Two parameter scaling in the crossover from symmetry class BDI to AI

Saumitran Kasturirangan, Alex Kamenev, and Fiona J. Burnell
Phys. Rev. B 105, 174204 – Published 10 May 2022

Abstract

The transport statistics of the 1D chain and metallic armchair graphene nanoribbons with hopping disorder are studied, with a focus on understanding the crossover between the zero-energy critical point and the localized regime at larger energy. In this crossover region, transport is found to be described by a two parameter scaling with the ratio s of system size to mean free path, and the product r of energy and scattering time. This two parameter scaling shows excellent data collapse across a wide a variety of system sizes, energies, and disorder strengths. The numerically obtained transport distributions in this regime are found to be well described by a Nakagami distribution, whose form is controlled up to an overall scaling by the ratio s/|lnr|2. For sufficiently small values of this parameter, transport appears virtually identical to that of the zero-energy critical point, while at large values, a Gaussian distribution corresponding to exponential localization is recovered. For intermediate values, the distribution interpolates smoothly between these two limits.

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  • Received 20 January 2022
  • Revised 3 May 2022
  • Accepted 4 May 2022

DOI:https://doi.org/10.1103/PhysRevB.105.174204

©2022 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Saumitran Kasturirangan1, Alex Kamenev1,2, and Fiona J. Burnell1

  • 1School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA
  • 2William I. Fine Theoretical Physics Institute, University of Minnesota, Minneapolis, Minnesota 55455, USA

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Issue

Vol. 105, Iss. 17 — 1 May 2022

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