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Current-carrying and superconducting systems can be treated withindensity-functional theory if suitable additional density variables (the currentdensity and the superconducting order parameter, respectively) are included inthe density-functional formalism. Here we show that the corresponding conjugatepotentials (vector and pair potentials, respectively) are {\it not} uniquelydetermined by the densities. The Hohenberg-Kohn theorem of these generalizeddensity-functional theories is thus weaker than the original one. We giveexplicit examples and explore some consequences.

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