# Statical Structures of the BCS-like Holographic Superfluid in AdS4 Spacetime

## TL;DR

This paper explores the properties of a BCS-like holographic superfluid in AdS4, analyzing sound speeds, soliton structures, and vortex solutions, revealing new static configurations and scaling behaviors as chemical potential varies.

## Contribution

It introduces novel double and triple dark soliton solutions and detailed vortex behaviors in the holographic superfluid model, expanding understanding of static configurations in this context.

## Key findings

- Sound speed approaches 1/2 with increasing chemical potential.
- Discovery of double and triple dark soliton solutions.
- Vortex size and charge depletion depend on chemical potential and winding number.

## Abstract

We investigate in detail the m^{2}=0 Abelian Higgs model in AdS4, which is considered as the holographic dual of the most BCS-like superfluid. In homogeneous and isotropic superfluid solutions, we calculate the sound speeds, square of which approaches to 1/2 with increasing chemical potential (lowering temperature). Then we present the single dark soliton solutions, which becomes thinner with increasing chemical potential. For the first time, we also find the interesting double and triple dark soliton solutions, which is unexpected and shows the possibility of more complicated static configurations. Finally, we investigate vortex solutions. For winding number n=1, the vortex becomes thinner with increasing chemical potential. At a given chemical potential, with increasing winding number, firstly the vortex becomes bigger and the charge density depletion becomes larger, then the charge density depletion settles down at a certain value and the growth of the vortex size is found to obey a scaling symmetry.