Density‐functional theory of the superconducting state

A density‐functional theory describing the superconducting state of matter is presented. The formalism leads to a set of single‐particle equations that are structurally similar to the Bogoliubov‐de Gennes equations but (in contrast to the latter) incorporate both normal and superconducting exchange‐correlation effects. It is demonstrated via a rigorous decoupling scheme that these single‐particle equations are equivalent to a set of normal Kohn‐Sham equations, and a BCS‐type gap equation to be solved self‐consistently with the Kohn‐Sham equations.