Ground State and Tkachenko Modes of a Rapidly Rotating Bose-Einstein Condensate in the Lowest Landau Level State

The Letter considers the ground state and the Tkachenko modes for a rapidly rotating Bose-Einstein condensate (BEC), when its macroscopic wave function is a coherent superposition of states analogous to the lowest Landau levels of a charge in a magnetic field. As well as in type II superconductors close to the critical magnetic field $H_{c2}$, this corresponds to a periodic vortex lattice. The exact value of the shear elastic modulus of the vortex lattice, which was known from the old works on type II superconductors, essentially exceeds the values calculated recently for BEC. This is important for comparison with observation of the Tkachenko mode in the rapidly rotating BEC.Comment: 5 pages, 1 figure; discussion edited, references added, numerical factors and typos correcte

Heat Capacity of Mesoscopic Superconducting Disks

We study the heat capacity of isolated giant vortex states, which are good angular momentum ($L$) states, in a mesoscopic superconducting disk using the Ginzburg-Landau (GL) theory. At small magnetic fields the $L$=0 state qualitatively behaves like the bulk sample characterized by a discontinuity in heat capacity at $T_c$. As the field is increased the discontinuity slowly turns into a continuous change which is a finite size effect. The higher $L$ states show a continuous change in heat capacity at $T_c$ at all fields. We also show that for these higher $L$ states, the behavior of the peak position with change in field is related to the paramagnetic Meissner effect (irreversible) and can lead to an unambiguous observation of positive magnetization in mesoscopic superconductors.Comment: Final versio

FFLO states and quantum oscillations in mesoscopic superconductors and superfluid ultracold Fermi gases

We have studied the distinctive features of the Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) instability and phase transitions in two--dimensional (2D) mesoscopic superconductors placed in magnetic field of arbitrary orientation and rotating superfluid Fermi gases with imbalanced state populations. Using a generalized version of the phenomenological Ginzburg-Landau theory we have shown that the FFLO states are strongly modified by the effect of the trapping potential confining the condensate. The phenomenon of the inhomogeneous state formation is determined by the interplay of three length scales: (i) length scale of the FFLO instability; (ii) 2D system size; (iii) length scale associated with the orbital effect caused either by the Fermi condensate rotation or magnetic field component applied perpendicular to the superconducting disc. We have studied this interplay and resulting quantum oscillation effects in both superconducting and superfluid finite -- size systems with FFLO instability and described the hallmarks of the FFLO phenomenon in a restricted geometry. The finite size of the system is shown to affect strongly the conditions of the observability of switching between the states with different vorticities.Comment: 11 pages, 5 figures, Submitted to PR

Stability of the vortex lattice in D-wave superconductors

Use is made of Onsager's hydrodynamic equation to derive the vibration spectrum of the vortex lattice in d-wave superconductor. In particular the rhombic lattice (i.e. the $45^\circ$ tilted square lattice) is found to be stable for $B>H_{cr}(t)$. Here $H_{cr}(t)$ denotes the critical field at which the vortex lattice transition takes place.Comment: 7 pages, Revte

Spin-Valve Effect of the Spin Accumulation Resistance in a Double Ferromagnet - Superconductor Junction

We have measured the transport properties of Ferromagnet - Superconductor nanostructures, where two superconducting aluminum (Al) electrodes are connected through two ferromagnetic iron (Fe) ellipsoids in parallel. We find that, below the superconducting critical temperature of Al, the resistance depends on the relative alignment of the ferromagnets' magnetization. This spin-valve effect is analyzed in terms of spin accumulation in the superconducting electrode submitted to inverse proximity effect

Paramagnetic Meissner effect in superconductors from self-consistent solutions of Ginzburg-Landau equations

The paramagnetic Meissner effect (PME) is observed in small superconducting samples, and a number of controversial explanations of this effect are proposed, but there is as yet no clear understanding of its nature. In the present paper PME is considered on the base of the Ginzburg-Landau theory (GL). The one-dimensional solutions are obtained in a model case of a long superconducting cylinder for different cylinder radii R, the GL-parameters \kappa and vorticities m. Acording to GL-theory, PME is caused by the presence of vortices inside the sample. The superconducting current flows around the vortex to screeen the vortex own field from the bulk of the sample. Another current flows at the boundary to screen the external field H from entering the sample. These screening currents flow in opposite directions and contribute with opposite signs to the total magnetic moment (or magnetization) of the sample. Depending on H, the total magnetization M may be either negative (diamagnetism), or positive (paramagnetism). A very complicated saw-like dependence M(H) (and other characteristics), which are obtained on the base of self-consistent solutions of the GL-equations, are discussed.Comment: 6 pages, 5 figures, RevTex, submitted to Phys. Rev.

Geometry-dependent critical currents in superconducting nanocircuits

In this paper we calculate the critical currents in thin superconducting strips with sharp right-angle turns, 180-degree turnarounds, and more complicated geometries, where all the line widths are much smaller than the Pearl length $\Lambda = 2 \lambda^2/d$. We define the critical current as the current that reduces the Gibbs free-energy barrier to zero. We show that current crowding, which occurs whenever the current rounds a sharp turn, tends to reduce the critical current, but we also show that when the radius of curvature is less than the coherence length this effect is partially compensated by a radius-of-curvature effect. We propose several patterns with rounded corners to avoid critical-current reduction due to current crowding. These results are relevant to superconducting nanowire single-photon detectors, where they suggest a means of improving the bias conditions and reducing dark counts. These results also have relevance to normal-metal nanocircuits, as these patterns can reduce the electrical resistance, electromigration, and hot spots caused by nonuniform heating.Comment: 29 pages, 24 figure

Crossed Andreev reflection and charge imbalance in diffusive NSN structures

We formulate a microscopic theory of non-local electron transport in three-terminal diffusive normal-superconducting-normal (NSN) structures with arbitrary interface transmissions. At low energies $\varepsilon$ we predict strong enhancement of non-local spectral conductance $g_{12} \propto 1/\varepsilon$ due to quantum interference of electrons in disordered N-terminals. In contrast, non-local resistance $R_{12}$ remains smooth at small $\varepsilon$ and, furthermore, is found to depend neither on parameters of NS interfaces nor on those of N-terminals. At higher temperatures $R_{12}$ exhibits a peak caused by the trade-off between charge imbalance and Andreev reflection. Our results are in a good agreement with recent experimental observations and can be used for quantitative analysis of future experiments.Comment: 4 pages, 3 figure