Transport and semiclassical dynamics of coupled quantum dots interacting with a local magnetic moment

TL;DR

This paper develops a semiclassical theory for magnetotransport in coupled quantum dots interacting with a local magnetic moment, revealing complex spin dynamics, current-induced magnetization, and oscillatory behaviors in electron transport.

Contribution

It introduces a nonlinear set of Ehrenfest equations for electron and spin dynamics in coupled quantum dots, incorporating spin coherences and anisotropic interactions, advancing understanding of spin-dependent transport phenomena.

Findings

Current-induced magnetization of the local spin observed.

Anisotropic coupling causes parametric oscillations in current.

Rich dynamics including Larmor precession and dissipative coherence effects.

Abstract

We present a theory of magnetotransport through a system of two coupled electronic orbitals, where the electron spin interacts with a (large) local magnetic moment via an exchange interaction. For the physical realization of such a set-up we have in mind, for example, semiconductor quantum dots coupled to an ensemble of nuclear spins in the host material or molecular orbitals coupled to a local magnetic moment. Using a semiclassical approximation, we derive a set of Ehrenfest equations of motion for the electron density matrix and the mean value of the external spin (Landau equations): Due to the spin coupling they turn out to be nonlinear and, importantly, also coherences between electron states with different spin directions need to be considered. The electronic spin-polarized leads are implemented in form of a Lindblad-type dissipator in the infinite bias limit. We have solved this involved dynamical system numerically for various isotropic and anisotropic coupling schemes. For isotropic spin coupling and spin-polarized leads we study the effect of current-induced magnetization of the attached spin and compare this with a single quantum dot set-up. We further demonstrate that an anisotropic coupling can lead to a rich variety of parametric oscillations in the average current reflecting the complicated interplay between the Larmor precession of the external spin and the dissipative coherent dynamics of the electron spin.