Generalized correlation functions for conductance fluctuations and the mesoscopic spin Hall effect

TL;DR

This paper derives universal formulas for conductance fluctuations in mesoscopic systems, revealing unique statistical behaviors at the symplectic-unitary crossover, with potential for experimental validation.

Contribution

It introduces generalized correlation functions for conductance fluctuations and analyzes their behavior in the mesoscopic spin Hall effect, especially at the crossover regime.

Findings

Universal expressions for spin and charge current fluctuations.

Deformed Lorentzian shape lines for correlation functions.

Distinct statistical features at the symplectic-unitary crossover.

Abstract

We study the spin-Hall conductance fluctuations in ballistic mesoscopic systems. We obtain universal expressions for the spin and charge current fluctuations, cast in terms of current-current autocorrelation functions. We show that the latter are conveniently parametrized as deformed Lorentzian shape lines, functions of an external applied magnetic field and the Fermi energy. We find that the charge current fluctuations show quite unique statistical features at the symplectic-unitary crossover regime. Our findings are based on an evaluation of the generalized transmission coefficients correlation functions within the stub model and are amenable to experimental test.