  In the BCS theory of superconductivity, one assumes that all Cooper pairs
have the same center of mass momentum. This is indeed enforced by self
consistency, if the pairing interaction is momentum independent. Here, we show
that for an attractive nearest neighbor interaction, this is different. In this
case, stable solutions with pairs with momenta q and -q coexist and, for a
sufficiently strong interaction, one of these states becomes the groundstate of
the superconductor. This finite-momentum pairing state is accompanied by a
charge order with wave vector 2q. For a weak pairing interaction, the
groundstate is a d-wave superconductor.
