Kinetic theory of tilted Dirac cone materials

We formulate the Boltzmann kinetic equations for interacting electrons with tilted Dirac cones in two space dimensions characterized by a tilt parameter $0\le \zeta <1$. By solving the linearized Boltzmann equation, we find that the broadening of the Drude pole is enhanced by $\kappa \left(\zeta \right)\times {(1-{\zeta }^2)}^{-1/2}$, 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 $\kappa$ that arises from the interactions cannot be obtained from a simple coordinate change and are more pronounced for electrons in a $\zeta$-deformed Minkowski spacetime of tilted Dirac fermions.