Charge susceptibility and conductances of a double quantum dot

TL;DR

This paper analyzes the charge susceptibility and conductance properties of a double quantum dot system using nonequilibrium Green functions, providing analytical results for noninteracting cases and extending to interactions, relevant for solid state qubits.

Contribution

It offers analytical expressions for current and conductance in double quantum dots and extends the analysis to include interactions, advancing understanding of quantum dot transport properties.

Findings

Analytical expression for electrical current in noninteracting double quantum dots.

Charge susceptibility peaks as a function of gate voltages.

Extension of the model to interacting quantum dots.

Abstract

We calculate the charge susceptibility and the linear and differential conductances of a double quantum dot coupled to two metallic reservoirs both at equilibrium and when the system is driven away from equilibrium. This work is motivated by recent progress in the realization of solid state spin qubits. The calculations are performed by using the Keldysh nonequilibrium Green function technique. In the noninteracting case, we give the analytical expression for the electrical current and deduce from there the linear conductance as a function of the gate voltages applied to the dots, leading to a characteristic charge stability diagram. We determine the charge susceptibility which also exhibits peaks as a function of gate voltages. We show how the study can be extended to the case of an interacting quantum dot.