Condensate flow in holographic models in the presence of dark matter

TL;DR

This paper analyzes holographic superconductor and superfluid models with dark matter sectors, revealing how dark matter parameters influence critical temperature and chemical potential, with a focus on analytical methods and different spacetime backgrounds.

Contribution

It provides an analytical study of dark matter effects on holographic superconductors and superfluids, highlighting the dependence of critical parameters on dark matter coupling and velocity.

Findings

Current shows linear dependence on temperature difference near transition.

Dark matter parameters affect critical chemical potential and transition temperature.

Dark matter does not influence the current value.

Abstract

Holographic model of a three-dimensional current carrying superconductor or superfluid with {\it dark matter} sector described by the additional $U(1)$-gauge field coupled to the ordinary Maxwell one, has been studied in the probe limit. We investigated analytically by the Sturm-Liouville variational method, the holographic s-wave and p-wave models in the background of the AdS soliton as well as five-dimensional AdS black hole spacetimes. The two models of p-wave superfluids were considered, the so called $SU(2)$ and the Maxwell-vector. Special attention has been paid to the dependence of the critical chemical potential and critical transition temperature on the velocity of the condensate and {\it dark matter} parameters. The current $J$ in holographic three-dimensional superconductor studied here, shows the linear dependence on $T_c-T$ for both s and p-wave symmetry. This is in a significant contrast with the previously obtained results for two-dimensional superconductors, which reveal the $(T-T_c)^{3/2}$ temperature dependence. The coupling constant $\alpha$, as well as, chemical potential $\mu_D$ and the velocity $S_D$ of the {\it dark matter}, affect the critical chemical potential of the p-wave holographic $SU(2)$ system. On the other hand, $\alpha$, {\it dark matter} velocity $S_D$ and density $\rho_D$ determine the actual value of the transition temperature of the same superconductor/superfluid set up. However, the {\it dark matter} does not affect the value of the current.