Superconducting single-electron transistor and the phi-modulation of supercurrent

TL;DR

This paper derives an analytical expression for the supercurrent in a superconducting single-electron transistor (SSET) using an analogy with a harmonic oscillator, providing insights into supercurrent modulation.

Contribution

It introduces a novel analytical approach to calculate supercurrent in SSETs by modeling the Hamiltonian as a discrete harmonic oscillator.

Findings

Supercurrent expression closely matches that from a continuous harmonic oscillator model.

Analytical method simplifies understanding of supercurrent behavior in SSETs.

Provides a foundation for further studies on supercurrent modulation in superconducting devices.

Abstract

An analytical expression for the supercurrent of a superconducting single-electron transistor (SSET) is derived. The derivation is based on analogy between the model Hamiltonian for E_J>E_C and a discrete, one-dimensional harmonic oscillator (1DDHO). The resulting supercurrent is nearly identical to the supercurrent obtained from a continuous harmonic oscillator Hamiltonian.