BCS versus Overhauser pairing in dense (2+1)-dimensional QCD

We compare the BCS and Overhauser effect as competing mechanisms for the destabilization of the quark Fermi surface at an asymptotically large chemical potential, for the special case of 2 space and 1 time dimensions. We use the framework of perturbative one-gluon exchange, which dominates the pairing at μ/g²≫ 1. With screening in matter, we show that in the weak coupling limit the Overhauser effect can compete with the BCS effect only for a sufficiently large number of colors. Both the BCS and the Overhauser gaps are of order g⁴/μ in the Landau gauge.