Rate equations for Coulomb blockade with ferromagnetic leads

TL;DR

This paper introduces a density-matrix rate-equation approach for analyzing Coulomb blockade in systems with ferromagnetic leads, capturing correlations beyond standard models and applicable to complex multi-electron scenarios.

Contribution

It develops a versatile density-matrix formalism for Coulomb blockade with ferromagnetic leads, extending analysis capabilities beyond traditional rate equations.

Findings

Density-matrix approach captures correlations in degenerate states.

Formalism applies to arbitrary electron numbers and lead polarizations.

May be necessary even with unpolarized leads for multi-level systems.

Abstract

We present a density-matrix rate-equation approach to sequential tunneling through a metal particle weakly coupled to ferromagnetic leads. The density-matrix description is able to deal with correlations between degenerate many-electron states that the standard rate equation formalism in terms of occupation probabilities cannot describe. Our formalism is valid for an arbitrary number of electrons on the dot, for an arbitrary angle between the polarization directions of the leads, and with or without spin-orbit scattering on the metal particle. Interestingly, we find that the density-matrix description may be necessary even for metal particles with unpolarized leads if three or more single-electron levels contribute to the transport current and electron-electron interactions in the metal particle are described by the `universal interaction Hamiltonian'.