Anomalous transport in normal-superconducting and ferromagnetic-superconducting nanostructures

TL;DR

This paper investigates the temperature and voltage dependence of conductance in mesoscopic superconductor-normal metal and superconductor-ferromagnet structures, revealing new peaks and non-monotonic behaviors linked to proximity effects and Zeeman splitting.

Contribution

It predicts a new maximum in conductance variation at a temperature where the superconductor's energy gap matches the Thouless energy, and analyzes voltage effects in ferromagnetic-superconductor structures.

Findings

Two peaks in conductance variation at different temperatures.

Non-monotonic voltage dependence at Zeeman splitting energies.

Temperature T_1 determined by phase-breaking length in certain regimes.

Abstract

We have calculated the temperature dependence of the conductance variation ($\delta S(T)$) of mesoscopic superconductor normal metal(S/N) structures, in the diffusive regime, analysing both weak and strong proximity effects. We show that in the case of a weak proximity effect there are two peaks in the dependence of $\delta S(T)$ on temperature. One of them (known from previous studies) corresponds to a temperature $T_1$ of order of the Thouless energy ($\epsilon_{Th}$), and another, newly predicted maximum, occurs at a temperature $T_2$ where the energy gap in the superconductor $\Delta(T_2)$ is of order $\epsilon_{Th}$. In the limit $L_{\phi}<L$ the temperature $T_1$ is determined by $D \hbar /L^2_{\phi}$ ($L_{\phi}$ is the phase breaking length), and not $\epsilon_{Th}$. We have also calculated the voltage dependence $ \delta S(V)$ for a S/F structure (F is a ferromagnet) and predict non-monotonic behaviour at voltages of order the Zeeman splitting.