Abstract
Using the standard Bardeen-Cooper-Schrieffer (BCS) theory, we revise microscopic derivation of the superconductor-insulator boundary conditions for the Ginzburg-Landau (GL) model. We obtain a negative contribution to free energy in the form of surface integral. Boundary conditions for the conventional superconductor have the form $\textbf{n} \cdot \nabla \psi = \text{const} \psi$. These are shown to follow from considering the order parameter reflected in the boundary. The boundary conditions are also derived for more general GL models with higher-order derivatives and pair-density-wave states. It shows that the boundary states with higher critical temperature and the boundary gap enhancement, found recently in BCS theory, are also present in microscopically-derived GL theory. In the case of an applied external field, we show that the third critical magnetic-field value $H_{c3}$ is higher than what follows from the de Gennes boundary conditions and is also significant in type-I regime.
Highlights
Superconductivity in the Ginzburg-Landau (GL) model [1] is described by a complex-valued field ψ (r), which is called an order parameter or gap
It was recently shown microscopically that boundaries of superconductors can have (i) higher critical temperature and (ii) the gap can be enhanced at the scale of the bulk coherence length
VII we introduce the magnetic field and give a microscopic assessment of how γ < 0 enhances the third critical magnetic field Hc3
Summary
Superconductivity in the Ginzburg-Landau (GL) model [1] is described by a complex-valued field ψ (r), which is called an order parameter or gap. To solve for ψ near a boundary of superconductor one has to take into account the influence of the material outside the sample This is done by a microscopically derived boundary condition for ψ or, equivalently, by an additional surface term Fsurf [ψ] in the free-energy functional. It was recently shown microscopically that boundaries of superconductors can have (i) higher critical temperature and (ii) the gap can be enhanced at the scale of the bulk coherence length. We call this enhancement of superconductivity the boundary state. Evidence for a substantially enhanced superconductivity near the boundary was reported in some elemental and hightemperature superconductors, see, e.g., Refs. VII we introduce the magnetic field and give a microscopic assessment of how γ < 0 enhances the third critical magnetic field Hc3
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