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 {\it 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.