Superconductivity from D3/D7: Holographic Pion Superfluid

TL;DR

The authors construct a D3/D7 holographic model at zero quark mass with finite isospin chemical potential and show a flavored superconducting transition driven by a mesonic (pionic) condensate. They compute frequency-dependent conductivity, revealing a DC delta function, and analyze a superfluid/supercurrent phase with a phase diagram where the transition shifts from second to first order as the superfluid velocity increases. The study also characterizes the second-sound mode, superfluid density, and energy-gap relations, and finds that transverse scalar condensates do not form in this setup due to a blocking mechanism. Overall, the work illustrates how holographic methods capture pion-like condensation and associated superconducting phenomena in a large-Nc, N=4-like setting with probe flavor branes.

Abstract

We show that a D3/D7 system (at zero quark mass limit) at finite isospin chemical potential goes through a superconductor (superfluid) like phase transition. This is similar to a flavored superfluid phase studied in QCD literature, where mesonic operators condensate. We have studied the frequency dependent conductivity of the condensate and found a delta function pole in the zero frequency limit. This is an example of superconductivity in a string theory context. Consequently we have found a superfluid/supercurrent type solution and studied the associated phase diagram. The superconducting transition changes from second order to first order at a critical superfluid velocity. We have studied various properties of the superconducting system like superfluid density, energy gap, second sound etc. We investigate the possibility of the isospin chemical potential modifying the embedding of the flavor branes by checking whether the transverse scalars also condense at low temperature. This however does not seem to be the case.

Figures (8)

• Figure 1: Plot of the zero mode at $\mu=4$
• Figure 2: Plot of the condensate with $1/\mu$
• Figure 3: Speed of second sound as a function of $1/\mu$
• Figure 4: Plot of the real part of $\frac{\sigma}{\mu}$ with $\mu=7.57 \mu_c, 2.52 \mu_c, 1.71 \mu_c, 1.37 \mu_c, 1.13 \mu_c$ (gradually from red to green curves). The blue curve is for the exact frequency response at $\mu=\mu_c=4$.
• Figure 5: Plot of superfluid density with $1/\mu$.