Optimal quantum pump in the presence of a superconducting lead

TL;DR

This paper develops a theoretical framework for understanding quantum pumping in hybrid normal-superconductor quantum dot systems, deriving expressions for electric and heat currents, and establishing bounds on heat current related to shot noise.

Contribution

It introduces a general scattering matrix approach for parametric pumping in hybrid systems with superconducting leads, extending previous normal system results.

Findings

Derived a general expression for pumped electric and heat currents.

Established a lower bound for pumped heat current related to shot noise.

Connected heat current, electric current, and shot noise in hybrid quantum systems.

Abstract

We investigate the parametric pumping of a hybrid structure consisting of a normal quantum dot, a normal lead and a superconducting lead. Using the time dependent scattering matrix theory, we have derived a general expression for the pumped electric current and heat current. We have also derived the relationship among the instantaneous pumped heat current, electric current, and shot noise. This gives a lower bound for the pumped heat current in the hybrid system similar to that of the normal case obtained by Avron et al.