Vortex lattice structural transitions: a Ginzburg-Landau model approach

We analyze the rhombic to square vortex lattice phase transition in anisotropic superconductors using a variant of Ginzburg-Landau theory. The mean-field phase diagram is determined to second order in the anisotropy parameter, and shows a reorientation transition of the square vortex lattice with respect to the crystal lattice. We then derive the long-wavelength elastic moduli of the lattices, and use them to show that thermal fluctuations produce a reentrant rhombic to square lattice transition line, similar to recent studies which used a nonlocal London model.     

Nonequilibrium phase transitions of vortex matter in three-dimensional layered superconductors

Large-scale simulations on the three-dimensional (3D) frustrated anisotropic XY model have been performed to study the nonequilibrium phase transitions of vortex matter in weak random pinning potential in layered superconductors. The first-order phase transition from the moving Bragg glass to the moving smectic is clarified, based on thermodynamic quantities. A washboard noise is observed in the moving Bragg glass in 3D simulations for the first time. It is found that the activation of the vortex loops plays the dominant role in the dynamical melting at high drive.     

Vortices in superconducting bulk, films and SQUIDs

The properties of the ideal periodic vortex lattice in bulk superconductors and in films of any thickness can be calculated from Ginzburg-Landau theory by an iteration method using Fourier series. The London theory yields general analytic expressions for the magnetic field and energy of arbitrary arrangements of straight or curved vortex lines. The elasticity of the vortex lattice is highly nonlocal. The magnetic response of superconductors of realistic shapes like thin and thick strips and disks or thin rectangular plates or films, containing pinned vortices, can be computed within continuum theory by solving an integral equation. A useful example is a thin square with a central hole and a radial slit, used as superconducting quantum interference device (SQUID).     

Effects of point defects on the phase diagram of vortex states in high- T(c) superconductors in the B parallel to c axis

The phase diagram for the vortex states of high- T(c) superconductors with point defects in the B--> parallel to c axis is drawn by large-scale Monte Carlo simulations. The vortex slush (VS) phase is found between the vortex glass (VG) and vortex liquid (VL) phases. The first-order transition between this novel normal phase and the VL phase is characterized by a sharp jump of the density of dislocations. The first-order transition between the Bragg glass (BG) and VG or VS phases is also clarified. These two transitions are compared with the melting transition between the BG and VL phases.     

Theory of equilibrium flux lattice in UPt3 under magnetic field parallel to hexagonal crystal axis

We investigate Abrikosov lattice structures in the unconventional superconductor UPt (3) under magnetic field parallel to the hexagonal crystal axis. Only the two-dimensional E2 superconducting state among the many other states of different symmetry is compatible with the recent observation [A. Huxley et al., Nature (London) 406, 160 (2000)] of the flux lattice in the A phase misaligned with crystallographic directions. It is shown that the inequality of the London penetration depths in the basal plane directions resulting from the superposition of hexagonal crystal and superconducting state anisotropies leads for E2 to a slightly distorted triangular flux lattice.     

Antiferromagnetism and hole pair checkerboard in the vortex state of high T(c) superconductors

We propose a microscopic state for the vortex phase of BSCO superconductors. Around the vortex core or above H(c2), the d wave hole pairs form a checkerboard localized in the antiferromagnetic background. We discuss this theory in connection with recent STM experiments.     

Why an ac magnetic field shifts the irreversibility line in type-II superconductors

We show that for a thin superconducting strip placed in a transverse dc magnetic field--the typical geometry of experiments with high-T(c) superconductors--the application of a weak ac magnetic field perpendicular to the dc field generates a dc voltage in the strip. This voltage leads to the decay of the critical currents circulating in the strip, and eventually the equilibrium state of the superconductor is established. This relaxation is not due to thermally activated flux creep but to the "walking" motion of vortices in the two-dimensional critical state of the strip with in-plane ac field. Our theory explains the shaking effect that was used for detecting phase transitions of the vortex lattice in superconductors.     

Lawrence–Doniach model in London approximation as a system of 2D Coulomb particles of two kinds

Thermodynamical properties of layered superconductors with Josephson coupling in zero magnetic field are discussed. It is shown that the Lawrence–Doniach model of layered superconductors in the London approximation can be presented as a system of classical Coulomb particles of two kinds. This representation includes both Josephson and 2D vortex subsystems in absolutely symmetrical way. The model was analyzed by means of the real-space renormalization group approach and in the mean field approximation. It is found that there is no a second order phase transition in the system. Instead of this the model demonstrates the qualitative change of the system properties which can look as a phase transition for experimental purposes.     

Helical instability of a straight Abrikosov vortex in an anisotropic superconductor

Because of attraction of the parallel currents forming an Abrikosov vortex, the vortex energy per unit length decreases, under bending of the vortex, by a quantity proportional to the square of the curvature. Solving the London equation in an approximation allowing for this effect makes it possible to calculate the energy of an Abrikosov vortex in the form of a helix whose length and pitch are much larger than the correlation length, whose curvature is small compared to the reciprocal London length, and whose slope in relation to an axis coinciding with the direction in which the vortex energy is the highest is also small. When the anisotropy is large, which is characteristic of high-T _c superconductors, the energy of such an Abrikosov vortex is lower than that of a straight Abrikosov vortex. Certain consequences of the fact that the Abrikosov vortices in a high-T _c superconductor are helical are discussed. Among these is a phase transition that breaks the symmetry between Abrikosov vortices shaped like right-and left-hand helixes in relation to the magnetic field. Zh. éksp. Teor. Fiz. 111, 1869–1878 (May 1997)     

Vortex-lattice melting in magnesium diboride in terms of the elastic theory

In the framework of elastic theory, we study the vortex-lattice melting transitions in magnesium diboride for magnetic fields both parallel and perpendicular to the anisotropy axis. Using the parameters from experiments, the vortex-lattice melting lines in the H-T diagram are located systematically by various groups of Lindemann numbers. It is observed that the theoretical result for the vortex melting with parallel and perpendicular fields agrees well with the experimental data. Therefore, it is suggested that the phenomenological elastic theory is universal to various type-II superconductors, including two- and multi-band superconductors.     

Pronounced enhancement of the lower critical field and critical current deep in the superconducting state of PrOs4Sb12

We have observed an unexpected enhancement of the lower critical field H(c1)(T) and the critical current I(c)(T) deep in the superconducting state below T approximately 0.6 K (T/T(c) approximately 0.3) in the filled skutterudite heavy fermion superconductor PrOs(4)Sb(12). From a comparison of the behavior of H(c1)(T) with that of the heavy fermion superconductors U(1-x)Th(x)Be(13) and UPt(3), we speculate that the enhancement of H(c1)(T) and I(c)(T) in PrOs(4)Sb(12) reflects a transition into another superconducting phase that occurs below T/T(c) approximately 0.3. An examination of the literature reveals unexplained anomalies in other physical properties of PrOs(4)Sb(12) near T/T(c) approximately 0.3 that correlate with the features we have observed in H(c1)(T) and I(c)(T).     

Effect of surface Andreev bound states on the Bean-Livingston barrier in d-wave superconductors

We study the influence of surface Andreev bound states in d-wave superconductors on the Bean-Livingston surface barrier for entry of a vortex line into a strongly type-II superconductor. Starting from Eilenberger theory, we derive a generalization of London theory to incorporate the anomalous surface currents arising from the Andreev bound states. This allows us to find an analytical expression for the modification of the Bean-Livingston barrier in terms of a single parameter describing the influence of the Andreev bound states. We find that the field of first vortex entry is significantly enhanced. Also, the depinning field for vortices near the surface is renormalized. Both effects are temperature dependent and depend on the orientation of the surface relative to the d-wave gap.     

Magnetic resonance line profile in thin superconducting films

Solutions of the modified London equations are derived for a vortex lattice in a thin film from high-temperature superconductors. The nuclear magnetic resonance line profile in the thin film from high-temperature superconductors of different thicknesses d is calculated with allowance for variable inhomogeneity of the local magnetic field of the vortex lattice. It is demonstrated that the nuclear magnetic resonance line profile changes significantly with d, which can give additional information on the superconductor parameters (including the symmetry type of the vortex lattice and the anisotropy parameter Γ). __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 16–19, November, 2005.     

Inertial mass of the Abrikosov vortex

We show that a large contribution to the inertial mass of the Abrikosov vortex comes from transversal displacements of the crystal lattice. The corresponding part of the mass per unit length of the vortex line is M(l)=(m(2)(e)c(2)/64 pi alpha(2)mu lambda(4)(L))ln((lambda(L)/xi), where m(e) is the bare electron mass, c is the speed of light, alpha=e(2)/Planck's over 2 pi c approximately 1/137 is the fine structure constant, mu is the shear modulus of the solid, lambda(L) is the London penetration length, and xi is the coherence length. In conventional superconductors, this mass can be comparable to or even greater than the vortex core mass computed by Suhl [Phys. Rev. Lett. 14, 226 (1965)]].     

Symmetrical aspects of the cooperative pseudo Jahn-Teller effect in high-Tc superconductors

A microscopical model for the structural phase transitions in high-T_c La₂CuO₄-type superconductors is presented. This model is based on the cooperative pseudo Jahn-Teller effect. The most attention is paid to the symmetrical aspects of the approach. The developed theory predicts the possibility of the re-entrant structural phase transition from the orthorhombic phase to the tetragonal one in the doped superconductors. This prediction is in agreement with the experimental observation. The important consequences for the mechanism of superconductivity that followed from the structural phase transitions are under consideration too.     

5f electron localization-delocalization transition from UPd3 to UPt3

The electronic structures of URh (3), UPd (3), UPt (3), and UAu (3) are calculated with the self-interaction corrected local-spin-density approximation. We find that only in URh (3) the f electrons are fully delocalized. UPt (3) has one f electron localized at each U site, while a localized f(2) configuration of the U ion is found for UPd (3). It is predicted that, upon application of a pressure of 25 GPa, UPd (3) will acquire the f(1) configuration and possibly exhibit heavy-fermion behavior. We find that UAu (3) is characterized by the same mixed localized-delocalized f-electron manifold as UPd (3).     

Majorana modes at the ends of superconductor vortices in doped topological insulators

Recent experiments have observed bulk superconductivity in doped topological insulators. Here we ask whether vortex Majorana zero modes, previously predicted to occur when s-wave superconductivity is induced on the surface of topological insulators, survive in these doped systems with metallic normal states. Assuming inversion symmetry, we find that they do but only below a critical doping. The critical doping is tied to a topological phase transition of the vortex line, at which it supports gapless excitations along its length. The critical point depends only on the vortex orientation and a suitably defined SU(2) Berry phase of the normal state Fermi surface. By calculating this phase for available band structures we determine that superconducting p-doped Bi(2)Te(3), among others, supports vortex end Majorana modes. Surprisingly, superconductors derived from topologically trivial band structures can support Majorana modes too.     

Theory of specific heat of vortex liquid of high T_c superconductors

Superconducting thermal fluctuation(STF) plays an important role in both thermodynamic and transport properties in the vortex liquid phase of high T_c superconductors.It was widely observed in the vicinity of the critical transition temperature.In the framework of Ginz burg-Landau-La wrence-Doniach theory in magnetic field,a self-consistent analysis of STF including all Landau levels is given.Besides that,we calculate the contribution of STF to specific heat in vortex liquid phase for high T_c cuprate superconductors,and the fitting results are in good agreement with experimental data.     

Spin-triplet superconductivity in UNi(2)Al(3) revealed by the (27)Al Knight shift measurement

We report (27)Al Knight shift ( (27)K) measurement on a single-crystal UNi(2)Al(3) that reveals a coexistence of superconductivity and a spin-density-wave (SDW) type of magnetic ordering ( T(SDW) = 4.5 K). The spin part of (27)K, (27)K(s), does not change down to 50 mK across the superconducting (SC) transition temperature T(c) approximately 0.9 K. In contrast with the isostructural compound UPd(2)Al(3) ( T(c) approximately 2 K), which was identified to be a spin-singlet d-wave superconductor, the behavior of (27)K strongly supports that UNi(2)Al(3) , like UPt(3) and Sr(2)RuO(4), belongs to a class of spin-triplet SC pairing state superconductors.