Size, Shape and Impurity Effects on Superconducting critical temperature.*

Bulk superconductors have their own critical temperatures Tc. However, for a nano-structured superconductor, Tc depends on size and shape of the superconductor [1]. Nishizaki showed that the high pressure torsion on bulks of Nb makes Tc higher, because the torsion makes many nano-sized fine grains in the bulks [2]. However the high pressure torsion on bulks of V makes Tc lower, and Nishizaki discussed that the decrease of Tc is caused by impurities in the bulks of V. We studied size, shape, and impurity effects on Tc, by solving the Gor'kov equations, using the finite element method. We found that smaller and narrower superconductors show higher Tc. We found how size and shape affects Tc by studying spacial order parameter distributions and quasi-particle eigen-energies [3]. Also we studied the impurity effects on Tc, and found that Tc decreases with increase of scattering rate by impurities. [1] H. Suematsu, M. Kato and T. Ishida, J. Phys.: Conf. Ser. 150 (2009) 052250. [2] T. Nishizakiet al., Physica C 493 (2013) 132. [3] M. Umeda, M. Kato, O.Sato IEEE Trans. Appl. Supercond. 26 (2016) 8600104.