Algorithm for obtaining the gradient expansion of the local density of states and the free energy of a superconductor

We present an efficient algorithm for obtaining the gauge-invariant gradient expansion of the local density of states and the free energy of a clean superconductor. Our method is based on a new mapping of the semiclassical linearized Gorkov equations onto a pseudo-Schroedinger equation for a three-component wave-function psi(x), where one component is directly related to the local density of states. Because psi(x) satisfies a linear equation of motion, successive terms in the gradient expansion can be obtained by simple linear iteration. Our method works equally well for real and complex order parameter, and in the presence of arbitrary external fields. We confirm a recent calculation of the fourth order correction to the free energy by Kosztin, Kos, Stone and Leggett [Phys. Rev. B 58, 9365 (1998)], who obtained a discrepancy with an earlier result by Tewordt [Z. Phys. 180, 385 (1964)]. We also give the fourth order correction to the local density of states, which has not been published before.Comment: 12 preprint pages, added remark concerning Eilenberger equation, accepted for publication in Phys. Rev.

Magnetic field of Josephson vortices outside superconductors

We consider the structure of Josephson vortices approaching the junction boundary with vacuum in large area Josephson junctions with the Josephson length $\lambda_J$ large relative to the London penetration depth $\lambda_L$. Using the stability argument for one-dimentional solitons with respect to 2D perturbations, it is shown that on the scale $\lambda_J$ the Josephson vortices do not spread near the boundary in the direction of the junction. %, which is in a striking difference with behavior of Abrikosov vortices exiting superconductors. The field distribution in vacuum due to the Josephson vortex is evaluated, the information needed for the Scanning SQUID Microscopy.Comment: 5 RevTeX pages, 3 eps figures. The second version includes more detailed explanations and corrections, and slightly modified figure

Thermodynamic Potential for Superfluid 3He in Aerogel

We present a free energy functional for superfluid 3He in the presence of homogeneously distributed impurity disorder which extends the Ginzburg-Landau free energy functional to all temperatures. We use the new free energy functional to calculate the thermodynamic potential, entropy, heat capacity and density of states for the B-phase of superfluid 3He in homogeneous, isotropic aerogel.Comment: 10 pages, 4 figure

Quantum tunneling between paramagnetic and superconducting states of a nanometer-scale superconducting grain placed in a magnetic field

We consider the process of quantum tunneling between the superconducting and paramagnetic states of a nanometer-scale superconducting grain placed in a magnetic field. The grain is supposed to be coupled via tunneling junction to a normal metallic contact that plays a role of the spin reservoir. Using the instanton method we find the probability of the quantum tunneling process and express it in terms of the applied magnetic field, order parameter of the superconducting grain and conductance of the tunneling junction between the grain and metallic contact

Theory of the Normal/Superfluid interface in population imbalanced Fermi gases

We present a series of theoretical studies of the boundary between a superfluid and normal region in a partially polarized gas of strongly interacting fermions. We present mean-field estimates of the surface energy in this boundary as a function of temperature and scattering length. We discuss the structure of the domain wall, and use a previously introduced phenomonological model to study its influence on experimental observables. Our microscopic mean-field calculations are not consistent with the magnitude of the surface tension found from our phenomonological modelling of data from the Rice experiments. We conclude that one must search for novel mechanisms to explain the experiments.Comment: 15 pages, 9 figures (13 subfigures) -- v2: minor change

Anisotropy of the upper critical field in superconductors with anisotropic gaps. Anisotropy parameters of MgB2

The upper critical field Hc2 is evaluated for weakly-coupled two-band superconductors. By modeling the actual bands and the gap distribution of MgB2 by two Fermi surface spheroids with average parameters of the real material, we show that H_{c2,ab}/H_{c2,c} increases with decreasing temperature in agreement with available data.Comment: 4 pages, 2 figure

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

The Gradient Expansion for the Free-Energy of a Clean Superconductor

We describe a novel method for obtaining the gradient expansion for the free energy of a clean BCS superconductor. We present explicit results up to fourth order in the gradients of the order parameter.Comment: 33 pages, Late

Gauge Invariance and Hall Terms in the Quasiclassical Equations of Superconductivity

This paper presents a careful derivation of the quasiclassical equations of superconductivity so that a manifest gauge invariance is retained with respect to the space-time arguments of the quasiclassical Green's function $\hat{g}$. The terms responsible for the Hall effect naturally appear from the derivation. The equations are applicable to clean as well as dirty superconductors for an arbitrary external frequency much smaller than the Fermi energy. Thus, they will form a basis toward a complete microscopic understanding of the Hall effect in type-II superconductors.Comment: 9 pages, 1 figur

A Two-dimensional Superconductor in a Tilted Magnetic Field - new states with finite Cooper-pair momentum

Varying the angle Theta between applied field and the conducting planes of a layered superconductor in a small interval close to the plane-parallel field direction, a large number of superconducting states with unusual properties may be produced. For these states, the pair breaking effect of the magnetic field affects both the orbital and the spin degree of freedom. This leads to pair wave functions with finite momentum, which are labeled by Landau quantum numbers 0<n<\infty. The stable order parameter structure and magnetic field distribution for these states is found by minimizing the quasiclassical free energy near H_{c2} including nonlinear terms. One finds states with coexisting line-like and point-like order parameter zeros and states with coexisting vortices and antivortices. The magnetic response may be diamagnetic or paramagnetic depending on the position within the unit cell. The structure of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states at Theta=0 is reconsidered. The transition n->\infty of the paramagnetic vortex states to the FFLO-limit is analyzed and the physical reason for the occupation of higher Landau levels is pointed out.Comment: 24 pages, 11 figure