Collective modes in Fulde-Ferrell-Larkin-Ovchinnikov superconductors: The role of long-range Coulomb interaction and signatures in density response

TL;DR

This paper explores the collective excitations in FFLO superconductors, revealing how long-range Coulomb interactions affect these modes and proposing density response measurements as a detection method.

Contribution

It provides a detailed theoretical analysis of collective modes in FFLO states, highlighting the impact of Coulomb interactions and linking elastic modes to observable density responses.

Findings

Long-range Coulomb interaction gaps out the phase mode.

Other collective modes remain unaffected by Coulomb interaction.

Density-density response can detect the elastic mode signature.

Abstract

We theoretically investigate collective excitations in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states of Pauli-limited superconducting films. When the long-range Coulomb interaction is absent, excitation spectra consist of two gapless and three gapped modes. The gapless modes are the Nambu-Goldstone modes associated with the spontaneous breaking of the ${\rm U}(1)$ symmetry and the translational symmetry. The gapped modes include the Higgs mode and the twofold degenerate modes that cause the oscillation of the domain width and grayness of FFLO nodal planes. We find that the long-range Coulomb interaction only gaps out the gapless phase mode through the Anderson-Higgs mechanism, while the other modes remain unaffected. Furthermore, the field evolution of the dispersion of the gapless elastic mode, the Nambu-Goldstone mode associated with the translational symmetry breaking, is associated with that of the bandwidth of the mid-gap Andreev bound states. We demonstrate that the signature of the elastic mode can be detected by measuring the density-density response function.