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 δG 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(δG), which is compared to the numerically exact distribution obtained using the scattering matrix approach. We show that P(δG) 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 δG<0 depend on the anisotropy of the dispersion.