Tunable superconducting critical temperature in ballistic hybrid structures with strong spin-orbit coupling

TL;DR

This paper provides a theoretical and numerical analysis of how strong spin-orbit coupling influences the superconducting transition temperature in hybrid structures, revealing that $T_c$ can be tuned via spin-orbit strength and magnetic orientation.

Contribution

It introduces a comprehensive model for the effects of Rashba spin-orbit coupling on superconducting critical temperature in various hybrid structures, including the role of exchange field orientation.

Findings

Spin-orbit coupling increases the critical temperature in magnetic fields.

Enhanced spin-orbit coupling boosts the superconducting gap in the density of states.

Tuning $T_c$ is possible with a single ferromagnetic layer in ballistic structures.

Abstract

We present a theoretical description and numerical simulations of the superconducting transition in hybrid structures including strong spin-orbit interactions. The spin-orbit coupling is taken to be of Rashba type for concreteness, and we allow for an arbitrary magnitude of the spin-orbit strength as well as an arbitrary thickness of the spin-orbit coupled layer. This allows us to make contact with the experimentally relevant case of enhanced interfacial spin-orbit coupling via atomically thin heavy metal layers. We consider both interfacial spin-orbit coupling induced by inversion asymmetry in an S/F-junction, as well as in-plane spin-orbit coupling in the ferromagnetic region of an S/F/S- and an S/F-structure. Both the pair amplitudes, local density of states and critical temperature show dependency on the Rashba strength and, importantly, the orientation of the exchange field. In general, spin-orbit coupling increases the critical temperature of a proximity system where a magnetic field is present, and enhances the superconducting gap in the density of states. We perform a theoretical derivation which explains these results by the appearance of long-ranged singlet correlations. Our results suggest that $T_c$ in ballistic spin-orbit coupled superconducting structures may be tuned by using only a single ferromagnetic layer.