Disorder correction to the minimal conductance of a nodal-point semimetal

Abstract

We consider the disorder-induced correction to the minimal conductance of an anisotropic two-dimensional Dirac node or a three-dimensional Weyl node. An analytical expression is derived for the correction $\delta G$ to the conductance of a finite-size sample by an arbitrary potential, without taking the disorder average, in second-order perturbation theory. Considering a generic model of a short-range disorder potential, this result is used to compute the probability distribution $P(\delta G)$, which is compared to the numerically exact distribution obtained using the scattering matrix approach. We show that $P(\delta G)$ is Gaussian when the sample has a large width-to-length ratio, and study how the expectation value, the standard deviation, and the probability of finding $\delta G < 0$ depend on the anisotropy of the dispersion.