Abstract
The normal density of a translation-invariant superfluid often vanishes at zero temperature, as is observed in superfluid Helium and conventional superconductors described by BCS theory. Here we show that this need not be the case. We investigate the normal density in models of quantum critical superfluids using gauge-gravity duality. Models with an emergent infrared Lorentz symmetry lead to a vanishing normal density. On the other hand, models which break the isotropy between time and space may enjoy a nonvanishing normal density, depending on the spectrum of irrelevant deformations around the underlying quantum critical ground state. Our results may shed light on recent measurements of the superfluid density and low energy spectral weight in superconducting overdoped cuprates.
Highlights
Introduction.—Much of traditional superfluid and BEC superconductor phenomenology can be explained by Landau and Tisza’s simple two-fluid hydrodynamical model [1,2] and its relativistic generalizations [3,4,5,6,7,8,9]
In this Letter, we tackle this question by combining methods using superfluid hydrodynamics and gaugegravity duality
We review translation and time-reversal invariant superfluid hydrodynamics and show that the hydrodynamic equations are not enough to conclude that (1) is true
Summary
CPHT, CNRS, École Polytechnique, IP Paris, F-91128 Palaiseau, France (Received 13 January 2020; accepted 8 April 2020; published 22 April 2020). Using holographic models with quantum critical dynamics in the infrared as examples, we show (1) holds for strongly coupled superfluids with an emergent Lorentz symmetry, in agreement with [10,11]. This is consistent with the superfluid effective field theory discussed in [21,22,23]. Even after explicitly breaking translations, we show this conclusion does not change These findings may suggest the anomalously low superfluid density and suppression of spectral weight observed in [12,15] might be a consequence of the quantum critical properties of the superconducting phase of overdoped cuprates. Ρðn0Þ in superfluid hydrodynamics.—we review relativistic, charged, superfluid hydrodynamics, 0031-9007=20=124(16)=161604(7)
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