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Using the standard Bardeen-Cooper-Schrieffer (BCS) theory, we revisemicroscopic derivation of the superconductor-insulator boundary conditions forthe Ginzburg-Landau (GL) model. We obtain a negative contribution to freeenergy in the form of surface integral. Boundary conditions for theconventional superconductor have the form $\textbf{n} \cdot \nabla \psi =\text{const} \psi$. These are shown to follow from considering the orderparameter reflected in the boundary. The boundary conditions are also derivedfor more general GL models with higher-order derivatives and pair-density-wavestates. It shows that the boundary states with higher critical temperature andthe boundary gap enhancement, found recently in BCS theory, are also present inmicroscopically-derived GL theory. In the case of an applied external field, weshow that the third critical magnetic-field value $H_{c3}$ is higher than whatfollows from the de Gennes boundary conditions and is also significant intype-I regime.

physical review. b./physical review. b

Microscopic derivation of superconductor-insulator boundary conditions  for Ginzburg-Landau theory revisited. Enhanced superconductivity at  boundaries with and without magnetic field