Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1702.05138 · Physical review. B./Physical review. B

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

Rufus Boyack, Chien‐Te Wu, Brandon Anderson, Kathryn Levin

Published Jun 2, 2017• 11 citations
arXivHTMLPDF

Abstract

In this paper we demonstrate the necessity of including the generally omitted collective-mode contributions in calculations of the Meissner effect for nonuniform superconductors. We consider superconducting pairing with nonzero 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 not only that the collective-mode contributions are appreciable but also 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 stable superfluidity well before the mean-field order parameter vanishes.

DOI
10.1103/physrevb.95.214501

Related papers

Electromagnetic response of superconductors in the presence of multiple collective modes

Rufus Boyack, Pedro L. S. Lopes

Collective-mode fluctuations play an essential role in ensuring the electromagnetic response of superfluids is gauge invariant. The contribution of these fluctuations, however, is known to drop out from the Meissner response of uniform superfluids. The same phenomenon is not so established in the context of nonuniform superfluids. To clarify this issue, we revisit how collective modes appear in the Meissner effect. We find that their contribution vanishes both in uniform and nonuniform systems, unless an external length scale is present---as in Fulde-Ferrell or finite-sized superfluids. As examples, we consider $s$-wave and chiral $p+ip$ superconductors. To facilitate this analysis, we formulate a path-integral matrix methodology for computing the response of fermionic fluids in the presence of multiple collective modes. Closed-form expressions are provided, incorporating effects from phase and amplitude of the superconducting order parameter and electronic density fluctuations. All microscopic symmetries and invariances are manifestly satisfied in this approach, and it can be straightforwardly extended to other scenarios.

arXiv:1909.10530•Physical review. B./Physical review. B•Mar 9, 2020•9 citations

Establishing a consistent theory of transport in strongly correlated Fermi superfluids

Rufus Boyack

A diagrammatic method of obtaining exact gauge-invariant response functions in strongly correlated Fermi superfluids is implemented for several example condensed matter systems of current interest. These include: topological superfluids, high temperature superconductors, and superfluids with finite center-of-mass momentum pairing known as Fulde-Ferrell superfluids. Much of the literature on these systems has focused on single-particle properties or alternatively has invoked simple approximations to treat response functions. The goal is to show that, for this wide class of topical problems, one can compute exact response functions. This enables assessment of the validity of different physical scenarios and allows a very broad class of experiments to be addressed.,The method developed is based on deriving the full electromagnetic vertex, which satisfies the Ward-Takahashi identity, and determining the collective modes in a manner compatible with the self-consistent gap equation. In the condensed phase of a superfluid and a superconductor, where gauge invariance is spontaneously broken, it is crucial to determine the collective modes from the gap equation in a manner which restores gauge invariance. Our diagrammatic framework provides a very general and powerful method for obtaining these collective modes in a variety of strongly correlated Fermi superfluids. We show that a full electromagnetic vertex satisfying the Ward-Takahashi identity ensures the $f$-sum rule is satisfied and thus charge is conserved. ,This diagrammatic method is implemented for both normal and superfluid phases. While there are no collective modes in the normal phase, the Ward-Takahashi identity plays a similarly important role. In particular, for the normal phase we study Rashba spin-orbit coupled Fermi gases with intrinsic pairing in the absence and presence of a magnetic field. Exact density and spin response functions are obtained, even in the absence of a spin conservation law, providing signatures of topological order. Another set of examples studied in the normal phase include a broad collection of models of the cuprate pseudogap. For these cases too, the exact response functions are obtained and signatures of each model are identified. A detailed discussion of the superfluid phase is provided by the study of Fulde-Ferrell superfluids. The generally omitted collective modes are computed and the exact gauge-invariant response is obtained. The first complete calculation of the superfluid density, incorporating the collective mode contribution and without any assumptions on the size of the gap, is provided. It is found that the amplitude mode causes the superfluid to become unstable at temperatures much lower than the mean-field transition temperature.,As an alternative to the diagrammatic approach, the functional path integral technique for Fermi superfluids is presented. While this approach is widely studied in the literature, it is of restricted utility, in comparison to the diagrammatic approach presented here, due to the inability to perform the functional integral except in very limited cases. A short coming in the current literature is identified, in that the standard method of deriving gauge-invariant electrodynamics leads to a violation of the compressibility sum rule. It is found that to satisfy this sum rule the amplitude mode of the order parameter must be incorporated. A reformulation of the path integral method for Fermi superfluids is derived, which has both gauge-invariant electrodynamics and thermodynamics compatible with the compressibility sum rule, to all orders of approximation.

•Aug 1, 2017•1 citation

Dynamical excitations of one-dimensional Fulde-Ferrell pairing Fermi superfluid

Peng Zou, Huaisong Zhao, Feng Yuan +1 more

We theoretically investigate a one-dimensional Fulde-Ferrell Fermi superfluid at a finite effective Zeeman field $h$, and study entire dynamical excitations related to density perturbation. By calculating the density dynamic structure factor, we find anisotropic dynamical excitations in both collective modes and single-particle excitations. Along the direction of centre-of-mass momentum $p$, there are two obvious gapless collective modes with different speed. The lower collective modes is from the usual gauge symmetry breaking and has a larger speed than the one in the negative direction of $p$. The higher one is due to the direction spontaneous symmetry breaking of centre-of-mass momentum $p$, and separates two kinds of single-particle excitations in the positive $p$ direction. However, this higher mode disappears in the opposite direction of $p$, where two single-particle excitations overlap with each other. These signals of dynamical excitations can do help to distinguish Fulde-Ferrell superfluid from the conventional Bardeen-Cooper-Schrieffer superfluid in the future experiment.

arXiv:2401.02269•Jan 4, 2024•0 citations

Fate of a strongly correlated d -wave superconductor in a Zeeman field: The Fulde-Ferrel-Larkin-Ovchinnikov perspective

Anushree Datta, Kun Yang, Amit Ghosal

The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase is an unconventional superconducting state found under the influence of a strong Zeeman field. This phase is identified by finite center-of-mass momenta in the Cooper pairs, causing the pairing amplitude to oscillate in real space. Repulsive correlations, on the other hand, smear out spatial inhomogeneities in $d$-wave superconductors. We investigate the FFLO state in a strongly correlated $d$-wave superconductor within a consolidated framework of Hartree-Fock-Bogoliubov theory and the Gutzwiller approximation. We find that the crucial effects of strong correlations lie in shifting the BCS-FFLO phase boundary towards a lower Zeeman field and thereby enlarging the window of the FFLO phase. In the FFLO state, our calculation features a sharp midgap peak in the density of states, indicating the formation of strongly localized Andreev bound states. We also find that the signatures of the FFLO phase survive even in the presence of an additional translational-symmetry-breaking competing order in the ground state. This is demonstrated by considering a broken-symmetry ground state with a simultaneous presence of the $d$-wave superconducting order and a spin-density wave order, often found in unconventional superconductors.

arXiv:1902.02758•Physical review. B./Physical review. B•Jul 16, 2019•6 citations

Cavity-induced Fulde-Ferrell-Larkin-Ovchinnikov superfluids of ultracold Fermi gases

Zhen Zheng, Z. D. Wang

Motivated by recent experimental advances in ultracold atomic gases placed in cavities, we study the influence of the atom-cavity coupling on the Fermi gases trapped in optical lattices. By adiabatic elimination of the cavity photon field, the atom-cavity coupling gives rise to effective long-range interactions. It results in a variety of two-body scattering processes, during which the atomic pairs can acquire an additional center-of-mass momentum. This reveals the possibility of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluids in which the atomic pairing momentum is nonzero. By inspecting the phase diagram at the mean-field level, we confirm that the FFLO superfluid phase coexists with the zero-momentum pairing, and is the ground state that hosts the lowest energy. Furthermore, the order parameter characterizing the non-zero-momentum pairing does not vanish as long as the cavity-induced interaction is present.

arXiv:2003.08602•Physical Review A•Feb 19, 2020•7 citations

Entire set of dynamical excitations of a one-dimensional Fulde-Ferrell-pairing Fermi superfluid based on momentum excitation

Peng Zou, Huaisong Zhao, Feng Yuan +1 more

We theoretically investigate a one-dimensional Fulde-Ferrell Fermi superfluid at a finite effective Zeeman field $h$ and study all of the dynamical excitations related to density perturbation. By calculating the density dynamic structure factor, we find anisotropic dynamical excitations in both collective modes and single-particle excitations. Along the direction of center-of-mass momentum $p$, there are two obvious gapless collective modes with different speeds and two kinds of continuous regimes related to single-particle excitation. The lower collective modes are from the usual gauge symmetry breaking and have a larger speed than the one in the negative direction of $p$. The higher one is due to the direction spontaneous symmetry breaking of center-of-mass momentum $p$ and separates a gapless lower-branch single-particle excitation from the other gapped higher-branch single-particle excitation in the positive $p$ direction. However, this higher mode disappears in the opposite direction of $p$, where two single-particle excitations overlap with each other. These signals of dynamical excitations could help to distinguish a Fulde-Ferrell superfluid from the conventional Bardeen-Cooper-Schrieffer superfluid in future experiments.

Physical Review A•May 20, 2024•2 citations
In this paper we demonstrate the necessity of including the generally omitted collective-mode contributions in calculations of the Meissner effect for nonuniform superconductors. We consider superconducting pairing with nonzero 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 not only that the collective-mode contributions are appreciable but also 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 stable superfluidity well before the mean-field order parameter vanishes.
Collective-mode fluctuations play an essential role in ensuring the electromagnetic response of superfluids is gauge invariant. The contribution of these fluctuations, however, is known to drop out from the Meissner response of uniform superfluids. The same phenomenon is not so established in the context of nonuniform superfluids. To clarify this issue, we revisit how collective modes appear in the Meissner effect. We find that their contribution vanishes both in uniform and nonuniform systems, unless an external length scale is present---as in Fulde-Ferrell or finite-sized superfluids. As examples, we consider sss-wave and chiral p+ipp+ipp+ip superconductors. To facilitate this analysis, we formulate a path-integral matrix methodology for computing the response of fermionic fluids in the presence of multiple collective modes. Closed-form expressions are provided, incorporating effects from phase and amplitude of the superconducting order parameter and electronic density fluctuations. All microscopic symmetries and invariances are manifestly satisfied in this approach, and it can be straightforwardly extended to other scenarios.
A diagrammatic method of obtaining exact gauge-invariant response functions in strongly correlated Fermi superfluids is implemented for several example condensed matter systems of current interest. These include: topological superfluids, high temperature superconductors, and superfluids with finite center-of-mass momentum pairing known as Fulde-Ferrell superfluids. Much of the literature on these systems has focused on single-particle properties or alternatively has invoked simple approximations to treat response functions. The goal is to show that, for this wide class of topical problems, one can compute exact response functions. This enables assessment of the validity of different physical scenarios and allows a very broad class of experiments to be addressed.,The method developed is based on deriving the full electromagnetic vertex, which satisfies the Ward-Takahashi identity, and determining the collective modes in a manner compatible with the self-consistent gap equation. In the condensed phase of a superfluid and a superconductor, where gauge invariance is spontaneously broken, it is crucial to determine the collective modes from the gap equation in a manner which restores gauge invariance. Our diagrammatic framework provides a very general and powerful method for obtaining these collective modes in a variety of strongly correlated Fermi superfluids. We show that a full electromagnetic vertex satisfying the Ward-Takahashi identity ensures the fff-sum rule is satisfied and thus charge is conserved. ,This diagrammatic method is implemented for both normal and superfluid phases. While there are no collective modes in the normal phase, the Ward-Takahashi identity plays a similarly important role. In particular, for the normal phase we study Rashba spin-orbit coupled Fermi gases with intrinsic pairing in the absence and presence of a magnetic field. Exact density and spin response functions are obtained, even in the absence of a spin conservation law, providing signatures of topological order. Another set of examples studied in the normal phase include a broad collection of models of the cuprate pseudogap. For these cases too, the exact response functions are obtained and signatures of each model are identified. A detailed discussion of the superfluid phase is provided by the study of Fulde-Ferrell superfluids. The generally omitted collective modes are computed and the exact gauge-invariant response is obtained. The first complete calculation of the superfluid density, incorporating the collective mode contribution and without any assumptions on the size of the gap, is provided. It is found that the amplitude mode causes the superfluid to become unstable at temperatures much lower than the mean-field transition temperature.,As an alternative to the diagrammatic approach, the functional path integral technique for Fermi superfluids is presented. While this approach is widely studied in the literature, it is of restricted utility, in comparison to the diagrammatic approach presented here, due to the inability to perform the functional integral except in very limited cases. A short coming in the current literature is identified, in that the standard method of deriving gauge-invariant electrodynamics leads to a violation of the compressibility sum rule. It is found that to satisfy this sum rule the amplitude mode of the order parameter must be incorporated. A reformulation of the path integral method for Fermi superfluids is derived, which has both gauge-invariant electrodynamics and thermodynamics compatible with the compressibility sum rule, to all orders of approximation.
We theoretically investigate a one-dimensional Fulde-Ferrell Fermi superfluid at a finite effective Zeeman field hhh, and study entire dynamical excitations related to density perturbation. By calculating the density dynamic structure factor, we find anisotropic dynamical excitations in both collective modes and single-particle excitations. Along the direction of centre-of-mass momentum ppp, there are two obvious gapless collective modes with different speed. The lower collective modes is from the usual gauge symmetry breaking and has a larger speed than the one in the negative direction of ppp. The higher one is due to the direction spontaneous symmetry breaking of centre-of-mass momentum ppp, and separates two kinds of single-particle excitations in the positive ppp direction. However, this higher mode disappears in the opposite direction of ppp, where two single-particle excitations overlap with each other. These signals of dynamical excitations can do help to distinguish Fulde-Ferrell superfluid from the conventional Bardeen-Cooper-Schrieffer superfluid in the future experiment.
The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase is an unconventional superconducting state found under the influence of a strong Zeeman field. This phase is identified by finite center-of-mass momenta in the Cooper pairs, causing the pairing amplitude to oscillate in real space. Repulsive correlations, on the other hand, smear out spatial inhomogeneities in ddd-wave superconductors. We investigate the FFLO state in a strongly correlated ddd-wave superconductor within a consolidated framework of Hartree-Fock-Bogoliubov theory and the Gutzwiller approximation. We find that the crucial effects of strong correlations lie in shifting the BCS-FFLO phase boundary towards a lower Zeeman field and thereby enlarging the window of the FFLO phase. In the FFLO state, our calculation features a sharp midgap peak in the density of states, indicating the formation of strongly localized Andreev bound states. We also find that the signatures of the FFLO phase survive even in the presence of an additional translational-symmetry-breaking competing order in the ground state. This is demonstrated by considering a broken-symmetry ground state with a simultaneous presence of the ddd-wave superconducting order and a spin-density wave order, often found in unconventional superconductors.
Motivated by recent experimental advances in ultracold atomic gases placed in cavities, we study the influence of the atom-cavity coupling on the Fermi gases trapped in optical lattices. By adiabatic elimination of the cavity photon field, the atom-cavity coupling gives rise to effective long-range interactions. It results in a variety of two-body scattering processes, during which the atomic pairs can acquire an additional center-of-mass momentum. This reveals the possibility of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluids in which the atomic pairing momentum is nonzero. By inspecting the phase diagram at the mean-field level, we confirm that the FFLO superfluid phase coexists with the zero-momentum pairing, and is the ground state that hosts the lowest energy. Furthermore, the order parameter characterizing the non-zero-momentum pairing does not vanish as long as the cavity-induced interaction is present.
We theoretically investigate a one-dimensional Fulde-Ferrell Fermi superfluid at a finite effective Zeeman field hhh and study all of the dynamical excitations related to density perturbation. By calculating the density dynamic structure factor, we find anisotropic dynamical excitations in both collective modes and single-particle excitations. Along the direction of center-of-mass momentum ppp, there are two obvious gapless collective modes with different speeds and two kinds of continuous regimes related to single-particle excitation. The lower collective modes are from the usual gauge symmetry breaking and have a larger speed than the one in the negative direction of ppp. The higher one is due to the direction spontaneous symmetry breaking of center-of-mass momentum ppp and separates a gapless lower-branch single-particle excitation from the other gapped higher-branch single-particle excitation in the positive ppp direction. However, this higher mode disappears in the opposite direction of ppp, where two single-particle excitations overlap with each other. These signals of dynamical excitations could help to distinguish a Fulde-Ferrell superfluid from the conventional Bardeen-Cooper-Schrieffer superfluid in future experiments.