Local density of states in the vortex lattice in a type II superconductor

Local density of states (LDOS) in the triangular vortex lattice is investigated based on the quasi-classical Eilenberger theory. We consider the case of an isotropic s-wave superconductor with the material parameter appropriate to NbSe_2. At a weak magnetic field, the spatial variation of the LDOS shows cylindrical structure around a vortex core. On the other hand, at a high field where the core regions substantially overlap each other, the LDOS is sixfold star-shaped structure due to the vortex lattice effect. The orientation of the star coincides with the experimental data of the scanning tunneling microscopy. That is, the ray of the star extends toward the nearest-neighbor (next nearest-neighbor) vortex direction at higher (lower) energy.Comment: 10 pages, RevTex, 32 figure

Coherence in the Quasi-Particle 'Scattering' by the Vortex Lattice in Pure Type-II Superconductors

The effect of quasi-particle (QP) 'scattering' by the vortex lattice on the de-Haas van-Alphen oscillations in a pure type-II superconductor is investigated within mean field,asymptotic perturbation theory. Using a 2D electron gas model it is shown that, due to a strict phase coherence in the many-particle correlation functions, the 'scattering' effect in the asymptotic limit ($\sqrt{E_F/\hbar\omega_c}\gg 1$) is much weaker than what is predicted by the random vortex lattice model proposed by Maki and Stephen, which destroys this coherence . The coherent many particle configuration is a collinear array of many particle coordinates, localized within a spatial region with size of the order of the magnetic length. The amplitude of the magnetization oscillations is sharply damped just below $$ because of strong $180^{\circ}$ out of phase magnetic oscillations in the superconducting condensation energy ,which tend to cancel the normal electron oscillations. Within the ideal 2D model used it is found, however, that because of the relative smallness of the quartic and higher order terms in the expansion, the oscillations amplitude at lower fields does not really damp to zero, but only reverses sign and remains virtually undamped well below $H_{c2}$. This conclusion may be changed if disorder in the vortex lattice, or vortex lines motion will be taken into account. The reduced QP 'scattering' effect may be responsible for the apparent crossover from a strong damping of the dHvA oscillations just below $H_{c2}$ to a weaker damping at lower fields observed experimentally in several 3D superconductors.Comment: 26 pages, Revtex no Figure

The Current Carried by Bound States of a Superconducting Vortex

We investigate the spectrum of quasiparticle excitations in the core of isolated pancake vortices in clean layered superconductors. Analysis of the spectral current density shows that both the circular current around the vortex center as well as any transport current through the vortex core is carried by localized states bound to the core by Andreev scattering. Hence the physical properties of the core are governed in clean high-$\kappa$ superconductors (e.g. the cuprate superconductors) by the Andreev bound states, and not by normal electrons as it is the case for traditional (dirty) high-$\kappa$ superconductors.Comment: 17 pages in a RevTex (3.0) file plus 5 Figures in PostScript. Submitted to Physical Review

Field dependence of the vortex structure in chiral p-wave superconductors

To investigate the different vortex structure between two chiral pairing p_x +(-) i p_y, we calculate the pair potential, the internal field, the local density of states, and free energy in the vortex lattice state based on the quasiclassical Eilenberger theory, and analyze the magnetic field dependence. The induced opposite chiral component of the pair potential plays an important role in the vortex structure. It also produces H^{1/2}-behavior of the zero-energy density of states at higher field. These results are helpful when we understand the vortex states in Sr2RuO4.Comment: 11 pages, 10 figures, to be published in Phys. Rev.

Effects of gap anisotropy upon the electronic structure around a superconducting vortex

An isolated single vortex is considered within the framework of the quasiclassical theory. The local density of states around a vortex is calculated in a clean type II superconductor with an anisotropy. The anisotropy of a superconducting energy gap is crucial for bound states around a vortex. A characteristic structure of the local density of states, observed in the layered hexagonal superconductor 2H-NbSe2 by scanning tunneling microscopy (STM), is well reproduced if one assumes an anisotropic s-wave gap in the hexagonal plane. The local density of states (or the bound states) around the vortex is interpreted in terms of quasiparticle trajectories to facilitate an understanding of the rich electronic structure observed in STM experiments. It is pointed out that further fine structures and extra peaks in the local density of states should be observed by STM.Comment: 11 pages, REVTeX; 20 PostScript figures; An Animated GIFS file for the star-shaped vortex bound states is available at http://mp.okayama-u.ac.jp/~hayashi/vortex.htm

Superconductivity in High Magnetic Field:Excitation Spectrum and Tunneling Properties

The quasiparticle excitation spectrum of a type-II superconductor placed in high magnetic field is shown to be gapless. The gap turns to zero at the points in the MBZ which are in correspondence with the vortex lattice in real space. When the field decreases below certain critical value, branch crossing occur and gaps starts opening up at the Fermi surface.The strong dispersion around gapless points leads to algebraic temperature dependence in the thermodynamic functions and the algebraic voltage dependence in the tunneling conductance between the microscope tip and superconductor in an STM experiment.Comment: 16 pages+$figures (on request), REVTE