The long-range spin-singlet proximity effect for the Josephson system with single-crystal ferromagnet due to its band structure features

TL;DR

This paper explains the long-range proximity effect in a ferromagnetic nanowire using a band structure-based theoretical model, highlighting how anisotropies and effective masses influence superconducting correlations.

Contribution

It introduces a novel theoretical approach connecting band structure features with the long-range proximity effect in ferromagnets, considering effective mass differences and Fermi surface anisotropy.

Findings

Effective exchange interaction can be fully compensated along certain crystallographic directions.

The model aligns with experimental observations of long-range proximity effects.

Comparison with previous theories highlights unique band structure considerations.

Abstract

The possible explanation of the long-range proximity effect observed in the single-crystalline cobalt nanowire sandwiched between two tungsten superconducting electrodes [Wang, M. \textit{et al}. \textit{ Nat. Phys}. \textbf{6}, 389 (2010)] is proposed. The theoretical approach is based on the features of band structure of a ferromagnet. To connect the exchange field with the momentum of quasiparticles the distinction between their effective masses in majority and minority spin bands and the Fermi surface anisotropy are taken into account. The derived Eilenberger-like equations allow to obtain the renormalized effective exchange interaction that can be completely compensated for some crystallographic direction under certain conditions. The proposed theoretical model is also compared with previous approaches.