TY - JOUR
T1 - Boundary conditions, dimensionality, topology and size dependence of the superconducting transition temperature
AU - Fink, Herman J.
AU - Haley, Stephen B.
AU - Giuraniuc, Claudiu V.
AU - Kozhevnikov, Vladimir F.
AU - Indekeu, Joseph O.
N1 - J.O.I. wishes to thank Ben Widom, to whom this paper is dedicated, for his guidance, over the years, during numerous expeditions in the wondrous field of critical phenomena. Discussions with D.S. McLachlan are acknowledged. This research is supported, in part, by K.U. Leuven Fellowship F/03/066 for V.F.K. and by FWO project G.0237.05.
PY - 2005/11/1
Y1 - 2005/11/1
N2 - For various sample geometries (slabs, cylinders, spheres, hypercubes), de Gennes' boundary condition parameter b is used to study its effect upon the transition temperature Tc of a superconductor. For b > 0 the order parameter at the surface is decreased, and as a consequence Tc is reduced, while for b < 0 the order parameter at the surface is increased, thereby enhancing Tc of a specimen in zero magnetic field. Exact solutions, derived by Fink and Haley (Int. J. mod. Phys. B, 17, 2171 (2003)), of the order parameter of a slab of finite thickness as a function of temperature are presented, both for reduced and enhanced transition (nucleation) temperatures. At the nucleation temperature the order parameter approaches zero. This concise review closes with a link established between de Gennes' microscopic boundary condition and the Ginzburg-Landau phenomenological approach, and a discussion of some relevant experiments. For example, applying the boundary condition with b < 0 to tin whiskers elucidates the increase of Tc with strain.
AB - For various sample geometries (slabs, cylinders, spheres, hypercubes), de Gennes' boundary condition parameter b is used to study its effect upon the transition temperature Tc of a superconductor. For b > 0 the order parameter at the surface is decreased, and as a consequence Tc is reduced, while for b < 0 the order parameter at the surface is increased, thereby enhancing Tc of a specimen in zero magnetic field. Exact solutions, derived by Fink and Haley (Int. J. mod. Phys. B, 17, 2171 (2003)), of the order parameter of a slab of finite thickness as a function of temperature are presented, both for reduced and enhanced transition (nucleation) temperatures. At the nucleation temperature the order parameter approaches zero. This concise review closes with a link established between de Gennes' microscopic boundary condition and the Ginzburg-Landau phenomenological approach, and a discussion of some relevant experiments. For example, applying the boundary condition with b < 0 to tin whiskers elucidates the increase of Tc with strain.
UR - http://www.scopus.com/inward/record.url?scp=29544434881&partnerID=8YFLogxK
U2 - 10.1080/00268970500226189
DO - 10.1080/00268970500226189
M3 - Article
AN - SCOPUS:29544434881
SN - 0026-8976
VL - 103
SP - 2969
EP - 2978
JO - Molecular Physics
JF - Molecular Physics
IS - 21-23 SPEC. ISS.
ER -