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

TL;DR

This paper develops a Ginzburg-Landau theory for finite momentum superconductivity, revealing how superfluid stiffness suppression near Lifshitz points influences phase transitions and the emergence of FFLO/PDW states.

Contribution

It introduces a sixth-order derivative Ginzburg-Landau model capturing the interplay of zero and finite momentum superconductivity, including Lifshitz points and bicritical regimes.

Findings

Superfluid stiffness vanishes at Lifshitz points, enabling transition to FF states.

Bicritical regions feature near-degenerate FF and LO/PDW states.

Finite momentum superconductivity can occur with arbitrarily weak pair-hopping at strong attraction.

Abstract

We derive the effective Ginzburg-Landau theory for finite momentum (FFLO/PDW) superconductivity without spin population imbalance from a model with local attraction and 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 the phase diagram contains a line of Lifshitz points where vanishing superfluid stiffness induces a continuous change to a long wavelength Fulde-Ferrell (FF) state. For larger pair-hopping there is a bicritical region where the pair-momentum changes discontinuously. Here the FF type state is near degenerate with the Larkin-Ovchinnikov (LO) or Pair-Density-wave (PDW) type state. At the intersection of these two regimes there is a "Super-Lifshitz" point with extra soft fluctuations. The instability to finite momentum superconductivity occurs for arbitrarily weak pair-hopping for sufficiently large attraction suggesting that even a small repulsive pair-hopping may be significant in a microscopic model of strongly correlated superconductivity. Several generic features of the model may have bearing on the cuprate superconductors, including the suppression of superfluid stiffness in proximity to a Lifshitz point as well as the existence of subleading FFLO order (or vice versa) in the bicritical regime.