# Collective mode contributions to the Meissner effect: Fulde-Ferrell and pair-density wave superfluids

## TL;DR

This paper emphasizes the importance of including collective mode contributions, especially the amplitude (Higgs) mode, in calculating the Meissner effect for non-uniform superconductors like Fulde-Ferrell and pair-density wave states, revealing their significant impact on superfluid density.

## Contribution

It demonstrates that collective mode contributions, particularly the amplitude mode, are crucial for accurately describing the Meissner effect in non-uniform superconductors, a factor often neglected in prior work.

## Key findings

- Collective modes significantly affect the superfluid density in non-uniform superconductors.
- The amplitude (Higgs) mode plays a key role in pair-density wave superconductors.
- Collective mode effects can destroy superfluidity before the order parameter vanishes.

## Abstract

In this paper we demonstrate the necessity of including the generally omitted collective mode contributions in calculations of the Meissner effect for non-uniform superconductors. We consider superconducting pairing with non-zero center of mass momentum, as is relevant to high transition temperature cuprates, cold atoms, and quantum chromodynamic superconductors. For the concrete example of the Fulde-Ferrell phase we present a quantitative calculation of the superfluid density, showing the collective mode contributions are not only appreciable but that they derive from the amplitude mode of the order parameter. This latter mode (related to the Higgs mode in a charged system) is generally viewed as being invisible in conventional superconductors. However, our analysis shows that it is extremely important in pair-density wave type superconductors, where it destroys superfluidity well before the mean-field order parameter vanishes.