2007/06/16 by Zhidong Hao, Hao, Zhidong
Engineering · Physics and Astronomy · #Physics of Superconductivity and Magnetism #Superconducting Materials and Applications #cond-mat.supr-con
paper · pdf · doi:10.48550/arxiv.0706.2394
16 pages, 11 figures
arxiv created 2007/06/16 · arxiv updated 2009/12/01
We present a microscopic theory for superconductivity in a magnetic field based on a local approximation approach. We derive an expression for free energy density F as a function of temperature T and vector potential \bf a, and two basic equations of the theory: the first is an implicit solution for energy gap parameter amplitude |Δ\bf k| as a function of wave vector \bf k, temperature T and vector potential \bf a; and the second is a London-like relation between electrical current density \bf j and vector potential \bf a, with an ``effective superconducting electron density'' ns that is both T- and \bf a-dependent. The two equations allow determination of spatial variations of \bf a and |Δ\bf k| in a superconductor for given temperature T, applied magnetic field \bf Ha and sample geometry. The theory shows the existence of a ``partly-paired state,'' in which paired electrons (having |Δ\bf k|>0) and de-paired electrons (having |Δ\bf k|=0) co-exist. Such a ``partly-paired state'' exists even at T=0 when Ha is above a threshold for a given sample, giving rise to a non-vanishing Knight shift at T=0 for Ha above the threshold. We expect the theory to be valid for highly-local superconductors for all temperatures and magnetic fields below the superconducting transition. In the low-field limit, the theory reduces to the local-limit result of BCS. As examples, we apply the theory to the case of a semi-infinite superconductor in an applied magnetic field \bf Ha parallel to the surface of the superconductor and the case of an isolated vortex in an infinite superconductor, and determine, in each case, spatial variations of quantities such as \bf a and |Δ\bf k|. We also calculate...