Spin-galvanic response to non-equilibrium spin injection in superconductors with spin-orbit coupling

Abstract

We show that nonequilibrium spin injection into a superconductor can generate an anomalous supercurrent or induce a phase gradient, even for spin voltages below the superconducting gap. Our mechanism does not require breaking time-reversal symmetry in the effective superconducting Hamiltonian, but instead relies on nonequilibrium spin injection. We further demonstrate that superconductivity enhances spin injection due to the large quasiparticle density of states near the pairing gap, an effect that persists well below the gap. This contrasts with earlier works predicting the absence of spin injection at zero temperature and small spin voltages. Our results provide a natural explanation for long-standing experimental observations of spin injection in superconductors and predict novel effects arising from spin-charge coupling, including the electrical control of anomalous phase gradients in superconducting systems with spin-orbit coupling. These effects are broadly testable in a variety of materials and hybrid superconducting structures.

Figures (3)

• Figure 1: (a) Schematic of the system under investigation: A normal metal(N) layer sits atop a superconductor. A spin polarized current is injected from a ferromagnetic lea (F). This results in spin accumulations within the normal metal layer, which diffuses toward the region of the metal that lies above the superconductor (S). (b)
• Figure 2: (a) Spectral spin at the injector point, $x=0$ for different values of $l_S$, $T=0$, and $\tilde{\lambda}=0.1$. (b) Dependence of the spin density at $x=\xi_0$ on the spin voltage for different temperatures, $\tilde{\lambda}=0.05$, and $l_S=\xi_0$. (c) Spatial dependency of the injected spin density in the normal state (dashed lines) and superconducting state (solid lines) for two different values of $l_S$, $\tilde{\lambda}=0.05$, $T=0$, and $V_S=0.5\Delta_0$. (d) Temperature dependence of the non-local resistance measured in the setup of Fig. \ref{['Fig:Setup']}(b) for different values of $l_S$, and $\tilde{\lambda}=10^{-3}$. The detector is situated at a distance $2\xi_0$ from the injector.
• Figure 3: The spin voltage dependence of the ratio between the current induced in the superconducting loop of Fig. \ref{['Fig:Setup']}(d) and its value in the normal state for $l_S=L=\xi_0$, and $\eta=0.01\Delta_0$.