Gap Anisotropy and de Haas-van Alphen Effect in Type-II Superconductors

We present a theoretical study on the de Haas-van Alphen (dHvA) oscillation in the vortex state of type-II superconductors, with a special focus on the connection between the gap anisotropy and the oscillation damping. Numerical calculations for three different gap structures clearly indicate that the average gap along extremal orbits is relevant for the magnitude of the extra damping, thereby providing a support for experimental efforts to probe gap anisotropy through the dHvA signal. We also derive an analytic formula for the extra damping which gives a good fit to the numerical results.Comment: 5 pages, 1 figure, changes in Introductio

Quasiparticle Density of States of Clean and Dirty s-Wave Superconductors in the Vortex State

The quasiparticle density of states (DOS) in the vortex state has been probed by specific heat measurements under magnetic fields (H) for clean and dirty s-wave superconductors, Y(Ni1-xPtx)2B2C and Nb1-xTaxSe2. We find that the quasiparticle DOS per vortex is appreciably H-dependent in the clean-limit superconductors, while it is H-independent in the dirty superconductors as expected from a conventional rigid normal electron core picture. We discuss possible origins for our observations in terms of the shrinking of the vortex core radius with increasing H.Comment: 5 pages, 4 figures, to appear in J. Phys. Soc. Jpn. Vol. 68 No.

Ginzburg-Landau-Gor'kov Theory of Magnetic oscillations in a type-II 2-dimensional Superconductor

We investigate de Haas-van Alphen (dHvA) oscillations in the mixed state of a type-II two-dimensional superconductor within a self-consistent Gor'kov perturbation scheme. Assuming that the order parameter forms a vortex lattice we can calculate the expansion coefficients exactly to any order. We have tested the results of the perturbation theory to fourth and eight order against an exact numerical solution of the corresponding Bogoliubov-de Gennes equations. The perturbation theory is found to describe the onset of superconductivity well close to the transition point $H_{c2}$. Contrary to earlier calculations by other authors we do not find that the perturbative scheme predicts any maximum of the dHvA-oscillations below $H_{c2}$. Instead we obtain a substantial damping of the magnetic oscillations in the mixed state as compared to the normal state. We have examined the effect of an oscillatory chemical potential due to particle conservation and the effect of a finite Zeeman splitting. Furthermore we have investigated the recently debated issue of a possibility of a sign change of the fundamental harmonic of the magnetic oscillations. Our theory is compared with experiment and we have found good agreement.Comment: 39 pages, 8 figures. This is a replacement of supr-con/9608004. Several sections changed or added, including a section on the effect of spin and the effect of a conserved number of particles. To be published in Phys. Rev.

Absence of Persistent Magnetic Oscillations in Type-II Superconductors

We report on a numerical study intended to examine the possibility that magnetic oscillations persist in type II superconductors beyond the point where the pairing self-energy exceeds the normal state Landau level separation. Our work is based on the self-consistent numerical solution for model superconductors of the Bogoliubov-deGennes equations for the vortex lattice state. In the regime where the pairing self-energy is smaller than the cyclotron energy, magnetic oscillations resulting from Landau level quantization are suppressed by the broadening of quasiparticle Landau levels due to the non-uniform order parameter of the vortex lattice state, and by splittings of the quasiparticle bands. Plausible arguments that the latter effect can lead to a sign change of the fundamental harmonic of the magnetic oscillations when the pairing self-energy is comparable to the cyclotron energy are shown to be flawed. Our calculations indicate that magnetic oscillations are strongly suppressed once the pairing self-energy exceeds the Landau level separation.Comment: 7 pages, revtex, 7 postscript figure

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

Optically induced coherent intra-band dynamics in disordered semiconductors

On the basis of a tight-binding model for a strongly disordered semiconductor with correlated conduction- and valence band disorder a new coherent dynamical intra-band effect is analyzed. For systems that are excited by two, specially designed ultrashort light-pulse sequences delayed by tau relatively to each other echo-like phenomena are predicted to occur. In addition to the inter-band photon echo which shows up at exactly t=2*tau relative to the first pulse, the system responds with two spontaneous intra-band current pulses preceding and following the appearance of the photon echo. The temporal splitting depends on the electron-hole mass ratio. Calculating the population relaxation rate due to Coulomb scattering, it is concluded that the predicted new dynamical effect should be experimentally observable in an interacting and strongly disordered system, such as the Quantum-Coulomb-Glass.Comment: to be published in Physical Review B15 February 200

Superconducting fluctuation corrections to ultrasound attenuation in layered superconductors

We consider the temperature dependence of the sound attenuation and sound velocity in layered impure metals due to superconducting fluctuations of the order parameter above the critical temperature. We obtain the dependence on material properties of these fluctuation corrections in the hydrodynamic limit, where the electron mean free path is much smaller than the wavelength of sound and where the electron collision rate is much larger than the sound frequency. For longitudinal sound propagating perpendicular to the layers, the open Fermi surface condition leads to a suppression of the divergent contributions to leading order, in contrast with the case of paraconductivity. The leading temperature dependent corrections, given by the Aslamazov-Larkin, Maki-Thompson and density of states terms, remain finite as T->Tc. Nevertheless, the sensitivity of new ultrasonic experiments on layered organic conductors should make these fluctuations effects measurable.Comment: 13 pages, 6 figures. Accepted for PRB. Added discussion on incoherent interlayer tunneling and other small modifications suggested by referee

Theory of de Haas-van Alphen Effect in Type-II Superconductors

Theory of quasiparticle spectra and the de Haas-van Alphen (dHvA) oscillation in type-II superconductors are developed based on the Bogoliubov-de Gennes equations for vortex-lattice states. As the pair potential grows through the superconducting transition, each degenerate Landau level in the normal state splits into quasiparticle bands in the magnetic Brillouin zone. This brings Landau-level broadening, which in turn leads to the extra dHvA oscillation damping in the vortex state. We perform extensive numerical calculations for three-dimensional systems with various gap structures. It is thereby shown that (i) this Landau-level broadening is directly connected with the average gap at H=0 along each Fermi-surface orbit perpendicular to the field H; (ii) the extra dHvA oscillation attenuation is caused by the broadening around each extremal orbit. These results imply that the dHvA experiment can be a unique probe to detect band- and/or angle-dependent gap amplitudes. We derive an analytic expression for the extra damping based on the second-order perturbation with respect to the pair potential for the Luttinger-Ward thermodynamic potential. This formula reproduces all our numerical results excellently, and is used to estimate band-specific gap amplitudes from available data on NbSe_2, Nb_3Sn, and YNi_2B_2C. The obtained value for YNi_2B_2C is fairly different from the one through a specific-heat measurement, indicating presence of gap anisotropy in this material. C programs to solve the two-dimensional Bogoliubov-de Gennes equations are available at http://phys.sci.hokudai.ac.jp/~kita/index-e.html .Comment: 16 pages, 11 figure

Anomalous magnetic field dependence of the thermodynamic transition line in the isotropic superconductor (K,Ba)Bi03

Thermodynamic (specific heat, reversible magnetization, tunneling spectroscopy) and transport measurements have been performed on high quality (K,Ba)BiO$_3$ single crystals. The temperature dependence of the magnetic field $H_{Cp}$ corresponding to the onset of the specific heat anomaly presents a clear positive curvature. $H_{Cp}$ is significantly smaller than the field $H_\Delta$ for which the superconducting gap vanishes but is closely related to the irreversibility line deduced from transport data. Moreover, the temperature dependence of the reversible magnetization present a strong deviation from the Ginzburg--Landau theory emphasazing the peculiar nature of the superconducting transition in this material.Comment: 4 pages, 4 figures, 28 reference