Vortex states in nanoscale superconducting squares: The influence of quantum confinement (original) (raw)
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Physical Review Letters, 2012
Vortex matter in mesoscopic superconductors is known to be strongly affected by the geometry of the sample. Here we show that in nanoscale superconductors with coherence length comparable to the Fermi wavelength the shape resonances of the order parameter results in an additional contribution to the quantum topological confinement-leading to unconventional vortex configurations. Our Bogoliubov-de Gennes calculations in a square geometry reveal a plethora of asymmetric, giant multivortex, and vortex-antivortex structures, stable over a wide range of parameters and which are very different from those predicted by the Ginzburg-Landau theory. These unconventional states are relevant for high-T c nanograins, confined Bose-Einstein condensates, and graphene flakes with proximity-induced superconductivity.
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".
Electronic structure of multiquantum giant vortex states in mesoscopic superconducting disks
Proceedings of the National Academy of Sciences, 2002
We report self-consistent calculations of the microscopic electronic structure of the so-called giant vortex states. These novel multiquantum vortex states, detected by recent magnetization measurements on submicron disks, are qualitatively different from the Abrikosov vortices in the bulk. We find that, in addition to multiple branches of bound states in the core region, the local tunneling density of states exhibits Tomasch oscillations due to the single-particle interference arising from quantum confinement. These features should be directly observable by scanning tunneling spectroscopy. 74.20.Fg,
Stable Vortex-Antivortex Molecules in Mesoscopic Superconducting Triangles
Physical Review Letters, 2003
A thermodynamically stable vortex-antivortex pattern has been revealed in mesoscopic type I superconducting triangles, contrary to type II superconductors where similar patterns are unstable. The stable vortex-antivortex "molecule" appears due to the interplay between two factors: a repulsive vortex-antivortex interaction in type I superconductors and the vortex confinement in the triangle.
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.
Stabilized vortex-antivortex molecules in a superconducting microdisk with a magnetic nanodot on top
Physical Review B, 2007
Symmetry-induced vortex-antivortex molecules in submicrometer superconducting polygons in homogeneous magnetic field became of general interest following the prediction of Chibotaru et al. ͓Nature ͑London͒ 408, 833 ͑2000͔͒. Recently, Carballeira et al. ͓Phys. Rev. Lett. 95, 237003 ͑2005͔͒ found that these fascinating structures can be enforced by a magnetic dot placed on top of the sample. Here, we show that vortex-antivortex configurations can actually be induced in a superconducting disk by the above magnet with perpendicular magnetization, in spite of the nonzero net flux penetrating the sample and the absence of polygonal geometrical constraints. Our study is done within the Ginzburg-Landau formalism and shows that confinement makes vortex-antivortex states metastable ͑i.e., with higher energy͒ compared to the conventional vortex states; nevertheless, these states can be experimentally observed, and we propose a procedure for their realization, under a magnet with tilted magnetic moment.
Vortex states and magnetization curve of square mesoscopic superconductors
Physical Review B
The structure of the vortex states in a square mesoscopic superconductor is analyzed in detail using the numerical simulation within the time-dependent Ginzburg-Landau ͑TDGL͒ theory. Various vortex states ͑vortices, vortex molecules, multiquanta vortices͒ are observed and the magnetization curve is obtained. Different changes in vortex structures are identified with the peculiarities on the magnetization curve. Stability of a state consisting of vortices and antivortices is discussed.
Vortex–antivortex states in nanostructured superconductor–ferromagnet hybrids
Physica C: Superconductivity, 2010
The formation of vortex-antivortex states in a superconducting film with a square array of magnetic dipoles magnetized perpendicularly to the film is investigated in the framework of the time-dependent Ginzburg-Landau equations. It is shown that a possible route to obtain equilibrium states is obtained following an experimentally realizable field-cooling procedure. The states thus obtained demonstrate a rich variety of phases, depending on magnetic moment intensity and dipole array-to-superconducting film distance. For instance, in the region of the phase diagram where each dipoles is able to generate N = 2 vortex-antivortex pairs, the antivortices induced by the negative stray fields of the dipoles undergo two transitions before ultimately merging into doubly-quantized giant antivortices. For N = 4, a state consisting on a three-quanta giant vortex below each dipole and an interstitial vortex-antivortex molecule was observed. Such state is thermodynamically stable and is induced by the fourfold symmetry of the dipole array, similar to symmetry-induced vortex-antivortex molecules found in mesoscopic superconductors.
From vortex molecules to the Abrikosov lattice in thin mesoscopic superconducting disks
Physical Review B, 2004
Stable vortex states are studied in large superconducting thin disks (for numerical purposes we considered disks with radius R =50). Configurations containing more than 700 vortices were obtained using two different approaches: the nonlinear Ginzburg-Landau (GL) theory and the London approximation. To obtain better agreement with results from the GL theory we generalized the London theory by including the spatial variation of the order parameter following Clem's ansatz. We find that configurations calculated in the London limit are also stable within the Ginzburg-Landau theory for up to ϳ230 vortices. For large values of the vorticity (typically, L տ 100), the vortices are arranged in an Abrikosov lattice in the center of the disk, which is surrounded by at least two circular shells of vortices. A Voronoi construction is used to identify the defects present in the ground state vortex configurations. Such defects cluster near the edge of the disk, but for large L also grain boundaries are found which extend up to the center of the disk.
Vortex?antivortex patterns in mesoscopic superconductors
Physica B: Condensed Matter, 2003
We have studied the nucleation of superconductivity in mesoscopic structures of different shape (triangle, square and rectangle). This was made possible by using an analytical gauge transformation for the vector potential A which gives A n ¼ 0 for the normal component along the boundary line of the rectangle. As a consequence the superconductorvacuum boundary condition reduces to the Neumann boundary condition. By solving the linearized Ginzburg-Landau equation with this boundary condition we have determined the field-temperature superconducting phase boundary and the corresponding vortex patterns. The comparison of these patterns for different structures demonstrates that the critical parameters of a superconductor can be manipulated and fine-tuned through nanostructuring.