Effects of Spin-Orbit Interactions on Tunneling via Discrete Energy Levels in Metal Nanoparticles

TL;DR

This paper investigates how spin-orbit interactions influence the energy levels and tunneling behavior in aluminum nanoparticles, revealing effects on g-factors, level crossings, and current transport, with implications for superconducting properties.

Contribution

It provides a unified understanding of spin-orbit effects on discrete energy levels and tunneling in metal nanoparticles, incorporating experimental observations and a simple Hamiltonian model.

Findings

Spin-orbit scattering reduces the effective g-factor.

Avoided crossings occur between spin-up and spin-down levels.

Magnetic-field-dependent changes in tunneling current are observed.

Abstract

The presence of spin-orbit scattering within an aluminum nanoparticle affects measurements of the discrete energy levels within the particle by (1) reducing the effective g-factor below the free-electron value of 2, (2) causing avoided crossings as a function of magnetic field between predominantly-spin-up and predominantly-spin-down levels, and (3) introducing magnetic-field-dependent changes in the amount of current transported by the tunneling resonances. All three effects can be understood in a unified fashion by considering a simple Hamiltonian. Spin-orbit scattering from 4% gold impurities in superconducting aluminum nanoparticles produces no dramatic effect on the superconducting gap at zero magnetic field, but we argue that it does modify the nature of the superconducting transition in a magnetic field.