Coulomb effects in a ballistic one-channel S-S-S device

TL;DR

This paper develops a quantum mechanical theory of Coulomb oscillations in a superconducting device with a small grain connected to two leads, predicting periodic Josephson current variations with gate voltage.

Contribution

It introduces a novel theoretical framework for Coulomb effects in a ballistic one-channel superconducting device with finite capacitance and analyzes the Josephson current behavior.

Findings

Josephson energy exhibits two minima degenerate at phase difference π.

Josephson current and fluctuations are periodic in induced charge with period 2e.

The theory applies to low-temperature, small-capacitance superconducting systems.

Abstract

We develop a theory of Coulomb oscillations in superconducting devices in the limit of small charging energy $E_C \ll \Delta$. We consider a small superconducting grain of finite capacity connected to two superconducting leads by nearly ballistic single-channel quantum point contacts. The temperature is supposed to be very low, so there are no single-particle excitations on the grain. Then the behavior of the system may be described as quantum mechanics of the superconducting phase on the island. The Josephson energy as a function of this phase has two minima which become degenerate at the phase difference on the leads equal to $\pi$, the tunneling amplitude between them being controlled by the gate voltage at the grain. We find the Josephson current and its low-frequency fluctuations and predict their periodic dependence on the induced charge $Q_x=C V_g$ with period $2e$.