S. V. Yampolskii

Magnetic pinning of vortices in a superconducting film: The (anti)vortex-magnetic dipole interaction energy in the London approximation

The interaction between a superconducting vortex or antivortex in a superconducting film and a magnetic dipole with in- or out-of-plane magnetization is investigated within the London approximation. The dependence of the interaction energy on the dipole-vortex distance and the film thickness is studied, and analytical results are obtained in limiting cases. We show how the short range interaction with the magnetic dipole makes the co-existence of vortices and antivortices possible. Different configurations with vortices and antivortices are investigated.

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 such as 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 K. 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 behavior is not found for the case of large κ, i.e., type-II superconductivity.

Vortex charge in mesoscopic superconductors

The electric charge density in mesoscopic superconductors with circular symmetry, i.e., disks and cylinders, is studied within the phenomenological Ginzburg-Landau approach. We found that even in the Meissner state there is a charge redistribution in the sample which makes the sample edge become negatively charged. In the vortex state there is a competition between this Meissner charge and the vortex charge which may change the polarity of the charge at the sample edge with increasing magnetic field. It is shown analytically that in spite of the charge redistribution the mesoscopic sample as a whole remains electrically neutral.

Multi-vortex states of a thin superconducting disk in a step-like external magnetic field

The vortex states in a thin mesoscopic disk are investigated within the phenomenological Ginzburg-Landau theory in the presence of a step-like external magnetic field with zero average which could model the field resulting from a ferromagnetic disk or a current carrying loop. The regions of existence of the multi-vortex state and the giant vortex state are found. We analyzed the phase transitions between them and found regions in which ring-shaped vortices contribute. Furthermore, we found a vortex state consisting of a central giant vortex surrounded by a collection of anti-vortices that are located in a ring around this giant vortex.Abstract The vortex states in a thin mesoscopic disk are investigated within the phenomenological Ginzburg–Landau theory in the presence of a step-like external magnetic field with zero average which could model the field resulting from a ferromagnetic disk or a current carrying loop. The regions of existence of the multi-vortex state and the giant vortex (GV) state are found. We analyzed the phase transitions between them and found regions in which ring-shaped vortices contribute. Furthermore, we found a vortex state consisting of a central GV surrounded by a collection of anti-vortices that are located in a ring around this GV.

Magnetic coupling between mesoscopic superconducting rings

Abstract Using the nonlinear Ginzburg–Landau theory we investigated the dependence of the magnetic coupling between two concentric mesoscopic superconducting rings on their thickness. The size of this magnetic coupling increases with the thickness of the rings.

Giant vortices in small mesoscopic disks: an approximate description

Abstract We present an approximate description of the giant vortex state in a thin mesoscopic superconducting disk within the phenomenological Ginzburg–Landau approach. Analytical asymptotic expressions for the energies of the states with fixed vorticity are obtained when a small magnetic flux is accumulated in the disk. The spectrum of the lowest Landau levels of such a disk is also discussed.

Electric Charges in Superconducting Mesoscopic Samples

The distribution of the electric charge density in mesoscopic superconducting disks and cylinders is studied within the phenomenological Ginzburg-Landau approach. We found that even in the Meissner state the mesoscopic sample exhibits a non-uniform charge distribution such that a region near the sample edge becomes negatively charged. When vortices are inside the sample there is a superposition of the negative charge located at the vortex core and this Meissner charge, and, as a result, the charge at the sample edge changes sign as a function of the applied magnetic field.