Vortex phases in mesoscopic cylinders with suppressed surface superconductivity

Vortex structures in mesoscopic cylinder placed in external magnetic field are studied under the general de Gennes boundary condition for the order parameter corresponding to the suppression of surface superconductivity. The Ginzburg-Landau equations are solved based on trial functions for the order parameter for vortex-free, single-vortex, multivortex, and giant vortex phases. The equilibrium vortex diagrams in the plane of external field and cylinder radius and magnetization curves are calculated at different values of de Gennes "extrapolation length" characterizing the boundary condition for the order parameter. The comparison of the obtained variational results with some available exact solutions shows good accuracy of our approach.Comment: RevTex, 11 pages, 10 figure

Vortices on a superconducting nanoshell: phase diagram and dynamics

In superconductors, the search for special vortex states such as giant vortices focuses on laterally confined or nanopatterned thin superconducting films, disks, rings, or polygons. We examine the possibility to realize giant vortex states and states with non-uniform vorticity on a superconducting spherical nanoshell, due to the interplay of the topology and the applied magnetic field. We derive the phase diagram and identify where, as a function of the applied magnetic field, the shell thickness and the shell radius, these different vortex phases occur. Moreover, the curved geometry allows these states (or a vortex lattice) to coexist with a Meissner state, on the same curved film. We have examined the dynamics of the decay of giant vortices or states with non-uniform vorticity into a vortex lattice, when the magnetic field is adapted so that a phase boundary is crossed.Comment: 21 pages, 9 figure

Variational method to study vortex matter in mesoscopic superconductors

A simple variational model is proposed to analyze the superconducting state in long cylindrical type-II superconductor placed in the external magnetic field. In the framework of this model, it is possible to solve the Ginzburg-Landau equations for the states with axially symmetric distributions of the order parameter. Phase transitions between different superconducting states are studied in the presence of external magnetic field and an equilibrium phase diagram of thin cylinder is obtained. The lower critical field of the cylindrical type-II superconductor with arbitrary values of radius and Ginzburg-Landau parameter is found. The field dependence of the magnetization of thin cylinder, which can carry several magnetic flux quanta, is calculated.Comment: 10 pages, 5 figures, submitted to Physica

Magnetic resonance within vortex cores in the B phase of superfluid 3^3He

We investigate a magnetic susceptibility of vortices in the B phase of multicomponent triplet superfluid $^3$He focusing on a contribution of bound fermionic states localized within vortex cores. Several order parameter configurations relevant to different types of quantized vortices in $^3$He B are considered. It is shown quite generally that an ac magnetic susceptibility has a sharp peak at the frequency corresponding to the energy of interlevel spacing in the spectrum of bound fermions. We suggest that measuring of a magnetic resonance within vortex cores can provide a direct probe of a discrete spectrum of bound vortex core excitations

Dependence of the vortex configuration on the geometry of mesoscopic flat samples

The influence of the geometry of a thin superconducting sample on the penetration of the magnetic field lines and the arrangement of vortices are investigated theoretically. We compare superconducting disks, squares and triangles with the same surface area having nonzero thickness. The coupled nonlinear Ginzburg-Landau equations are solved self-consistently and the important demagnetization effects are taken into account. We calculate and compare quantities like the free energy, the magnetization, the Cooper-pair density, the magnetic field distribution and the superconducting current density for the three geometries. For given vorticity the vortex lattice is different for the three geometries, i.e. it tries to adapt to the geometry of the sample. This also influences the stability range of the different vortex states. For certain magnetic field ranges we found a coexistence of a giant vortex placed in the center and single vortices toward the corners of the sample. Also the H-T phase diagram is obtained.Comment: 9 pages, 17 figures (submitted to Phys. Rev. B

Superconducting properties of mesoscopic cylinders with enhanced surface superconductivity

The superconducting state of an infinitely long superconducting cylinder surrounded by a medium which enhances its superconductivity near the boundary is studied within the nonlinear Ginzburg-Landau theory. This enhancement can be due to the proximity of another superconductor or due to surface treatment. Quantities like the free energy, the magnetization and the Cooper-pair density are calculated. Phase diagrams are obtained to investigate how the critical field and the critical temperature depend on this surface enhancement for different values of the Ginzburg-Landau parameter \kappa. Increasing the superconductivity near the surface leads to higher critical fields and critical temperatures. For small cylinder diameters only giant vortex states nucleate, while for larger cylinders multivortices can nucleate. The stability of these multivortex states also depends on the surface enhancement. For type-I superconductors we found the remarkable result that for a range of values of the surface extrapolation length the superconductor can transit from the Meissner state into superconducting states with vorticity L > 1. Such a behaviour is not found for the case of large \kappa, i.e. type-II superconductivity.Comment: submitted to Phys. Rev.

Chiral CP^2 skyrmions in three-band superconductors

It is shown that under certain conditions, three-component superconductors (and in particular three-band systems) allow stable topological defects different from vortices. We demonstrate the existence of these excitations, characterized by a $CP^2$ topological invariant, in models for three-component superconductors with broken time reversal symmetry. We term these topological defects "chiral $GL^{(3)}$ skyrmions", where "chiral" refers to the fact that due to broken time reversal symmetry, these defects come in inequivalent left- and right-handed versions. In certain cases these objects are energetically cheaper than vortices and should be induced by an applied magnetic field. In other situations these skyrmions are metastable states, which can be produced by a quench. Observation of these defects can signal broken time reversal symmetry in three-band superconductors or in Josephson-coupled bilayers of $s_\pm$ and s-wave superconductors.Comment: minor presentation changes; replaced journal version; 30 pages, 21 figure

Type-1.5 superconductivity in multiband systems: the effects of interband couplings

In contrast to single-component superconductors, which are described at the level of Ginzburg-Landau theory by a single parameter \kappa and are divided in type-I \kappa1/\sqrt{2} classes, two-component systems in general possess three fundamental length scales and have been shown to possess a separate "type-1.5" superconducting state. In that state, as a consequence of the extra fundamental length scale, vortices attract one another at long range but repel at shorter ranges, and therefore should form clusters in low magnetic fields. In this work we investigate the appearance of type-1.5 superconductivity and the interpretation of the fundamental length scales in the case of two bands with substantial interband couplings such as intrinsic Josephson coupling, mixed gradient coupling and density-density interactions. We show that in the presence of substantial intercomponent interactions of the above types the system supports type-1.5 superconductivity with fundamental length scales being associated with the mass of the gauge field and two masses of normal modes represented by mixed combinations of the density fields.Comment: 19 pages, v.2: various additions, v.3: journal version (minor improvements in presentation