Hydrodynamic theory of quantum fluctuating superconductivity

We show that, in contrast to previously appeared arguments, the zero temperature limit of translation invariant superfluid hydrodynamics does not imply a vanishing normal charge density. This conclusion follows from consistently coupling the hydrodynamic theory to external sources. In addition, we investigate the normal density in holographic models of quantum critical superfluids.Here, models with an emergent IR Lorentz symmetry lead to a vanishing normal density with the velocity of second sound obeying Landau's conjecture in terms of the emergent infrared lightcone velocity, c 2 2 c 2 IR /d. On the other hand, models with an emergent dynamical Lifshitz exponent z > 1 may have a non-vanishing normal density, depending on the spectrum of irrelevant deformations around the underlying quantum critical groundstate. In this case, the velocity of fourth sound c 2 4 ρ s /dρ offers a crisp diagnostic of a non-vanishing normal density. We comment on the relevance of our results to recent measurements of the superfluid density and low energy spectral weight in overdoped cuprates.

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“…In dirty superfluids with broken translations, only fourth sound survives. In particular, (19) matches the expressions in [56].…”

Section: Low Temperature Behavior Of Hydrodynamic Modesmentioning

confidence: 57%

Normal Charge Densities in Quantum Critical Superfluids

Goutéraux

Mefford

2020

Phys. Rev. Lett.

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“…Moreover, the effective hydrodynamic description can be endowed to account for non-hydro damped modes and/or the possible spontaneous breaking of certain global symmetries. Specific examples of such generalization are the framework of generalized hydrodynamics [12], quasi-hydrodynamics [13,14] or just superfluid hydrodynamics [15]. Certainly, the same extension can be applied to spacetime symmetries like translations, which are essential to distinguish solids from fluids [16][17][18].…”

Section: Radelmonicomentioning

confidence: 99%

A unified description of translational symmetry breaking in holography

Ammon

Baggioli

Alba

2019

J. High Energ. Phys.

131

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We provide a complete and unified description of translational symmetry breaking in a simple holographic model. In particular, we focus on the distinction and the interplay between explicit and spontaneous breaking. We consider a class of holographic massive gravity models which allow to range continuously from one situation to the other. We study the collective degrees of freedom, the electric AC conductivity and the shear correlator in function of the explicit and spontaneous scales. We show the possibility of having a sound-to-diffusion crossover for the transverse phonons. Within our model, we verify the validity of the Gell-Mann-Oakes-Renner relation. Despite of strong evidence for the absence of any standard dislocation induced phase relaxation mechanism, we identify a novel relaxation scale controlled by the ratio between the explicit and spontaneous breaking scales. Finally, in the pseudospontaneous limit, we prove analytically the relation, which has been discussed in the literature, between this novel relaxation scale, the mass of the pseudo-phonons and the Goldstone diffusivity. Our numerical data confirms this analytic result.

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“…See Refs. [29,31] for applications of this Kubo formula to thin film incoherent superconductors. Generalized symmetries therefore allow to recast weak phase relaxation as weak breaking of higher form symmetries.…”

Section: Phase Relaxation and Vorticesmentioning

confidence: 99%

Superfluids as higher-form anomalies

2020

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We recast superfluid hydrodynamics as the hydrodynamic theory of a system with an emergent anomalous higher-form symmetry. The higher-form charge counts the winding planes of the superfluid -its constitutive relation replaces the Josephson relation of conventional superfluid hydrodynamics. This formulation puts all hydrodynamic equations on equal footing. The anomalous Ward identity can be used as an alternative starting point to prove the existence of a Goldstone boson, without reference to spontaneous symmetry breaking. This provides an alternative characterization of Landau phase transitions in terms of higher-form symmetries and their anomalies instead of how the symmetries are realized. This treatment is more general and, in particular, includes the case of BKT transitions. As an application of this formalism we construct the hydrodynamic theories of conventional (0-form) and 1-form superfluids.

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Hydrodynamic theory of quantum fluctuating superconductivity

Cited by 53 publications

References 86 publications

Normal Charge Densities in Quantum Critical Superfluids

Normal Charge Densities in Quantum Critical Superfluids

A unified description of translational symmetry breaking in holography

Superfluids as higher-form anomalies

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