Universal Spin Hall Conductance Fluctuations in Chaotic Dirac Quantum Dots

TL;DR

This paper demonstrates universal spin-Hall conductance fluctuations in chaotic Dirac quantum dots, emphasizing the role of chiral classes over traditional symmetry descriptions, with comprehensive analytical and numerical evidence.

Contribution

It provides the first complete analytical and numerical analysis of universal spin-Hall conductance fluctuations in chiral Dirac quantum dots, highlighting the importance of chiral symmetry classes.

Findings

Universal fluctuations of spin-Hall conductance are demonstrated.

Chiral classes dominate over Wigner-Dyson symmetries in these systems.

Analytical solutions resolve previous outstanding issues.

Abstract

We present complete analytical and numerical results that demonstrate the anomalous universal fluctuations of the spin-Hall conductance in chiral materials such as graphene and topological insulators. We investigated both the corresponding fluctuations, the Universal Fractionated and the Universal Quantized, and also the open channels orbital number crossover between the two regimes. In particular, we show that the Wigner-Dyson symmetries does not properly describe such conductances and the preponderant role of the chiral classes on the Dirac quantum dots. The results are analytical and solve outstanding issues.