Nonuniqueness and derivative discontinuities in density-functional theories for current-carrying and superconducting systems

Current-carrying and superconducting systems can be treated within density-functional theory if suitable additional density variables ~the current density and the superconducting order parameter, respectively! are included in the density-functional formalism. Here we show that the corresponding conjugate potentials ~vector and pair potentials, respectively! are not uniquely determined by the densities. The Hohenberg-Kohn theorem of these generalized density-functional theories is thus weaker than the original one. We give explicit examples and explore some consequences.