LAUSR

Since Bardeen-Cooper-Schrieffer theory of superconductivity is non-linear, it is difficult to study superconducting properties analytically. There is a more tractable linear criterion which determines a temperature Tl below which the system is superconducting. Here, we observe that there is a similar linear criterion which gives a temperature Tu above which no superconductivity occurs. We provide examples of translation invariant systems where Tu > Tl as well as systems where Tu = Tl. Furthermore, we estimate Tu for half-spaces and show that it is exponentially small in the weak coupling limit, exhibiting the same asymptotics as the critical temperature for full space.