As it is described in this question the BCS wave function has definite phase but indefinite electron number. Therefore the superconducting order parameter $\langle \phi| c_{k \uparrow}c_{-k \downarrow} |\phi\rangle$ can be nonzero. However one can construct a wave function with definite particle number. In that case the order parameter $\langle N|c_{k \uparrow}c_{-k \downarrow} |N\rangle$ will be zero!
Why does the order parameter depend on our choice of the wave function?
