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

Zheng Shi, Björn Sbierski, and Piet W. Brouwer
Phys. Rev. B 102, 024204 – Published 21 July 2020

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.

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  • Received 25 February 2020
  • Accepted 13 July 2020

DOI:https://doi.org/10.1103/PhysRevB.102.024204

©2020 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Zheng Shi1, Björn Sbierski1,2, and Piet W. Brouwer1

  • 1Dahlem Center for Complex Quantum Systems and Physics Department, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
  • 2Department of Physics, University of California, Berkeley, California 94720, USA

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Issue

Vol. 102, Iss. 2 — 1 July 2020

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