Weak localization correction to the density of transmission eigenvalues in the presence of magnetic field and spin-orbit coupling for a chaotic quantum dot

TL;DR

This paper calculates the weak localization correction to transmission eigenvalues in chaotic quantum dots, considering magnetic field and spin-orbit effects, and applies results to conductance, shot noise, and charge distribution.

Contribution

It introduces a comprehensive Random Matrix Theory framework including magnetic and spin-orbit effects for chaotic quantum dots, with practical applications to transport properties.

Findings

Derived correction formulas for conductance, shot noise, and charge cumulants.

Interpreted results in terms of Cooperon modes.

Enhanced understanding of quantum interference effects in mesoscopic systems.

Abstract

We calculated the weak localization correction to the density of the transmission eigenvalues in the case of chaotic quantum dots in the framework of Random Matrix Theory including the parametric dependence on the magnetic field and spin-orbit coupling. The result is interpreted in terms of spin singlet and triplet Cooperon modes of conventional diagrammatic perturbation theory. As simple applications, we obtained the weak localization correction to the conductance, the shot noise power and the third cumulant of the distribution of the transmitted charge.