Chemical potential and boundary resistance at normal-superconducting interfaces

The ideas of Pippard, Shepherd & Tindall (1970) and of Rieger, Scalapino & Mercereau (1971) about what happens when normal current is converted to supercurrent at an interface are re-examined. It is found that near such an interface the pair energy of the superfluid is no longer equal to the Fermi energy, and careful consideration of the chemical potentials involved shows that measurable electric fields may exist inside the superconductor. The size of this effect is determined by the degree of imbalance between electron-like and hole-like excitations, which in turn depends on the rates of processes which restore this balance (branch-crossing processes). The paper contains first a reconsideration of the meaning of chemical potential and the supercurrent equations in such non-equilibrium situations, then a detailed re-assessment of the calculation of the boundary resistance by Pippard et al. (which is substantially modified), and finally some criticisms of the approach used by Rieger et al. which is based on time-dependent Ginzburg-Landau theory.