Subharmonic Gap Structure in Superconductor/Ferromagnet/Superconductor Junctions

TL;DR

This paper investigates the subharmonic gap structure in superconductor/ferromagnet/superconductor junctions, revealing how spin-dependent tunneling probabilities and Andreev bound states influence subgap current steps and spin currents at finite temperatures.

Contribution

It provides analytical calculations of split subgap current steps and explores the emergence of spin current subgap structure for odd steps in magnetic junctions.

Findings

Subgap electric current steps are split due to Andreev bound states at finite temperature.

Spin current exhibits subgap structure only for odd steps when spin-dependent tunneling is present.

Analytical expressions for the first two subgap steps are derived.

Abstract

The behavior of dc subgap current in magnetic quantum point contact is discussed for the case of low-transparency junction with different tunnel probabilities for spin-up ($D_\uparrow$) and spin-down ($D_\downarrow$) electrons. Due to the presence of Andreev bound states $\pm \epsilon_0$ in the system the positions of subgap electric current steps $eV_n = (\Delta \pm \epsilon_0)/n$ are split at temperature $T \neq 0$ with respect to the nonmagnetic result $eV_n=2\Delta/n$. It is found that under the condition $D_\uparrow \neq D_\downarrow$ the spin current also manifests subgap structure, but only for odd values of $n$. The split steps corresponding to $n=1,2$ in subgap electric and spin currents are analytically calculated and the following steps are described qualitatively.