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

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.

Universal features of spin transport and breaking of unitary symmetries

“…The latter are similar to those of the β = 4 ensemble at large N , a finding already reported in Ref. [11] for specific fourterminal setups, but deviate from it at small N . Our finding does not invalidate Dyson's classification-the latter gives a complete classification of unitary scattering matrices and unless one introduces chiral or particle-hole symmetries [12,13], there is no new ensemble to be found.…”

“…The SO coupling strength K so is related to the SO rotation time τ so (in units of the stroboscopic period) through τ so = 32π 2 /K 2 so M 2 [23]. From (11), we construct the quasienergy-dependent scattering matrix as…”

Quantum Interference Effects for the Electronic Fluctuations in Quantum Dots

“…Our study provides several important regimes and show a great possibility to measure [27,28] the effect of quantum interference in nonequilibrium fluctuations in chaotic nonideal nanostructures. The conclusion that the Zeeman effect has strong phenomenological implications to the temporal fluctuations of the conductance (noise) is a useful information on spintronics for future investigations following the perspective of [29]. Another interesting future study is to investigate the role of the Zeeman effect and temperature on universal conductance fluctuations following this work and [30].…”

Mesoscopic Fluctuations: Nuclei, Quantum Dots, and Beyond

“…In collaboration with Hussein, we have shown that the correlation functions of the charge and spin currents in multi-terminal chaotic quantum dots exhibit quite peculiar universal relationships as a function of the ratio of the open channels at the transverse and longitudinal terminals. These results indicate the path for developing efficient setup geometries for the measurement of spin current [23].…”