Nonlinear Response Approach to Cooper Pair Tunneling in Ultrasmall SIS Junctions

TL;DR

This paper develops a nonlinear response framework to analyze Cooper pair tunneling in ultrasmall SIS junctions, highlighting the role of higher order effects and environmental dissipation at zero temperature.

Contribution

It introduces a nonlinear response approach to calculate Cooper pair tunneling, incorporating higher order perturbation theory and environmental effects.

Findings

Cooper pair current is derived from higher order perturbation theory.

Supercurrent depends on the dissipative component of the Josephson current.

Analysis is performed at zero temperature.

Abstract

Single-charge tunneling in ultrasmall voltage biased SIS junctions in a high-impedance electromagnetic environment is considered. The Cooper pair current is calculated at T=0 on the basis of the elementary tunnel Hamiltonian for quasiparticles. Therefore, the transfer of Cooper pairs emerges automatically as an effect of higher order perturbation theory. The supercurrent also depends on the dissipative part of the Josephson current amplitude.