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

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

Induced Kramer-Pesch-Effect in a Two Gap Superconductor: Application to MgB2

The size of the vortex core in a clean superconductor is strongly temperature dependent and shrinks with decreasing temperature, decreasing to zero for T -> 0. We study this so-called Kramer-Pesch effect both for a single gap superconductor and for the case of a two gap superconductor using parameters appropriate for Magnesium Diboride. Usually, the Kramer-Pesch effect is absent in the dirty limit. Here, we show that the Kramer-Pesch effect exists in both bands of a two gap superconductor even if only one of the two bands is in the clean limit and the other band in the dirty limit, a case appropriate for MgB2. In this case an induced Kramer-Pesch effect appears in the dirty band. Besides numerical results we also present an analytical model for the spatial variation of the pairing potential in the vicinity of the vortex center that allows a simple calculation of the vortex core radius even in the limit T -> 0.Comment: 12 pages, 12 figure

Superconducting Gap Modulation in Weak Stripe States

The superconducting gap modulation is investigated in the presence of a weak stripe structure, using the Bogoliubov-de Gennes theory on the two-dimensional Hubbard model with nearest-neighbor site pairing interaction. We calculate the local density of states and discuss the recently observed scanning tunneling spectroscopy spectra with four lattice periodicity on Bi_2 Sr_2 Ca Cu_2 O_{8+delta} We also consider the spectral weight in the reciprocal space, where the Fermi surface and the superconducting gap are modulated by the band folding effect of the stripe structure.Comment: 4 pages, 4 figures, to be published in J. Phys. Soc. Jp

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

Vortex State and Field-Angle Resolved Specific Heat Oscillation for H // ab in d-Wave Superconductors

When magnetic field is applied parallel to the ab plane in d_{x^2-y^2}-wave superconductors, the transition of stable vortex lattice structure, spatial structure of local density of states, and specific heat oscillation by rotation of magnetic field orientation are investigated by quantitative calculations based on the selfconsistent Eilenberger theory. We estimate how the vortex state changes depending on the relative angle between the node-direction of the superconducting gap and magnetic field orientation. To reproduce the sign-change of specific heat oscillation observed in CeCoIn_5, our study is done by including strong paramagnetic effect. The quantitative theoretical calculations give decisive information to analyze the experimental data on the field-angle dependence, and establish the angle-resolved specific heat experiment as a spectroscopic means to identify the node-position of the superconducting gap.Comment: 9 pages, 13 figure

Site-selective nuclear magnetic relaxation time in a superconducting vortex state

The temperature and field dependences of the site-selective nuclear spin relaxation time T_1 around vortices are studied comparatively both for s-wave and d-wave superconductors, based on the microscopic Bogoliubov-de Gennes theory. Reflecting low energy electronic excitations associated with the vortex core, the site selective temperature dependences deviate from those of the zero-field case, and T_1 becomes faster with approaching the vortex core. In the core region, T_1^{-1} has a new peak below the superconducting transition temperature T_c. The field dependence of the overall T_1(T) behaviors for s-wave and d-wave superconductors is investigated and analyzed in terms of the local density of states. The NMR study by the resonance field dependence may be a new method to probe the spatial resolved vortex core structure in various conventional and unconventional superconductors.Comment: 14Pages, 26 figures, revte

Pauli Paramagnetic Effects on Vortices in Superconducting TmNi2B2C

The magnetic field distribution around the vortices in TmNi2B2C in the paramagnetic phase was studied experimentally as well as theoretically. The vortex form factor, measured by small-angle neutron scattering, is found to be field independent up to 0.6 Hc2 followed by a sharp decrease at higher fields. The data are fitted well by solutions to the Eilenberger equations when paramagnetic effects due to the exchange interaction with the localized 4f Tm moments are included. The induced paramagnetic moments around the vortex cores act to maintain the field contrast probed by the form factor.Comment: 4 pages, 4 figure

Theory of vortex lattice effects on STM spectra in d-wave superconductors

Theory of scanning tunneling spectroscopy of low energy quasiparticle (QP) states in vortex lattices of d-wave superconductors is developed taking account of the effects caused by an extremely large extension of QP wavefunctions in the nodal directions and the band structure in the QP spectrum. The oscillatory structures in STM spectra, which correspond to van Hove singularities are analysed. Theoretical calculations carried out for finite temperatures and scattering rates are compared with recent experimental data for high temperature cuprates.Comment: 4 pages, 3 eps figures, M2S-HTSC-VI conference paper, using Elsevier style espcrc2.st