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

Anisotropic Diamagnetic Response in Type-II Superconductors with Gap and Fermi-Surface Anisotropies

Effects of anisotropic gap structures on a diamagnetic response are investigated in order to demonstrate that the field-angle-resolved magnetization ($M_L(\chi)$) measurement can be used as a spectroscopic method to detect gap structures. Our microscopic calculation based on the quasiclassical Eilenberger formalism reveals that $M_L(\chi)$ in a superconductor with four-fold gap displays a four-fold oscillation reflecting the gap and Fermi surface anisotropies, and the sign of this oscillation changes at a field between $H_{c1}$ and $H_{c2}$. As a prototype of unconventional superconductors, magnetization data for borocarbides are also discussed.Comment: 5 pages, 4 figure

Specific heat and low-lying excitations in the mixed state for a type II superconductor

Low temperature behavior of the electronic specific heat $C(T)$ in the mixed state is by the self-consistent calculation of the Eilenberger theory. In addition to $\gamma T$-term ($\gamma$ is a Sommerfeld coefficient), $C(T)$ has significant contribution of $T^2$-term intrinsic in the vortex state. We identify the origin of the $T^2$-term as (i) V-shape density of states in the vortex state and (ii) Kramer-Pesch effect of vortex core shrinking upon lowering $T$. These results both for full-gap and line node cases reveal that the vortex core is a richer electronic structure beyond the normal core picture.Comment: Accepted in Phys. Rev. B. 5 pages, 5 figure

Effect of field dependent core size on reversible magnetization of high-κ\kappa superconductors

The field dependence of the vortex core size $\xi(B)$ is incorporated in the London model, in order to describe reversible magnetization $M(B,T)$ for a number of materials with large Ginzburg-Landau parameter $\kappa$. The dependence $\xi(B)$ is directly related to deviations in $M(\ln B)$ from linear behavior prescribed by the standard London model. A simple method to extract $\xi(B)$ from the magnetization data is proposed. For most materials examined, $\xi(B)$ so obtained decreases with increasing field and is in qualitative agreement both with behavior extracted from $\mu$SR and small angle neutron scattering data and with that predicted theoretically

Quasi-Classical Calculation of the Mixed-State Thermal Conductivity in s-Wave and d-Wave Superconductors

To see how superconducting gap structures affect the longitudinal component of mixed-state thermal conductivity kappa_{xx}(B), the magnetic-field dependences of kappa_{xx}(B) in s-wave and d-wave superconductors are investigated. Calculations are performed on the basis of the quasi-classical theory of superconductivity by fully taking account of the spatial variation of the normal Green's function, neglected in previous works, by the Brandt-Pesch-Tewordt approximation. On the basis of our result, we discuss the possibility of kappa_{xx}(B) measurement as a method of probing the gap structure.Comment: To appear in J. Phys. Soc. Jp

Reentrant vortex lattice transformation in four-fold symmetric superconductors

The physics behind the rhombic$\to$square$\to$rhombic flux line lattice transformation in increasing fields is clarified on the basis of Eilenberger theory. We demonstrate that this reentrance observed in LuNi$_2$B$_2$C is due to intrinsic competition between superconducting gap and Fermi surface anisotropies. The calculations reproduce not only it but also predict yet not found lock-in transition to a square lattice with different orientation in higher field. In view of physical origin given, this sequence of transitions is rather generic to occur in four-fold symmetric superconductors.Comment: 5 pages, 4 figures,submitted to Phys. Rev. Let

Thermodynamics and magnetic field profiles in low-kappa type-II superconductors

Two-dimensional low-kappa type-II superconductors are studied numerically within the Eilenberger equations of superconductivity. Depending on the Ginzburg-Landau parameter \kappa=\lambda/\xi vortex-vortex interaction can be attractive or purely repulsive. The sign of interaction is manifested as a first (second) order phase transition from Meissner to the mixed state. Temperature and field dependence of the magnetic field distribution in low-kappa type-II superconductors with attractive intervortex interaction is calculated. Theoretical results are compared to the experiment.Comment: 4 pages, 3 figure

Field-angle-dependent specific heat measurements and gap determination of a heavy fermion superconductor URu2Si2

To identify the superconducting gap structure in URu2Si2 we perform field-angle-dependent specific heat measurements for the two principal orientations in addition to field rotations, and theoretical analysis based on microscopic calculations. The Sommerfeld coefficient \gamma(H)'s in the mixed state exhibit distinctively different field-dependence. This comes from point nodes and substantial Pauli paramagnetic effect of URu2Si2. These two features combined give rise to a consistent picture of superconducting properties, including a possible first order transition of Hc2 at low temperatures.Comment: 4 pages, 5 figures, to appear in Phys. Rev. Let

Influence of gap structures to specific heat in oriented magnetic fields: Application to the orbital dependent superconductor, Sr2_2RuO4_4

We discuss influence of modulation of gap function and anisotropy of Fermi velocity to field angle dependences of upper critical field, $H_{c2}$, and specific heat, $C$, on the basis of the approximate analytic solution in the quasiclassical formalism. Using 4-fold modulation of the gap function and the Fermi velocity in the single-band model, we demonstrate field and temperature dependence of oscillatory amplitude of $H_{c2}$ and $C$. We apply the method to the effective two-band model to discuss the gap structure of Sr$_2$RuO$_4$, focusing on recent field angle-resolved experiments. It is shown that the gap structures with the intermediate magnitude of minima in $[100]$ direction for $\gamma$ band, and tiny minima of gaps in $[110]$ directions for $\alpha$ and $\beta$ bands give consistent behaviors with experiments. The interplay of the above two gaps also explains the anomalous temperature dependence of in-plane $H_{c2}$ anisotropy, where the opposite contribution from the passive $\alpha\beta$ band is pronounced near $T_c$.Comment: 7 pages, 11 figures in JPSJ forma