Currents induced by magnetic impurities in superconductors with spin-orbit coupling

Magnetoelectric effects in Josephson junctions

The review is devoted to the fundamental aspects and characteristic features of the magnetoelectric effects, reported in the literature on Josephson junctions (JJs). The main focus of the review is on the manifestations of the direct and inverse magnetoelectric effects in various types of Josephson systems. They provide a coupling of the magnetization in superconductor/ferromagnet/superconductor JJs to the Josephson current. The direct magnetoelectric effect is a driving force of spin torques acting on the ferromagnet inside the JJ. Therefore it is of key importance for the electrical control of the magnetization. The inverse magnetoelectric effect accounts for the back action of the magnetization dynamics on the Josephson subsystem, in particular, making the JJ to be in the resistive state in the presence of the magnetization dynamics of any origin. The perspectives of the coupling of the magnetization in JJs with ferromagnetic interlayers to the Josephson current via the magnetoelectric effects are discussed.

Supercurrent Induced by Chiral Coupling in Multiferroic/Superconductor Nanostructures

We study the transport and the superconducting dynamics in a layer of type II superconductor (SC) with a normal top layer that hosts a helical magnetic ordering that gives rise to spin-current-driven ferroelectric polarization. Proximity effects akin to this heterostructure result in an anisotropic supercurrent transport and modify the dynamic properties of vortices in the SC. The vortices can be acted upon and controlled by electric gating or other means that couple to the spin ordering in the top layer, which, in turn, alter the superconducting/helical magnet coupling characteristics. We demonstrate, using the time dependent Ginzburg-Landau approach, how the spin helicity of the top layer can be utilized for pinning and guiding the vortices in the superconducting layer.

In-gap states of magnetic impurity in quantum spin Hall insulator proximitized to a superconductor

We study in-gap states of a single magnetic impurity embedded in a honeycomb monolayer which is deposited on superconducting substrate. The intrinsic spin-orbit coupling induces the quantum spin Hall insulating (QSHI) phase gapped around the Fermi energy. Under such circumstances we consider the emergence of Shiba-like bound states driven by the superconducting proximity effect. We investigate their topography, spin-polarization and signatures of the quantum phase transition manifested by reversal of the local currents circulating around the magnetic impurity. These phenomena might be important for more exotic in-gap quasiparticles in such complex nanostructures as magnetic nanowires or islands, where the spin-orbit interaction along with the proximity induced electron pairing give rise to topological phases hosting the protected boundary modes.

Delocalisation of Majorana quasiparticles in plaquette-nanowire hybrid system

Interplay between superconductivity, spin-orbit coupling and magnetic field can lead to realisation of the topologically non–trivial states which in finite one dimensional nanowires are manifested by emergence of a pair of zero-energy Majorana bound states. On the other hand, in two dimensional systems the chiral edge states can appear. We investigate novel properties of the bound states in a system of mixed dimensionality, composed of one-dimensional nanowire connected with two-dimensional plaquette. We study this system, assuming either its part or the entire structure to be in topologically non–trivial superconducting state. Our results show delocalisation of the Majorana modes, upon leaking from the nanowire to the plaquette with some tendency towards its corners.

Spin-Orbit induced phase-shift in Bi2Se3 Josephson junctions

The transmission of Cooper pairs between two weakly coupled superconductors produces a superfluid current and a phase difference; the celebrated Josephson effect. Because of time-reversal and parity symmetries, there is no Josephson current without a phase difference between two superconductors. Reciprocally, when those two symmetries are broken, an anomalous supercurrent can exist in the absence of phase bias or, equivalently, an anomalous phase shift φ₀ can exist in the absence of a superfluid current. We report on the observation of an anomalous phase shift φ₀ in hybrid Josephson junctions fabricated with the topological insulator Bi₂Se₃ submitted to an in-plane magnetic field. This anomalous phase shift φ₀ is observed directly through measurements of the current-phase relationship in a Josephson interferometer. This result provides a direct measurement of the spin-orbit coupling strength and open new possibilities for phase-controlled Josephson devices made from materials with strong spin-orbit coupling.

Interplay between pairing and correlations in spin-polarized bound states

We investigate single and multiple defects embedded in a superconducting host, studying the interplay between the proximity-induced pairing and interactions. We explore the influence of the spin-orbit coupling on energies, polarization and spatial patterns of the bound (Yu-Shiba-Rusinov) states of magnetic impurities in a two-dimensional square lattice. We also address the peculiar bound states in the proximitized Rashba chain, resembling the Majorana quasiparticles, focusing on their magnetic polarization that has been recently reported by S. Jeon et al. (Science2017,358, 772). Finally, we study leakage of these polarized Majorana quasiparticles into side-attached nanoscopic regions and confront them with the subgap Kondo effect near to the singlet-doublet phase transition.

Impurity bound states in fully gapped d-wave superconductors with subdominant order parameters

Impurities in superconductors and their induced bound states are important both for engineering novel states such as Majorana zero-energy modes and for probing bulk properties of the superconducting state. The high-temperature cuprates offer a clear advantage in a much larger superconducting order parameter, but the nodal energy spectrum of a pure d-wave superconductor only allows virtual bound states. Fully gapped d-wave superconducting states have, however, been proposed in several cuprate systems thanks to subdominant order parameters producing d + is- or d + id'-wave superconducting states. Here we study both magnetic and potential impurities in these fully gapped d-wave superconductors. Using analytical T-matrix and complementary numerical tight-binding lattice calculations, we show that magnetic and potential impurities behave fundamentally different in d + is- and d + id'-wave superconductors. In a d + is-wave superconductor, there are no bound states for potential impurities, while a magnetic impurity produces one pair of bound states, with a zero-energy level crossing at a finite scattering strength. On the other hand, a d + id'-wave symmetry always gives rise to two pairs of bound states and only produce a reachable zero-energy level crossing if the normal state has a strong particle-hole asymmetry.

Composite Topological Excitations in Ferromagnet-Superconductor Heterostructures

We investigate the formation of a new type of composite topological excitation-the Skyrmion-vortex pair (SVP)-in hybrid systems consisting of coupled ferromagnetic and superconducting layers. Spin-orbit interaction in the superconductor mediates a magnetoelectric coupling between the vortex and the Skyrmion, with a sign (attractive or repulsive) that depends on the topological indices of the constituents. We determine the conditions under which a bound SVP is formed and characterize the range and depth of the effective binding potential through analytical estimates and numerical simulations. Furthermore, we develop a semiclassical description of the coupled Skyrmion-vortex dynamics and discuss how SVPs can be controlled by applied spin currents.

Magnetic chains on a triplet superconductor

The topological state of a two-dimensional triplet superconductor may be changed by an appropriate addition of magnetic impurities. A ferromagnetic magnetic chain at the surface of a superconductor with spin-orbit coupling may eliminate the edge states of a finite system giving rise to localized zero modes at the edges of the chain. The coexistence/competition between the two types of zero modes is considered. The reduction of the system to an effective 1d system gives partial information on the topological properties but the study of the two sets of zero modes requires a two-dimensional treatment. Increasing the impurity density from a magnetic chain to magnetic islands leads to a finite Chern number. At half-filling small concentrations are enough to induce chiral modes.