Linear conductance in Coulomb-blockade quantum dots in the presence of interactions and spin

TL;DR

This paper analyzes the linear conductance of Coulomb-blockade quantum dots considering interactions beyond charging energy, using rate equations in different thermalization regimes and deriving simplified expressions under spin-rotation invariance.

Contribution

It provides a comprehensive rate-equation framework for calculating conductance in quantum dots with complex interactions and spin effects, including closed-form solutions in specific limits.

Findings

Closed-form conductance solutions in elastic and rapid-thermalization limits.

Simplified conductance expressions for spin-rotation invariant Hamiltonians.

Identification of conditions where inelastic scattering impacts conductance.

Abstract

We discuss the calculation of the linear conductance through a Coulomb-blockade quantum dot in the presence of interactions beyond the charging energy. In the limit where the temperature is large compared with a typical tunneling width, we use a rate-equations approach to describe the transitions between the corresponding many-body states. We discuss both the elastic and rapid-thermalization limits, where the rate of inelastic scattering in the dot is either small or large compared with the elastic transition rate, respectively. In the elastic limit, we find several cases where a closed solution for the conductance is possible, including the case of a constant exchange interaction. In the rapid-thermalization limit, a closed solution is possible in the general case. We show that the corresponding expressions for the linear conductance simplify for a Hamiltonian that is invariant under spin rotations.