How spin-orbit interaction can cause electronic shot noise

TL;DR

This paper investigates how spin-orbit interaction influences shot noise in ballistic quantum dots, revealing a scaling law that connects spin precession length and shot noise suppression.

Contribution

It introduces a new understanding of shot noise suppression involving spin-orbit interaction and derives a scaling law based on the ratio of spin precession length to Fermi wavelength.

Findings

Shot noise suppression depends on the ratio l_{so}/lambda_F.

Derived a scaling law for shot noise in terms of spin precession length.

Computer simulations confirm the theoretical scaling behavior.

Abstract

The shot noise in the electrical current through a ballistic chaotic quantum dot with N-channel point contacts is suppressed for N --> infinity, because of the transition from stochastic scattering of quantum wave packets to deterministic dynamics of classical trajectories. The dynamics of the electron spin remains quantum mechanical in this transition, and can affect the electrical current via spin-orbit interaction. We explain how the role of the channel number N in determining the shot noise is taken over by the ratio l_{so}/lambda_F of spin precession length l_{so} and Fermi wave length lambda_F, and present computer simulations in a two-dimensional billiard geometry (Lyapunov exponent alpha, mean dwell time tau_{dwell}, point contact width W) to demonstrate the scaling (lambda_F/l_{so})^{1/alpha tau_{dwell}} of the shot noise in the regime lambda_F << l_{so} << W.