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 $0\le\zeta&lt;1$. Solving the linearized Boltzmann equation, we find that the broadening of the Drude pole is enhanced by $\kappa(\zeta)\times(1-\zeta<sup>2)<sup>{-1/2}$, where the $\kappa$ is interaction-induced enhancement factor. The intensity of the Drude pole is also anisotropically enhanced by $(1-\zeta<sup>2)<sup>{-1}$. The ubiquitous "redshift" factors $(1-\zeta<sup>2)<sup>{1/2}$ 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.