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Keywords:

  • Landau–Ginzburg equations;
  • superconductivity;
  • boundary conditions

Abstract

We derive the Ginzburg–Landau equations for superconductors in static magnetic fields. Instead of the square of the gauge-invariant gradient of the order-parameter wave function, we consider the quantum-mechanical expression for the kinetic energy in the Ginzburg–Landau energy functional. We introduce a new surface term in the free energy functional which results in the de Gennes interface conditions. The phenomenological Ginzburg–Landau theory thus contains three length scales which must be determined from microscopic theory: the Ginzburg–Landau coherence length, the London penetration depth, and the de Gennes length.