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A Cooper pair is a correlated pair of fermions associated with superconductivity. The conventional BCS ground state uses opposite-momentum, opposite-spin pair creation operators $c_{k\uparrow }^{†}{c}_{-k\downarrow }^{†}$. Their total momentum is zero for every relative momentum $k$; zero total momentum does not restrict $k$ to zero.

Superconductivity is a phase with vanishing electrical resistance and expulsion of magnetic flux from the bulk, the Meissner effect. Conventional microscopic BCS theory describes pairing of electrons into Cooper pairs.