No Arabic abstract
We explore correlations of inhomogeneous local density of states (LDoS) for impure superconductors with different symmetries of the order parameter (s-wave and d-wave) and different types of scatterers (elastic and magnetic impurities). It turns out that the LDoS correlation function of superconductor always slowly decreases with distance up to the phase-breaking length $l_{phi}$ and its long-range spatial behavior is determined only by the dimensionality, as in normal metals. On the other hand, the energy dependence of this correlation function is sensitive to symmetry of the order parameter and nature of scatterers. Only in the simplest case of s-wave superconductor with elastic scatterers the inhomogeneous LDoS is directly connected to the corresponding characteristics of normal metal.
A thin superconducting disk, with radius $R=4xi$ and height $H=xi$, is studied in the presence of an applied magnetic field parallel to its major axis. We study how the boundaries influence the decay of the order parameter near the edges for three-dimensional vortex states.
The few-layer transition metal dichalcogenides (TMDs) have been recently suggested as a platform for controlled unconventional superconductivity. We study the manifestations of unconventional triplet pairing in the density of states of a disordered TMD based monolayer. The conventional singlet pairing attraction is assumed to be the dominant pairing interaction. We map the phase diagrams of disordered Ising superconductors in the plane of temperature and the in-plane magnetic field. The latter suppresses singlet and promote triplet correlations. The triplet order parameters of a trivial (non-trivial) symmetry compete (cooperate) with the singlet order parameter which gives rise to a rich phase diagram. We locate the model-dependent phase boundaries and compute the order parameters in each of the distinct phases. With this information, we obtain the density of states by solving the Gorkov equation. The triplet components of the order parameters may change an apparent width of the density of states by significantly increasing the critical field. The triplet components of the order parameters lead to the density of states broadening significantly exceeding the broadening induced by magnetic field and disorder in the singlet superconductor.
In contrast to conventional s-wave superconductivity, unconventional (e.g. p or d-wave) superconductivity is strongly suppressed even by relatively weak disorder. Upon approaching the superconductor-metal transition, the order parameter amplitude becomes increasingly inhomogeneous leading to effective granularity and a phase ordering transition described by the Mattis model of spin glasses. One consequence of this is that at low enough temperatures, between the clean unconventional superconducting and the diffusive metallic phases, there is necessarily an intermediate superconducting phase which exhibits s-wave symmetry on macroscopic scales.
We calculate the density of states of a disordered inhomogeneous d-wave superconductor in a magnetic field. The field-induced vortices are assumed to be pinned at random positions and the effects of the scattering of the quasi-particles off the vortices are taken into account using the singular gauge transformation of Franz and Tesanovic. We find two regimes for the density of states: at very low energies the density of states follows a law rho(epsilon) sim rho_0 + |epsilon|^{alpha} where the exponent is close to 1. A good fit of the density of states is obtained at higher energies, excluding a narrow region around the origin, with a similar power law energy dependence but with alpha close to 2. Both at low and at higher energies rho_0 scales with the inverse of the magnetic length (sqrt{B}).
We study quasiparticle states on a surface of a topological insulator (TI) with proximity-induced superconductivity under an external magnetic field. An applied magnetic field creates two Majorana bound states: a vortex Majorana state localized inside a vortex core and an exterior Majorana state localized along a circle centered at the vortex core. We calculate the spin-resolved local density of states (LDOS) and demonstrate that the shrinking of the radius of the exterior Majorana state, predicted in Ref. [R. S. Akzyanov et al., Phys. Rev. B 94, 125428 (2016)], under a strong magnetic field can be seen in LDOS without smeared out by non-zero-energy states. The spin-resolved LDOS further reveals that the spin of the exterior Majorana state is strongly polarized. Accordingly, the induced odd-frequency spin-triplet pairs are found to be spin-polarized as well. In order to detect the exterior Majorana states, however, the Fermi energy should be closed to the Dirac point to avoid contributions from continuum levels. We also study a different two-dimensional topological-superconducting system where a two-dimensional electron gas with the spin-orbit coupling is sandwiched between an s-wave superconductor and a ferromagnetic insulator. We show that the radius of an exterior Majorana state can be tuned by an applied magnetic field. However, on the contrary to the results at a TI surface, neither the exterior Majorana state nor the induced odd-frequency spin-triplet pairs are spin-polarized. We conclude that the spin-polarization of the Majorana state is attributed to the spin-polarized Landau level which is characteristic for systems with the Dirac-like dispersion.