Method for finding the critical temperature of the island in a SET structure

TL;DR

This paper introduces a method to determine the critical temperature of a superconducting island in a single electron transistor by analyzing the zero-bias conductance slope change with temperature, supported by theoretical simulations.

Contribution

The paper presents a novel measurement technique for the critical temperature of superconducting islands in SETs, validated by numerical simulations and applied to Nb islands with high accuracy.

Findings

Critical temperature of Nb island up to 8.5 K

Gap energy of Nb island approximately 1.45 meV

Method accurately determines critical temperature and field

Abstract

We present a method to measure the critical temperature of the island of a superconducting single electron transistor. The method is based on a sharp change in the slope of the zero-bias conductance as a function of temperature. We have used this method to determine the superconducting phase transition temperature of the Nb island of an superconducting single electron transistor with Al leads. We obtain $T_\mathrm{c}^\mathrm{Nb}$ as high as 8.5 K and gap energies up to $\Delta_\mathrm{Nb}\simeq 1.45$ meV. By looking at the zero bias conductance as a function of magnetic field instead of temperature, also the critical field of the island can be determined. Using the orthodox theory, we have performed extensive numerical simulations of charge transport properties in the SET at temperatures comparable to the gap, which match very well the data, therefore providing a solid theoretical basis for our method.