Vortices on a superconducting nanoshell: Phase diagram and dynamics (original) (raw)

Coexistence of the Meissner and vortex states on a nanoscale superconducting spherical shell

Physical Review B, 2009

We show that on superconducting spherical nanoshells, the coexistence of the Meissner state with a variety of vortex patterns drives the phase transition to higher magnetic fields. The spherical geometry leads to a Magnus-Lorentz force pushing the nucleating vortices and antivortices towards the poles, overcoming local pinning centers, preventing vortex-antivortex recombination and leading to the appearance of a Meissner belt around the sphere's equator. In sufficiently small and thin spherical shells paramagnetic vortex states can be stable, enabling spatial separation of freely moving shells with different radii and vorticity in an inhomogeneous external magnetic field.

The Confinement of Vortices in Nano-Superconducting Devices

arXiv (Cornell University), 2017

We have investigated the confinement of 3-D vortices in specific cases of Type-II (κ = 2) nanosuperconducting devices. The emergent pattern of vortices greatly depends on the orientation of an applied magnetic field (transverse or longitudinal), and the size of the devices (a few coherence lengths ξ). Herein, cylindrical geometries are examined. The surface barriers become very significant in these nano-systems, and hence the characteristics of the vortices become highly sensitive to the shape of the system and direction of an applied field. It is observed that nano-cylindrical superconductors, depending on their sizes, can display either first or second order phase transitions, under the influence of a longitudinal field. In the confined geometries, nucleation of a giant vortex state composed of a n-quanta emerges for the longitudinal magnetic field.

Vortex states in mesoscopic superconducting squares: Formation of vortex shells

Physical Review B, 2008

We analyze theoretically and experimentally vortex configurations in mesoscopic superconducting squares. Our theoretical approach is based on the analytical solution of the London equation using Green's-function method. The potential-energy landscape found for each vortex configuration is then used in Langevin-type molecular-dynamics simulations to obtain stable vortex configurations. Metastable states and transitions between them and the ground state are analyzed. We present our results of the first direct visualization of vortex patterns in µm-sized Nb squares, using the Bitter decoration technique. We show that the filling rules for vortices in squares with increasing applied magnetic field can be formulated, although in a different manner than in disks, in terms of formation of vortex "shells".

Vortex structures in nano-sized pentagon and other shaped superconductors

Physica C: Superconductivity, 2013

Vortex structures in nano-sized superconductors are investigated using the Ginzburg-Landau equation. In order to investigate the various shaped superconductors, we adopt the Finite Element Method for numerical calculations. We show some vortex structures in a pentagon superconductor under an external field. We found that for a large pentagon superconductor, the vortex structure becomes a shell structure as in superconducting disks.

Vortex chains in anisotropic superconductors

Journal of Physics: Condensed Matter, 2005

T superconductors in small magnetic fields directed away from the crystal symmetry axes have been found to exhibit inhomogeneous chains of flux lines (vortices), in contrast to the usual regular triangular flux-line lattice. We review the experimental observations of these chains, and summarize the theoretical background that explains their appearance. We treat separately two classes of chains: those that appear in superconductors with moderate anisotropy due to an attractive part of the interaction between tilted flux lines, and those with high anisotropy where the tilted magnetic flux is created by two independent and perpendicular crossing lattices. In the second case it is the indirect attraction between a flux line along the layers (Josephson vortex) and a flux line perpendicular to the layers (pancake vortex stack) that leads to the formation of chains of the pancake vortex stacks. This complex system contains a rich variety of phenomena, with several different equilibrium phases, and an extraordinary dynamic interplay between the two sets of crossing vortices. We compare the theoretical predictions of these phenomena with the experimental observations made to date. We also contrast the different techniques used to make these observations. While it is clear that this system forms a wonderful playground for probing the formation of structures with competing interactions, we conclude that there are important practical implications of the vortex chains that appear in highly anisotropic superconductors.

Co-existence of the Meissner and vortex-state on a superconducting spherical shell

2009

We show that on superconducting spherical nanoshells, the co-existence of the Meissner state with a variety of vortex patterns drives the phase transition to higher magnetic fields. The spherical geometry leads to a Magnus-Lorentz force pushing the nucleating vortices and antivortices towards the poles, overcoming local pinning centers, preventing vortex-antivortex recombination and leading to the appearance of a Meissner belt around the sphere's equator. In sufficiently small and thin spherical shells paramagnetic vortex states can be stable, enabling spatial separation of freely moving shells with different radii and vorticity in an inhomogeneous external magnetic field.

Vortex shells in mesoscopic superconducting disks

Physical Review B, 2004

The distribution of vortices over different vortex shells in mesoscopic superconducting disks with sufficiently large sizes is investigated within the framework of the nonlinear Ginzburg-Landau theory. Keeping the total vorticity fixed, different vortex configurations can be found in which the vortices are distributed differently over the vortex shells. An overview is given of the different possible vortex configurations and the free energies of these states are compared. In general, the difference in the free energy between the possible vortex configurations with the same vorticity is much smaller than the difference in the free energy between vortex states with different vorticity. The transitions between different vortex states with the same and different vorticity are investigated. Contrary to small disks, the change in vorticity can be larger than one with increasing and decreasing magnetic field. Also a combination of a giant vortex state with a multivortex state can nucleate into a stable vortex state. The influence of the sample thickness is briefly studied. Our results are compared with those obtained from the London approximation which clearly shows the limited applicability of the latter.

Vortex phase separation in mesoscopic superconductors

Scientific Reports, 2013

We demonstrate that in mesoscopic type II superconductors with the lateral size commensurate with London penetration depth, the ground state of vortices pinned by homogeneously distributed columnar defects can form a hierarchical nested domain structure. Each domain is characterized by an average number of vortices trapped at a single pinning site within a given domain. Our study marks a radical departure from the current understanding of the ground state in disordered macroscopic systems and provides an insight into the interplay between disorder, vortex-vortex interaction, and confinement within finite system size. The observed vortex phase segregation implies the existence of the soliton solution for the vortex density in the finite superconductors and establishes a new class of nonlinear systems that exhibit the soliton phenomenon. V ortex matter in the presence of structural defects forms a wide variety of phases with specific properties depending on the relation between the vortex-vortex and vortex-defect interactions 1,2. The findings of Refs. 3, 4, which revealed significant enhancement of vortex pinning in high-temperature superconductors by ion irradiation, broke ground for a new direction in vortex physics. Heavy ions leave the tracks of the damaged amorphous material where superconductivity is suppressed. Thus the vortices penetrating the sample occupy columnar defects where the vortex energy is appreciably less than in the undamaged material. A theory of the resulting vortex Bose glass phase was developed in Refs. 5, 6, where the physics of flux lines in superconductors pinned by columnar defects was mapped onto boson localization in two dimensions. The distribution of vortices in the Bose glass state that forms in the infinite (i.e. thermodynamically large) samples, containing columnar defects, is a uniform one. A question about what happens to the Bose glass in the finite samples is most natural in view of explosively developing studies of small superconductors, i.e. superconductors with the lateral sizes R s comparable to the London screening length l or even with the coherence length j. Indeed even the samples without columnar defects reveal that the properties of the homogeneous vortex state change dramatically as R s l. The boundaries start to affect the distribution of vortices and makes it nonuniform. Experimental study of mesoscopic superconducting discs with the total vorticity L , 40 revealed formation of the concentric shells of vortices 7 in accord with the results of numerical simulations 8. The analysis of shell filling with increasing L allowed the authors of Ref. 7 to identify magic numbers corresponding to the appearance of consecutive new shells. At the same time, vortex distribution over the sample remains ''quasi-homogeneous'' with the vortex density gradually changing with the distance from the sample center. For example, the experimental and numerical studies of the samples containing a macroscopic number of vortices showed that, almost everywhere, vortices arrange themselves into a nearly perfect Abrikosov lattice, containing the few disclinations necessary to match the cylindrical symmetry of the sample. Only within a few, 2-3, shells adjacent to the surface, vortex distribution differs noticeably from that in the bulk. At the same time, theoretical consideration of the critical state in a superconducting slab containing a lattice of strong pins 9 predicted that instead of the expected in the critical state constant gradient in the vortex density a terraced piecewise vortex structure structure can form. This terraced vortex distribution, unexpected from the viewpoint of an orthodox concept of the critical state, is, formally, nothing but a standard soliton solution for the one-dimensional commensurate structures, which appeared first as a 1D model for dislocations 10,11. The physical reason for emerging such a structure is the competition between the effect of the critical current flowing uniformly through the slab and thus implying the constant gradient of the vortex density across the sample and the action of the lattice of strong pinning sites that tend to trap vortices enforcing them into a regular array with the commensurate period. As a result, a metastable structure forms, comprising vortex domains of a piecewise constant vortex density. The originally uniform current is compressed into the current filaments concentrated along the