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 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 , which is compared to the numerically exact distribution obtained using the scattering matrix approach. We show that 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 depend on the anisotropy of the dispersion.
- Received 25 February 2020
- Accepted 13 July 2020
DOI:https://doi.org/10.1103/PhysRevB.102.024204
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