  It is known that Berry curvature of the band structure of certain crystals
can lead to effective noncommutativity between spatial coordinates. Using the
techniques of twisted quantum field theory, we investigate the question of the
formation of a paired state of twisted fermions in such a system. We find that
to leading order in the noncommutativity parameter, the gap between the
non-interacting ground state and the paired state is {\it smaller} compared to
its commutative counterpart. This suggests that BCS type superconductivity, if
present in such systems, is more fragile and easier to disrupt.
