Relativistic framework for microscopic theories of superconductivity. I. The Dirac equation for superconductors

We present a unified treatment of relativistic effects in superconductors. The relativistically correct (Dirac-type) single-particle Hamiltonian describing the quasiparticle spectrum of superconductors is deduced from symmetry considerations and the requirement of the correct nonrelativistic limit. We provide a complete list of all order parameters consistent with the requirement of Lorentz covariance. This list contains the relativistic generalizations of the BCS and the triplet order parameters, among others. Furthermore, we present a symmetry classification of the order parameters according to their behavior under the Lorentz group, generalizing previous treatments that were based on the Galilei group. The considerations in this paper are based only on the concepts of pairing and Lorentz covariance. They can therefore be applied to all situations in which pairing takes place. This includes BCS-type superconductors, as well as the heavy-fermion compounds, high-temperature superconductors, pairing of neutrons and protons in neutron stars, and superfluid helium 3.