For a superconducting mesoscopic square loop, the superconducting state is described and the phase boundaries are analyzed on the basis of a self-consistent solution of the Ginzburg-Landau equations. There exists a qualitative difference in the nucleation of the superconducting state in a square and a circular mesoscopic loop. Due to the interplay of different kinds of symmetry, of the square loop and of the magnetic field, the order-parameter distribution is inhomogeneous in the loop. After clarification of the thermodynamical stability of the superconducting states, we turn to the analysis of the equilibrium states which can be realized in experiment. The problem of the $H-T$ superconducting phase boundary is discussed in detail. The calculated phase boundaries are in good agreement with the experimental data obtained for the Al mesoscopic superconducting square loops.

• Received 9 September 1997

DOI:https://doi.org/10.1103/PhysRevB.58.11703