We numerically investigate the electronic structures around a vortex core in a bilayer superconducting system, with s-wave pairing, Rashba spin-orbit coupling and Zeeman magnetic field, with use of the quasiclassical Green's function method. The Bardeen-Cooper-Schrieffer (BCS) phase and the so-called pair-density wave (PDW) phase appear in the temperature-magnetic-field phase diagram in a bulk uniform system [Phys. Rev. B 86, 134514 (2012)]. In the low magnetic field perpendicular to the layers, the zero-energy vortex bound states in the BCS phase are split by the Zeeman magnetic field. On the other hand, the PDW state appears in the high magnetic field, and sign of the order parameter is opposite between the layers. We find that the vortex core suddenly shrinks and the zero-energy bound states appear by increasing the magnetic field through the BCS-PDW transition. We discuss the origin of the change in vortex core structure between the BCS and PDW states by clarifying the relation between the vortex bound states and the bulk energy spectra. In the high magnetic field region, the PDW state and vortex bound states are protected by the spin-orbit coupling. These characteristic behaviors in the PDW state can be observed by scanning tunneling microscopy/spectroscopy.

Magnetization loss on a twisted superconducting (SC) tape in a ramped magnetic field is theoretically investigated through the use of a power law for the electric field-current density characteristics and a sheet current approximation. First, the Maxwell equation in a helicoidal coordinate system is derived to model a twisted SC tape, taking account of the response to the perpendicular field component in the steady state. We show that a loosely twisted tape can be viewed as the sum of a portion of tilted flat tapes of infinite length by examining the perpendicular field distribution on a twisted tape. The analytic formulae for both magnetization and loss power in the tilted flat tape approximation are verified based on the analytic solution of the reduced Maxwell equation in the loosely twisted tape limit of Lp → ∞ with the twist pitch length Lp. These analytic formulae show that both magnetization and loss power decrease by a factor of B(1 + 1/2n, 1/2)/π (where B is the beta function) for an arbitrary power of SC nonlinear resistivity n, compared with those in a flat tape of infinite length. Finally, the effect of the field-angle dependence of the critical current density Jc on the loss power is investigated, and we demonstrate that it is possible to obtain an approximate estimate of the loss power value via Jc in an applied magnetic field perpendicular to the tape surface (i.e., parallel to the c axis).

We theoretically investigate the quasiparticle scattering rate Γ inside a vortex core in the existence of non-magnetic impurities distributed randomly in a superconductor. We show that the dependence of Γ on the magnetic field direction is sensitive to the sign of the pair potential. The behavior of Γ is quite different between an s-wave and a d-wave pair potential, where these are assumed to have the same amplitude anisotropy, but a sign change only for the d-wave one. It is suggested that measurements of the microwave surface impedance with changing applied-field directions would be used for the phase-sensitive identification of pairing symmetry.

We theoretically investigate a non-magnetic impurity effect on the temperature dependence of the vortex core shrinkage (Kramer-Pesch effect) in a single-band s-wave superconductor. The Born limit and the unitary limit scattering are compared within the framework of the quasiclassical theory of superconductivity. We find that the impurity effect inside a vortex core in the unitary limit is weaker than in the Born one when a system is in the moderately clean regime, which results in a stronger core shrinkage in the unitary limit than in the Born one.