Sound modes in holographic superfluids

TL;DR

This work analyzes sound modes in a strongly interacting relativistic superfluid using a holographic AdS/CFT dual with a Maxwell field and a charged scalar in AdS$_5$. Through relativistic two-fluid hydrodynamics and a fully backreacted gravity model, it computes first, second, and fourth sound as functions of temperature, revealing that second sound at low $T$ does not conform to Landau's nonrelativistic incompressible limit. A key finding is the existence of a critical scalar charge $q_c(u)$ that governs the qualitative behavior of the sound modes, with monotonic second- and fourth-sound behavior emerging only above it. The results highlight substantial deviations from naive Landau theory in relativistic, strongly coupled holographic superfluids and illuminate the role of backreaction, thermodynamics, and quasi-particle dynamics in determining collective modes.

Abstract

Superfluids support many different types of sound waves. We investigate the relation between the sound waves in a relativistic and a non-relativistic superfluid by using hydrodynamics to calculate the various sound speeds. Then, using a particular holographic scalar gravity realization of a strongly interacting superfluid, we compute first, second and fourth sound speeds as a function of the temperature. The relativistic low temperature results for second sound differ from Landau's well known prediction for the non-relativistic, incompressible case.

Figures (7)

• Figure 1: (Color online) First, second and fourth sound for a holographic superfluid given by the bulk action \ref{['Sbulk']} and a scalar potential \ref{['E:potential']}. From bottom to top, the blue line corresponds to second sound, the green line to fourth sound, and the red line corresponds to first sound computed directly from \ref{['E:abc']}. Note that conformal invariance implies that first sound squared must be $1/3$ for our 3+1 dimensional system.
• Figure 2: (Color online) Second sound for a condensate of conformal dimension $3/2$, whose dynamics follow from the bulk action \ref{['Sbulk']} and a scalar potential \ref{['E:potential']}.
• Figure 3: (Color online) Fourth sound for a condensate of conformal dimension $3/2$ and charge $q=1$, whose dynamics follow from the bulk action \ref{['Sbulk']} and a scalar potential \ref{['E:potential']}.
• Figure 4: (Color online) Second sound for a condensate of conformal dimension $5/2$, whose dynamics follow from the bulk action \ref{['Sbulk']} and a scalar potential \ref{['E:potential']}.
• Figure 5: (Color online) Plots of the ratio of the heat capacity at constant chemical potential $C_{\mu}$ to $3 s$ for $\Delta = 5/2$. The $q=1$ curves for $u=0$, $u=1$ and $u=3$ have not been displayed --- they are of order 3 with a maximum around $T/T_c \sim 0.1$. The value of $3s/C_{\mu}$ for the $\Delta=3/2$ condensate is very similar to the one in the plot.