We investigate theoretically how the proximity effect in superconductor/ferromagnet hybrid structures with intrinsic spin-orbit coupling manifests in two measurable quantities, namely the density of states and critical temperature. To describe a general scenario, we allow for both Rashba and Dresselhaus type spin-orbit coupling. Our results are obtained via the quasiclassical theory of superconductivity, extended to include spin-orbit coupling in the Usadel equation and Kupriyanov-Lukichev boundary conditions. Unlike previous works, we have derived a Riccati parametrization of the Usadel equation with spin-orbit coupling which allows us to address the full proximity regime and not only the linearized weak proximity regime. First, we consider the density of states in both SF bilayers and SFS trilayers, where the spectroscopic features in the latter case are sensitive to the phase difference between the two superconductors. We find that the presence of spin-orbit coupling leaves clear spectroscopic fingerprints in the density of states due to its role in creating spin-triplet Cooper pairs. Unlike SF and SFS structures without spin-orbit coupling, the density of states in the present case depends strongly on the direction of magnetization. Moreover, we show that the spin-orbit coupling can stabilize spin-singlet superconductivity even in the presence of a strong exchange field h ∆. This leads to the possibility of a magnetically tunable minigap: changing the direction of the exchange field opens and closes the minigap. We also determine how the critical temperature T c of an SF bilayer is affected by spin-orbit coupling and, interestingly, demonstrate that one can achieve a spin-valve effect with a single ferromagnet. We find that T c displays highly non-monotonic behavior both as a function of the magnetization direction and the type and direction of the spin-orbit coupling, offering a new way to exert control over the superconductivity of proximity structures.

Spin transport via electrons is typically plagued by Joule heating and short decay lengths due to spin-flip scattering. It is known that dissipationless spin currents can arise when using conventional superconducting contacts, yet this has only been experimentally demonstrated when using intricate magnetically inhomogeneous multilayers, or in extreme cases such as half-metals with interfacial magnetic disorder. Moreover, it is unknown how such spin supercurrents decay in the presence of spin-flip scattering. Here, we present a method for generating a spin supercurrent by using only a single homogeneous magnetic element. Remarkably, the spin supercurrent generated in this way does not decay spatially, in stark contrast to normal spin currents that remain polarized only up to the spin relaxation length. We also expose the existence of a superconductivity-mediated torque even without magnetic inhomogeneities, showing that the different components of the spin supercurrent polarization respond fundamentally differently to a change in the superconducting phase difference. This establishes a mechanism for tuning dissipationless spin and charge flow separately, and confirms the advantage that superconductors can offer in spintronics.

In diffusive Josephson junctions the phase-difference φ between the superconductors strongly influences the spectroscopic features of the layer separating them. The observation of a uniform minigap and its phase modulation were only recently experimentally reported, demonstrating agreement with theoretical predictions up to now -a vanishing minigap at φ = π. Remarkably, we find that in the presence of intrinsic spin-orbit coupling a giant proximity effect due to spin-triplet Cooper pairs can develop at φ = π, in complete contrast to the suppressed proximity effect without spin-orbit coupling. We here report a combined numerical and analytical study of this effect, proving its presence solely based on symmetry arguments, which makes it independent of the specific parameters used in experiments. We show that the spectroscopic signature of the triplets is present throughout the entire ferromagnetic layer. Our finding offers a new way to artificially create, control and isolate spin-triplet superconductivity.

We derive the quasiclassical non-equilibrium Eilenberger and Usadel equations to first order in quantities small compared to the Fermi energy, valid for Dirac edge and surface electrons with spin-momentum locking p · σ σ σ, as relevant for topological insulators. We discuss in detail several of the key technical points and assumptions of the derivation, and provide a Riccati-parametrization of the equations. Solving first the equilibrium equations for S/N and S/F bilayers and Josephson junctions, we study the superconducting proximity effect in Dirac materials. Similarly to related works, we find that the effect of an exchange field depends strongly on the direction of the field. Only components normal to the transport direction lead to attenuation of the Cooper pair wavefunction inside the F. Fields parallel to the transport direction lead to phase-shifts in the dependence on the superconducting phase difference for both the charge current and density of states in an S/F/S-junction. Moreover, we compute the differential conductance in S/N and S/F bilayers with an applied voltage bias, and determine the dependence on the length of the N and F regions and the exchange field. arXiv:1606.01249v4 [cond-mat.mes-hall]

We demonstrate that spin supercurrents are conserved upon transmission through a conventional superconductor, even in the presence of spin-dependent scattering by impurities with magnetic moments or spin-orbit coupling. This is fundamentally different from conventional spin currents, which decay in the presence of such scattering, and this has important implications for the usage of superconducting materials in spintronic hybrid structures.