Anomalous Joule law in the adiabatic dynamics of a normal-superconductor quantum dot

TL;DR

This paper develops a comprehensive theory for the adiabatic charge and energy transport in a quantum dot coupled to normal and superconducting reservoirs, revealing an anomalous Joule law with four parallel channels including pairing effects.

Contribution

It introduces a generalized framework for adiabatic quantum dot dynamics incorporating Andreev processes and pairing fluctuations, highlighting an anomalous Joule law with four transport channels.

Findings

Energy dissipation follows a four-channel Joule law with universal resistance.

Pairing fluctuations induce an anomalous Joule component without net current.

The theory extends quantum RC circuit models to include superconducting effects.

Abstract

We formulate a general theory to study the time-dependent charge and energy transport of an adiabatically driven quantum dot in contact to normal and superconducting reservoirs at T=0. This setup is a generalization of a quantum RC circuit, with capacitive components due to Andreev processes and induced pairing fluctuations, in addition to the convencional normal charge fluctuations. The dynamics for the dissipation of energy is ruled by a Joule law of four channels in parallel with the universal B\"uttiker resistance R_0=e^2/2h per channel. Two transport channels are associated to the two spin components of the usual charge fluctuations, while the other two are associated to electrons and holes due to pairing fluctuations. The latter leads to an "anomalous" component of the Joule law and take place with a vanishing net current due to the opposite flows of electrons and holes.