wiedemann–Franz law for the Lorentz-operator-induced parts.