Suppression of superfluid stiffness near Lifshitz-point instability to finite momentum superconductivity*

We derive the effective Ginzburg-Landau theory for finite momentum (FFLO/PDW) superconductivity without spin population imbalance from a model with local attraction and a repulsive pair-hopping. We find that the GL free energy must include up to sixth order derivatives of the order parameter, providing a unified description of the interdependency of zero and finite momentum superconductivity. For weak pair-hopping, there is of a line of Lifshitz points with a continuous change from zero to finite momentum which for larger pair-hopping is replaced by a bicritical region where pair momentum changes discontinuously. Proximity to a Lifshitz point provides a mechanism for reduced superfluid stiffness and we discuss implications of the model for the cuprate superconductors.