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An approach to the Ginzburg–Landau problem for superconducting regular polygons is developed making use of an analytical gauge transformation for the vector potential A which gives An=0 for the normal component along the boundary line of different symmetric polygons. As a result the corresponding linearized Ginzburg–Landau equation reduces to an eigenvalue problem in the basis set of functions obeying Neumann boundary condition. Such basis sets are found analytically for several symmetric structures. The proposed approach allows for accurate calculations of the order parameter distributions at low calculational cost (small basis sets) for moderate applied magnetic fields. This is illustrated by considering the nucleation of superconductivity in squares, equilateral triangles and rectangles, where vortex patterns containing antivortices are obtained on the Tc–H phase boundary. The calculated phase boundaries are compared with the experimental Tc(H) curves measured for squares, triangles, disks, rectangles, and loops. The stability of the symmetry consistent solutions against small deviations from the phase boundary line deep into the superconducting state is investigated by considering the full Ginzburg–Landau functional. It is shown that below the nucleation temperature symmetry-switching or symmetry-breaking phase transitions can take place. The symmetry-breaking phase transition has the same structure as the pseudo-Jahn-Teller instability of high symmetry nuclear configurations in molecules. The existence of these transitions is predicted to be strongly dependent on the size of the samples. [ABSTRACT FROM AUTHOR]

Nucleation of superconductivity and vortex patterns have been studied in mesoscopic samples providing the crossover between square and rectangular geometries. The measured nucleation line,Tc(H), has been analyzed in the framework of the linearized Ginzburg-Landau theory. A very good agreement has been found between the theoreticalTc(H) boundary and the experimental data for rectangles with different aspect ratios. The superconductor/ferromagnet hybrids, such as magnetic Co/Pd dot in a superconducting loop and the dot on top of a superconducting disk have also been investigated. Pronounced effects of the dot on theTc(H) boundary have been found, including strong asymmetry with respect to the field polarity. [ABSTRACT FROM AUTHOR]

The nucleation of superconductivity in a mesoscopic equilateral triangle is studied experimentally by transport measurements and theoretically by using the linearized Ginzburg–Landau equation. The voltage and current leads, intrinsic to transport measurements, give rise to a broadening of the resistive transition R(T). However, by choosing the right resistance criterion to determine the experimental superconducting/normal phase boundary Tc(H) and by reducing the coupling between the triangle and the contacts, achieved by changing the shape of the contacts, this influence can be minimized. From the theoretical study, we found that the trigonal symmetry of the sample has a profound effect on the superconducting state in the presence of a magnetic field H leading, in particular, to the formation of antivortices in symmetry-consistent states. A good agreement between the theory and the experimental Tc(H) data is observed. [Copyright &y& Elsevier]

An approach to the Ginzburg–Landau problem for superconducting regular polygons is developed making use of an analytical gauge transformation for the vector potential A which gives An=0 for the normal component along the boundary line of an arbitrary regular polygon. As a result the corresponding linearised Ginzburg–Landau equation reduces to an eigenvalue problem in the basis set of functions obeying Neumann boundary condition. The proposed approach allows for accurate calculations of the order parameter distributions at low calculational cost (small basis sets) for moderate applied magnetic fields. This is illustrated by considering the nucleation of superconductivity in squares and equilateral triangles where novel vortex patterns containing and antivortex in the centre are obtained on the Tc–H phase boundary. The stability of these solutions against small deviations from the phase boundary line deeper into the superconducting state is investigated and the conditions for the experimental observation of the novel vortex patterns are discussed. [Copyright &y& Elsevier]