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

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 possibly relevant to high transition temperature cuprates, cold atoms, and color superconductors in quantum chromodynamics. 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 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.

Instability of Fulde-Ferrell-Larkin-Ovchinnikov states in atomic Fermi gases in three and two dimensions

“…As of this writing, Boyack et al [46] found that the superfluid density of a mean-field FF state vanishes in the direction transverse to the wavevector q, in agreement with our findings here.…”

Odd-frequency pair density wave correlations in underdoped cuprates

“…So, one-electron experimental probes, such as angle-resolved photoemission spectroscopy (ARPES) or scanning tunneling spectroscopy (STS), will not detect the induced PDW. However, twoelectron response functions, will have signatures of these PDW correlations, [129][130][131][132][133] and even be able to distinguish oddfrequency components. For example, the imaginary part of the density response function χ (q, Ω) can characterize various bosonic excitations or correlations at different momentum (q) and energies or frequencies (Ω) depending on the experimental probe.…”

“…It is possible that the so-called peak-dip-hump structure 138 in Raman intensity 112 as a function of frequency can find its explanation in terms of the OPDW. Finally, the OPDW might also leave distinct signatures in Josephson scanning tunneling measurements, 94 Meissner response 132 and other transport measurements. 95 Let us also comment on disorder-induced inhomogeneities that are intrinsic to all cuprate materials.…”

Electromagnetic response of superconductors in the presence of multiple collective modes

“…The importance of computing the superfluid density in the appropriate limiting fashion was discussed in Ref. [22], where it was shown that for the Fulde-Ferrell superfluid the amplitude collective mode contributes to the superfluid density. A general argument for why collective modes do not need to be considered in the superfluid density response of uniform superfluids is as follows [27].…”

“…In addition, Ref. [22] provided an explicit calculation of the electromagnetic (EM) response of the Fulde-Ferrell (FF) superfluid, which consists of finite-momentum Cooper pairs, and showed that the amplitude mode gives a significant contribution to the superfluid density. These issues motivate the current work, where we investigate the superfluid response for systems with nonuniform pairing, such as p-wave superfluids [23,24] and superconductors [25,26], and we provide a more general understanding on the type of superconductor where collective modes can contribute to the Meissner response.…”