The effect of nonmagnetic impurities on the local density of states in s-wave superconductors

We study the effect of nonmagnetic impurities on the local density of states (LDOS) in s-wave superconductors. The quasiclassical equations of superconductivity are solved selfconsistently to show how LDOS evolves with impurity concentration. The spatially averaged zero-energy LDOS is a linear function of magnetic induction in low fields, N(E=0)=cB/H_{c2}, for all impurity concentration. The constant of proportionality "c" depends weakly on the electron mean free path. We present numerical data for differential conductance and spatial profile of zero-energy LDOS which can help in estimating the mean free path through the LDOS measurement.Comment: 7 pages, 7 figures (high quality color figure available on request

NMR relaxation time around a vortex in stripe superconductors

Site-dependent NMR relaxation time $T_1({\bf r})$ is calculated in the vortex state using the Bogoliubov-de Gennes theory, taking account of possible "field-induced stripe'' states in which the magnetism arises locally around a vortex core in d-wave superconductivity. The recently observed huge enhancement $T_1^{-1}({\bf r})$ below $T_c$ at a core site in Tl$_2$Ba$_2$CuO$_6$ is explained. The field-induced stripe picture explains consistently other relevant STM and neutron experiments.Comment: 4 pages, 4 figure

Effect of the Vortices on the Nuclear Spin Relaxation Rate in the Unconventional Pairing States of the Organic Superconductor (TMTSF)2_2PF6_6

This Letter theoretically discusses quasiparticle states and nuclear spin relaxation rates $T_1^{-1}$ in a quasi-one-dimensional superconductor (TMTSF)$_2$PF$_6$ under a magnetic field applied parallel to the conduction chains. We study the effects of Josephson-type vortices on $T_1^{-1}$ by solving the Bogoliubov de Gennes equation for $p$-, $d$- or $f$-wave pairing interactions. In the presence of line nodes in pairing functions, $T_1^{-1}$ is proportional to $T$ in sufficiently low temperatures because quasiparticles induced by vortices at the Fermi energy relax spins. We also try to identify the pairing symmetry of (TMTSF)$_2$PF$_6$.Comment: 4+ pages, 4 figure

Majorana bound state in rotating superfluid 3He-A between parallel plates

A concrete and experimentally feasible example for testing the putative Majorana zero energy state bound in a vortex is theoretically proposed for a parallel plate geometry of superfluid $^3$He-A phase. We examine the experimental setup in connection with ongoing rotating cryostat experiments. The theoretical analysis is based on the well-established Ginzburg--Landau functional, supplemented by microscopic calculations of the Bogoliubov--de Gennes equation, both of which allow the precise location of the parameter regions of the Majorana state to be found in realistic situations.Comment: 5 pages, 4 figure

Majorana surface states of superfluid 3He A- and B-phases in a slab

Motivated by experiments on the superfluid 3He confined in a thin slab, we design a concrete experimental setup for observing the Majorana surface states. We solve the quasi-classical Eilenberger equation, which is quantitatively reliable, to evaluate several quantities, such as local density of states (LDOS), mass current for the A-phase, and spin current for the B-phase. In connection with realistic slab samples, we consider the upper and lower surfaces and the side edges including the corners with several thicknesses. Consequently the influence on the Majorana zero modes from the spatial variation of l-vector for the A-phase in thick slabs and the energy splitting of the zero-energy quasi-particles for the B-phase confined in thin slabs are demonstrated. The corner of slabs in the B-phase is accompanied by the unique zero-energy LDOS of corner modes. On the basis of the quantitative calculation, we propose several feasible and verifiable experiments to check the existence of the Majorana surface states, such as the measurement of specific heat, edge current, and anisotropic spin susceptibility.Comment: 13 pages, 10 figures, published versio

Vortex Structure in Superconducting Stripe States

The vortex structure in superconducting stripe states is studied according to the Bogoliubov-de Gennes theory on the two-dimensional Hubbard model with nearest-neighbor sites pairing interaction. The vortex is trapped at the outside region of the stripe line, where the superconductivity is weak. The superconducting coherence length along the stripe direction becomes long. There are no eminent low-energy electronic states even near the vortex core. These characters resemble the Josephson vortex in layered superconductors under a parallel field.Comment: LaTeX 5 pages (using jpsj macros) with 3 figure

Field Dependence of Electronic Specific Heat in Two-Band Superconductors

The vortex structure is studied in light of MgB$_2$ theoretically based on a two-band superconducting model by means of Bogoliubov-de Gennes framework. The field dependence of the electronic specific heat coefficient $\gamma (H)$ is focused. The exponent $\alpha$ in $\gamma (H)\propto H^{\alpha}$ is shown to become smaller by adjusting the gap ratio of the two gaps on the major and minor bands. The observed extremely small value $\alpha\sim 0.23$ could be explained reasonably well in this two-band model with the gap ratio $\sim 0.3$.Comment: 5 pages, 4 figures, to be published in J. Phys. Soc. Jp

Properties of the Ideal Ginzburg-Landau Vortex Lattice

The magnetization curves M(H) for ideal type-II superconductors and the maximum, minimum, and saddle point magnetic fields of the vortex lattice are calculated from Ginzburg-Landau theory for the entire ranges of applied magnetic fields Hc1 <= H < Hc2 or inductions 0 <= B < Hc2 and Ginzburg-Landau parameters sqrt(1/2) <= kappa <= 1000. Results for the triangular and square flux-line lattices are compared with the results of the circular cell approximation. The exact magnetic field B(x,y) and magnetization M(H, kappa) are compared with often used approximate expressions, some of which deviate considerably or have limited validity. Useful limiting expressions and analytical interpolation formulas are presented.Comment: 11 pages, 8 figure

Fermi Arc of Metallic Diagonal Stripes in High Tc Cuprates

Spectral weight is investigated for metallic diagonal stripe state in two dimensional Hubbard model, and Fermi arc observed by angle-resolved photoemission spectroscopy on LSCO is discussed. The Fermi arc coming from the mid-gap state of diagonal stripe appears near $(\frac{\pi}{2},\frac{\pi}{2})$ and equivalent position in the reciprocal space, and the gap opens below the mid-gap state. We show how these spectral weight structure depends on the phasing of stripes, i.e., site-centered or bond-centered stripes.Comment: 4 figure