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

Abstract

Using the standard Bardeen-Cooper-Schrieffer (BCS) theory, we microscopically derive 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 are shown to follow from considering the order parameter reflected in the boundary. These boundary conditions are also derived for more general GL models with higher-order derivatives and pairdensity-wave states. It allows us to describe the formation of boundary states with higher critical temperature and the gap enhancement in the GL theory. In the case of an applied external field, we show that the third critical magnetic field's value Hc3 is higher than what follows from the de Gennes boundary conditions.

The absence of superconductivity in the next-to-leading order Ginzburg-Landau functional for Bardeen-Cooper-Schrieffer superconductor

“…We note that our conclusions do not apply for spin imbalanced superconductors, where a higher-order generalizations of Ginzburg-Landau functional have energy minimizing solutions both for pair-density-wave states [24][25][26][27][28] and for homogeneous states [29].…”

Symmetries, length scales, magnetic response, and skyrmion chains in nematic superconductors

“…In general boundary conditions should be calculated microscopically and they are strongly affected by the Friedel oscillations of the density of states near the surface [31]. For our model we ignore the surface terms, F surf = 0, as we are interested in the functional form of the long range of asymptotic field behaviour away from the boundary, which is determined by bulk normal modes.…”

“…These boundary conditions are a result of x 1 < 0 being an insulator and are given in the Appendix. As we focus on the long range behaviour of the fields, we will ignore additional boundary terms that result from modification of the pairing near the surface [30,31].…”