We investigate theoretically the dependence of magnetization loss of a helically wound superconducting tape on the round core radius $R$ and the helical conductor pitch in a ramped magnetic field. Using the thin-sheet approximation, we identify the t
wo-dimensional equation that describes Faradays law of induction on a helical tape surface in the steady state. Based on the obtained basic equation, we simulate numerically the current streamlines and the power loss $P$ per unit tape length on a helical tape. For $R gtrsim w_0$ (where $w_0$ is the tape width), the simulated value of $P$ saturates close to the loss power $sim(2/pi)P_{rm flat}$ (where $P_{rm flat}$ is the loss power of a flat tape) for a loosely twisted tape. This is verified quantitatively by evaluating power loss analytically in the thin-filament limit of $w_0/Rrightarrow 0$. For $R lesssim w_0$, upon thinning the round core, the helically wound tape behaves more like a cylindrical superconductor as verified by the formula in the cylinder limit of $w_0/Rrightarrow 2pi$, and $P$ decreases further from the value for a loosely twisted tape, reaching $sim (2/pi)^2 P_{rm flat}$.
We investigate quasi-particle excitation modes and the topological number of a fractional-flux quantum vortex in a layered (multi-component) superconductor. The Bogoliubov equation for a half-flux quantum vortex is solved to show that there is no low
-lying Andreev bound state near zero energy in the core of a quantum vortex, which is surprisingly in contrast to the result for an inter-flux vortex. Related to this result, there are singular excitation modes that have opposite angular momenta, moving in the opposite direction around the core of the vortex. The topological index (skyrmion number) for a fractional-flux quantum vortex becomes fractional since the topological index is divided into two parts where one from the vortex (bulk) and the other from the kink (domain wall, boundary). The topological numbers for both the vortex and the kink (domain wall) are fractional, and their sum becomes an integer. This shows an interesting analogy between this result and the index theorem for manifolds with boundary. We argue that fractional-flux quantum vortices are not commutative each other and follow non-abelian statistics. This non-abelian statistics of vortices is different from that in p-wave superconductors.
We investigate theoretically the magnetization loss and electromagnetic coupling of twisted multi-filament superconducting (SC) tapes in a ramped magnetic field. Based on the two-dimensional reduced Faraday--Maxwell equation for a tape surface obtain
ed with a thin-sheet approximation, we simulate numerically the power loss $P$ per unit length on twisted multi-filament tapes in the steady state. The current density profile clearly shows electromagnetic coupling between the SC filaments upon increasing the field sweep rate $beta$. Although the $beta$ dependence of $P/beta$ for twisted multi-filament SC tapes closely resembles that for filaments in an alternating field, we show that the mechanism for electromagnetic coupling in a ramped field differs from that in an alternating field. We also identify the conditions under which electromagnetic coupling is suppressed for the typical sweep rate of a magnet used for magnetic resonance imaging.
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 Ma
xwell 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 $L_{rm p}rightarrow infty$ with the twist pitch length $L_{rm p}$. These analytic formulae show that both magnetization and loss power decrease by a factor of $B(1+1/2n,1/2)/pi$ (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 $J_{rm c}$ on the loss power is investigated, and we demonstrate that it is possible to obtain an approximate estimate of the loss power value via $J_{rm c}$ in an applied magnetic field perpendicular to the tape surface (i.e., parallel to the $c$ axis).
We study the excitation spectra and the wave functions of quasiparticle bound states at a vortex and an edge in bilayer Rashba superconductors under a magnetic field. In particular, we focus on the quasiparticle states at the zero energy in the pair-
density wave state in a topologically non-trivial phase. We numerically demonstrate that the quasiparticle wave functions with zero energy are localized at both the edge and the vortex core if the magnetic field exceed the critical value.
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 Greens function method. The Barde
en-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.
The Lang-Firsov Hamiltonian, a well-known solvable model of interacting fermion-boson system with sideband features in the fermion spectral weight, is generalized to have the time-dependent fermion-boson coupling constant. We show how to derive the t
wo-time Greens function for the time-dependent problem in the adiabatic limit, defined as the slow temporal variation of the coupling over the characteristic oscillator period. The idea we use in deriving the Greens function is akin to the use of instantaneous basis states in solving the adiabatic evolution problem in quantum mechanics. With such adiabatic Greens function at hand we analyze the transient behavior of the spectral weight as the coupling is gradually tuned to zero. Time-dependent generalization of a related model, the spin-boson Hamiltonian, is analyzed in the same way. In both cases the sidebands arising from the fermion-boson coupling can be seen to gradually lose their spectral weights over time. Connections of our solution to the two-dimensional Dirac electrons coupled to quantized photons are discussed.
We numerically study the electronic structure of a single vortex in two dimensional superconducting bilayer systems within the range of the mean-field theory. The lack of local inversion symmetry in the system is taken into account through the layer
dependent Rashba spin-orbit coupling. The spatial profiles of the pair potential and the local quasiparticle density of states are calculated in the clean spin-singlet superconductor on the basis of the quasiclassical theory. In particular, we discuss the characteristic core structure in the pair-density wave state, which is spatially modulated exotic superconducting phase in a high magnetic field.
We numerically study the effect of non-magnetic impurities on the vortex bound states in noncentrosymmetric systems. The local density of states (LDOS) around a vortex is calculated by means of the quasiclassical Greens function method. We find that
the zero energy peak of the LDOS splits off with increasing the impurity scattering rate.
We theoretically investigate the applied magnetic field-angle dependence of the flux-flow resistivity $rho_{rm f}(alpha_{rm M})$ for an uniaxially anisotropic Fermi surface. $rho_{rm f}$ is related to the quasiparticle scattering rate $varGamma$ insi
de a vortex core, which reflects the sign change in the superconducting pair potential. We find that $rho_{rm f}(alpha_{rm M})$ is sensitive to the sign-change in the pair potential and has its maximum when the magnetic field is parallel to the gap-node direction. We propose the measurement of the field-angle dependent oscillation of $rho_{rm f}(alpha_{rm M})$ as a phase-sensitive field-angle resolved experiment.
