Abstract
A relativistic generalization of the Bogolubov-de Gennes equations is derived where the particle and hole amplitudes are Dirac spinors. In the weakly relativistic limit one obtains, besides the usual spin-orbit, Darwin and kinetic energy corrections, a new “spin-orbit” and a new “Darwin” term involving the pair potential in place of the electrostatic potential. The results indicate the significance of the relativistic corrections for superconductors with a high Fermi velocity, a small coherence length or heavy elements in the lattice.
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