Kinetic theory of {\it tilted} Dirac cone materials

TL;DR

This paper develops a kinetic theory for interacting tilted Dirac fermions in two dimensions, revealing how tilt affects electrical response and interaction effects, with implications for understanding their underlying spacetime structure.

Contribution

It formulates Boltzmann equations for tilted Dirac materials and uncovers how tilt influences Drude response and interaction effects, linking them to a spacetime analogy.

Findings

Broadening of the Drude pole is enhanced by tilt-dependent factors.

The Drude pole intensity is anisotropically increased by tilt.

Interaction effects are more significant in a tilted Minkowski spacetime.

Abstract

We formulate the Boltzmann kinetic equations for interacting tilted Dirac fermions in two space dimensions characterized by a tilt parameter $0\le\zeta<1$. Solving the linearized Boltzmann equation, we find that the broadening of the Drude pole is enhanced by $\kappa(\zeta)\times(1-\zeta^2)^{-1/2}$, where the $\kappa$ is interaction-induced enhancement factor. The intensity of the Drude pole is also anisotropically enhanced by $(1-\zeta^2)^{-1}$. The ubiquitous "redshift" factors $(1-\zeta^2)^{1/2}$ can be regarded as a manifestation of an underlying spacetime structure in such solids. The additional broadening $\kappa$ indicates that interaction effects are more pronounced for electrons in a $\zeta$-deformed Minkowski spacetime of tilted Dirac fermions.