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The geometrical properties of a helical ferromagnet are shown theoretically to control the critical temperature of a proximity-coupled superconductor. Using the Usadel equation for diffusive spin transport, we provide self-consistent analysis of how curvature and torsion modulate the proximity effect. When the helix is attached to a piezoelectric actuator, the pitch of the helix -- and hence the superconducting transition -- can be controlled electrically.

We study the effect of ferromagnetic metals (FM) on the circularly polarized modes of an electromagnetic cavity and show that broken time-reversal symmetry leads to a dichroic response of the cavity modes. With one spin-split band, the Zeeman coupling between the FM electrons and cavity modes leads to an anticrossing for mode frequencies comparable to the spin splitting. However, this is only the case for one of the circularly polarized modes, while the other is unaffected by the FM, allowing for the determination of the spin-splitting of the FM using polarization-dependent transmission experiments. Moreover, we show that for two spin-split bands, also the lifetimes of the cavity modes display a polarization-dependent response. The change in photon lifetimes can be understood as a suppression due to level attraction with a continuum of Stoner modes with the same wavevector. The reduced lifetime of modes of only one polarization could potentially be used to engineer and control circularly polarized cavities., Comment: 5 pages, 3 figures

We show that tailoring the geometric curvature profile of magnets can be used for bespoke design of an effective non-relativistic spin-orbit coupling, which may be used to control proximity effects if the magnet is coupled to a superconductor. We consider proximity-coupled one-dimensional magnetic wires with variable curvatures, specifically three distinct shapes classified as J-, C-, and S-type. We demonstrate a chirality-dependent spin polarization of the superconducting correlations, and show the role of curvature in determining the ground state of mixed-chirality junctions. We speculate on how this may be implemented in novel device design, and include analysis of its usage in a spin-triplet SQUID, Comment: 11 pages, 6 figures

We propose that geometric curvature and torsion may be used to probe the quality of an uncompensated antiferromagnetic interface, using the proximity effect. We study a helix of antiferromagnetic wire coupled to a conventional superconductor, and show that a density of states measurement can give information about the quality of an uncompensated interface, crucial for many recently predicted antiferromagnetic proximity effects. Furthermore, we show that geometric curvature alone can result in long-ranged superconducting triplet correlations in the antiferromagnet, and we discuss the impact curvature and torsion can have on the future development of superconducting spintronic devices., Comment: 9 pages, 5 figures

A recent proof of concept showed that cavity photons can mediate superconducting (SC) signatures to a ferromagnetic insulator (FI) over a macroscopic distance [Phys. Rev. B, 102, 180506(R) (2020)]. In contrast with conventional proximity systems, this facilitates long-distance FI$\unicode{x2013}$SC coupling, local subjection to different drives and temperatures, and studies of their mutual interactions without proximal disruption of their orders. Here we derive a microscopic theory for these interactions, with an emphasis on the leading effect on the FI, namely, an induced anisotropy field. In an arbitrary practical example, we find an anisotropy field of $14 \unicode{x2013} 16$ $\mu$T, which is expected to yield an experimentally appreciable tilt of the FI spins for low-coercivity FIs such as Bi-YIG. We discuss the implications and potential applications of such a system in the context of superconducting spintronics., Comment: 17 pages, 8 figures

When applying an external magnetic field to a superconductor, orbital and Pauli paramagnetic pairbreaking effects govern the limit of the upper critical magnetic field that can be supported before superconductivity breaks down. Experimental studies have shown that many multiband superconductors exhibit values of the upper critical magnetic field that violate the theoretically predicted limit, giving rise to many studies treating the underlying mechanisms that allow this. In this work we consider spin-splitting induced by an external magnetic field in a superconductor with two relevant bands close to the Fermi level, and show that the presence of interband superconducting pairing produces high-field reentrant superconductivity violating the Pauli-Chandrasekhar-Clogston limit for the value of the upper critical magnetic field.

Coupling a conventional s-wave superconductor to a ferromagnet allows, via the proximity effect, to generate superconducting triplet correlations. This feature can be employed to achieve a superconducting triplet spin-valve effect in superconductor-ferromagnet (SF) hybrid structures, for example by switching the magnetizations of the ferromagnets between parallel and antiparallel configurations in F1SF2 and SF1F2 trilayers, or in SF bilayers with both Rashba and Dresselhaus SOC. It was recently reported that geometric curvature can control the generation of long ranged triplets. We use this property to show that the superconducting critical temperature of an SF hybrid nanowire can be tuned by varying the curvature of the ferromagnetic side alone, with no need of another ferromagnet or SOC. We show that the variation of the critical temperature as a function of the curvature can be exploited to obtain a robust, curvature-controlled, superconducting triplet spin-valve effect. Furthermore, we perform an analysis with the inclusion of spin-orbit coupling and explain how it modifies the spin-valve effect both quantitatively and qualitatively., Comment: 13 pages, 7 figures

We study the magnon-mediated pairing between fermions on the surface of a topological insulator (TI) coupled to a ferromagnetic insulator with a tilted mean field magnetization. Tilting the magnetization towards the interfacial plane reduces the magnetic band gap and leads to a shift in the effective TI dispersions. We derive and solve the self-consistency equation for the superconducting gap in two different situations, where we neglect or include the frequency dependence of the magnon propagator. Neglecting the frequency dependence results in p-wave Amperean solutions. We also find that tilting the magnetization into the interface plane favors Cooper pairs with center of mass momenta parallel to the magnetization vector, increasing $T_c$ compared to the out-of-plane case. Including the frequency dependence of the magnon propagator, and solving for a low number of Matsubara frequencies, we find that the eigenvectors of the Amperean solutions at the critical temperature are dominantly odd in frequency and even in momentum, thus opening the possibility for odd-frequency Amperean pairing., Comment: 11 pages, 8 figures, updated version

We study the inverse proximity effect in a bilayer consisting of a thin $s$- or $d$-wave superconductor (S) and a topological insulator (TI). Integrating out the topological fermions of the TI, we find that spin-orbit coupling is induced in the S, which leads to spin-triplet $p$-wave ($f$-wave) correlations in the anomalous Green's function for an $s$-wave ($d$-wave) superconductor. Solving the self-consistency equation for the superconducting order parameter, we find that the inverse proximity effect can be strong for parameters for which the Fermi momenta of the S and TI coincide. The suppression of the gap is approximately proportional to $e^{-1/\lambda}$, where $\lambda$ is the dimensionless superconducting coupling constant. This is consistent with the fact that a higher $\lambda$ gives a more robust superconducting state. For an $s$-wave S, the interval of TI chemical potentials for which the suppression of the gap is strong is centered at $\mu_{TI} = \pm\sqrt{2mv_F^2\mu}$, and increases quadratically with the hopping parameter $t$. Since the S chemical potential $\mu$ typically is high for conventional superconductors, the inverse proximity effect is negligible except for $t$ above a critical value. For sufficiently low $t$, however, the inverse proximity effect is negligible, in agreement with what has thus far been assumed in most works studying the proximity effect in S-TI structures. In superconductors with low Fermi energies, such as high-$T_c$ cuprates with $d$-wave symmetry, we again find a suppression of the order parameter. However, since $\mu$ is much smaller in this case, a strong inverse proximity effect can occur at $\mu_{TI}=0$ for much lower values of $t$. Moreover, the onset of a strong inverse proximity effect is preceded by an increase in the order parameter, allowing the gap to be tuned by several orders of magnitude by small variations in $\mu_{TI}$., Comment: 11 pages, 4 figures, updated version

Spin-valve structures are usually associated with the ability to modify the resistance of electrical currents. We here demonstrate a profoundly different effect of a spin-valve. In combination with a topological insulator and superconducting materials, we show that a spin-valve can be used to toggle quantum vortices in and out of existence. In the antiparallel configuration, the spin-valve causes superconducting vortex nucleation. In the parallel configuration, however, no vortices appear. This switching effect suggests a new way to control quantum vortices., Comment: 4 pages, 4 figures

We study the effective interactions between Dirac fermions on the surface of a three-dimensional topological insulator due to the proximity coupling to the magnetic fluctuations in a ferromagnetic or antiferromagnetic insulator. Our results show that the magnetic fluctuations can mediate attractive interactions between Dirac fermions of both Amperean and BCS type. In the ferromagnetic case, we find pairing between fermions with parallel momenta, so-called Amperean pairing, whenever the effective Lagrangian for the magnetic fluctuations does not contain a quadratic term. The pairing interaction also increases with increasing Fermi momentum, and is in agreement with previous studies in the limit of high chemical potential. If a quadratic term is present, the pairing is instead of BCS type above a certain chemical potential. In the antiferromagnetic case, BCS pairing occurs when the ferromagnetic coupling between magnons on the same sublattice exceeds the antiferromagnetic coupling between magnons on different sublattices. Outside this region in parameter space, we again find that Amperean pairing is realized., Comment: 9 pages, 6 figures, revised version

We study the superconducting order in a two-dimensional square lattice Hubbard model with weak repulsive interactions, subject to a Zeeman field and weak Rashba spin-orbit interactions. Diagonalizing the non-interacting Hamiltonian leads to two separate bands, and by deriving an effective low-energy interaction we find the mean field gap equations for the superconducting order parameter on the bands. Solving the gap equations just below the critical temperature, we find that superconductivity is caused by Kohn-Luttinger type interaction, while the pairing symmetry of the bands are indirectly affected by the spin-orbit coupling. The dominating attractive momentum channel of the Kohn-Luttinger term depends on the filling fraction $n$ of the system, and it is therefore possible to change the momentum dependence of the order parameter by tuning $n$. Moreover, $n$ also determines which band has the highest critical temperature. Rotating the magnetic field changes the momentum dependence from states that for small momenta reduce to a chiral $p_x \pm i p_y$ type state for out-of-plane fields, to a nodal p-wave type state for purely in-plane fields., Comment: 10 pages, 8 figures, revised version

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, 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., Comment: 13 pages, 5 figures. Accepted for publication in Phys. Rev. B