Hall potentiometer in the ballistic regime

We demonstrate theoretically how a two-dimensional electron gas can be used to probe local potential profiles using the Hall effect. For small magnetic fields, the Hall resistance is inversely proportional to the average potential profile in the Hall cross and is independent of the shape and the position of this profile in the junction. The bend resistance, on the other hand, is much more sensitive on the exact details of the local potential profile in the cross junction.Comment: 3 pages, 4 ps figure

Saddle point states and energy barriers for vortex entrance and exit in superconducting disks and rings

The transitions between the different vortex states of thin mesoscopic superconducting disks and rings are studied using the non-linear Ginzburg-Landau functional. They are saddle points of the free energy representing the energy barrier which has to be overcome for transition between the different vortex states. In small superconducting disks and rings the saddle point state between two giant vortex states, and in larger systems the saddle point state between a multivortex state and a giant vortex state and between two multivortex states is obtained. The shape and the height of the nucleation barrier is investigated for different disk and ring configurations.Comment: 10 pages, 18 figure

From vortex molecules to the Abrikosov lattice in thin mesoscopic superconducting disks

Stable vortex states are studied in large superconducting thin disks (for numerical purposes we considered with radius R = 50 \xi). 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 ~ 230 vortices. For large values of the vorticity (typically, L > 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.Comment: 15 pages, 10 figures, RevTex4, submitted to Phys. Rev.

Stationary phase slip state in quasi-one-dimensional rings

The nonuniform superconducting state in a ring in which the order parameter vanishing at one point is studied. This state is characterized by a jump of the phase by $\pi$ at the point where the order parameter becomes zero. In uniform rings such a state is a saddle-point state and consequently unstable. However, for non-uniform rings with e.g. variations of geometrical or physical parameters or with attached wires this state can be stabilized and may be realized experimentally.Comment: 6 pages, 7 figures, RevTex 4.0 styl

Effects of thermal fluctuations on the magnetic behavior of mesoscopic superconductors

We study the influence of thermal fluctuations on the magnetic behavior of square mesoscopic superconductors. The strength of thermal fluctuations are parameterized using the Ginzburg number, which is small ($G_i \approx 10^{-10}$) in low-$T_c$ superconductors and large in high-$T_c$ superconductors ($G_i \approx 10^{-4}$). For low-$T_c$ mesoscopic superconductors we found that the meta-stable states due to the surface barrier have a large half-life time, which leads to the hysteresis in the magnetization curves as observed experimentally. A very different behavior appears for high-$T_c$ mesoscopic superconductors where thermally activated vortex entrance/exit through surface barriers is frequent. This leads to a reduction of the magnetization and a non-integer average number of flux quanta penetrating the superconductor. The magnetic field dependence of the probability for the occurrence of the different vortex states and the fluctuations in the number of vortices are studied.Comment: 9 pages, 6 figures, submitted to Phys. Rev.

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.

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

Vortex structure of thin mesoscopic disks in the presence of an inhomogeneous magnetic field

The vortex states in a thin mesoscopic disk are investigated within the phenomenological Ginzburg-Landau theory in the presence of different ''model'' magnetic field profiles with zero average field which may result from a ferromagnetic disk or circulating currents in a loop near the superconductor. We calculated the dependences of both the ground and metastable states on the magnitude and shape of the magnetic field profile for different values of the order parameter angular moment, i.e. the vorticity. The regions of existence of the multi-vortex state and the giant vortex state are found. We analysed the phase transitions between these states and studied the contribution from ring-shaped vortices. A new transition between different multi-vortex configurations as the ground state is found. Furthermore, we found a vortex state consisting of a central giant vortex surrounded by a collection of anti-vortices which are located in a ring around this giant vortex. The limit to a disk with an infinite radius, i.e. a film, will also be discussed. We also extended our results to ''real'' magnetic field profiles and to the case in which an external homogeneous magnetic field is present.Comment: 17 pages, 23 figures. Submitted to PR