Parity Effects on Electron Tunneling through Small Superconducting Islands

TL;DR

This paper investigates how electron number parity influences tunneling in small superconducting islands, revealing temperature-dependent periodicity changes and complex effects on tunneling processes, supported by theoretical analysis including lead excitations.

Contribution

It provides a detailed theoretical analysis of parity effects on electron tunneling, including the influence of superconducting leads, explaining experimental observations.

Findings

Tunneling rates depend on electron parity and temperature.

System exhibits 2e-periodic behavior at low temperature, e-periodic at higher temperature.

Parity effects significantly alter I-V characteristics in superconducting transistors.

Abstract

Single electron tunneling into small superconducting islands is sensitive to the gap energy of the excitations created in the process and, hence, depends on the electron number parity. At low temperature the properties of the system are 2e-periodic in the applied gate voltage, turning e-periodic at higher temperature. We evaluate the tunneling rates and determine the probabilities for the even and odd state as well as the cross-over condition from the balance between different processes. Our analysis includes excitations in the leads. They are essential if the leads are superconducting. The influence of parity effects on single electron tunneling, Cooper pair tunneling, and the Andreev reflection in superconducting transistors yields rich structures in the I-V characteristic, which explains recent experimental findings.