Universal quantized spin-Hall conductance fluctuation in graphene

TL;DR

This paper theoretically investigates the universal fluctuation of quantized spin-Hall conductance in graphene, revealing a new universality class with a consistent fluctuation value across different models and a unique distribution shape.

Contribution

It demonstrates that quantized spin-Hall conductance fluctuation in graphene is universal and belongs to a new universality class, independent of symmetry class or model specifics.

Findings

Universal conductance fluctuation value of 0.285 e/4π

One-sided log-normal distribution of conductance with edge states

Universality across different symmetry models

Abstract

We report a theoretical investigation of quantized spin-Hall conductance fluctuation of graphene devices in the diffusive regime. Two graphene models that exhibit quantized spin-Hall effect (QSHE) are analyzed. Model-I is with unitary symmetry under an external magnetic field $B\ne 0$ but with zero spin-orbit interaction, $t_{SO}=0$. Model-II is with symplectic symmetry where B=0 but $t_{SO} \ne 0$. Extensive numerical calculations indicate that the two models have exactly the same universal QSHE conductance fluctuation value $0.285 e/4\pi$ regardless of the symmetry. Qualitatively different from the conventional charge and spin universal conductance distributions, in the presence of edge states the spin-Hall conductance shows an one-sided log-normal distribution rather than a Gaussian distribution. Our results strongly suggest that the quantized spin-Hall conductance fluctuation belongs to a new universality class.