Linear response of tilted anisotropic two-dimensional Dirac cones

TL;DR

This paper analyzes how anisotropic and tilted Dirac cones in 2D semimetals respond to electric fields and temperature gradients, considering magnetic field effects using semiclassical Boltzmann theory.

Contribution

It derives response coefficients for tilted anisotropic Dirac cones under electric, thermal, and magnetic fields, including recursive solutions and law validity analysis.

Findings

Magnetic field influences response only when perpendicular to the plane.

Derived response coefficients in absence and presence of magnetic field.

Discussed the validity of Mott relation and Wiedemann-Franz law.

Abstract

We investigate the behaviour of the linear-response coefficients, when in-plane electric field ($\mathbf E$) or/and temperature gradient ($\nabla_{\mathbf r} T$) is/are applied on a two-dimensional semimetal harbouring 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 $\mathbf B$. 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 $|\mathbf B|$. We discuss the validity of the Mott relation and the Wiedemann-Franz law for the Lorentz-operator-induced parts.