Kinetic theory of {\it tilted} Dirac cone materials

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.

11 pages, 2 figures, v2: appendix C is added for clarification