Analytic investigation of holographic phase transitions influenced by dark matter sector

TL;DR

This paper analytically explores how dark matter influences holographic phase transitions, revealing modifications in transition temperatures and critical chemical potentials through variational methods and stability analysis.

Contribution

It introduces an analytical approach to study dark matter effects on holographic phase transitions, including the impact on critical parameters and stability in AdS backgrounds.

Findings

Superconducting transition temperature scales as $ ho^{1/3}$ even with dark matter.

Dark matter coupling increases the critical chemical potential, making condensation harder.

Dark matter sector modifies the holographic droplet solutions and phase transition properties.

Abstract

We analytically study the phase transitions between s-wave holographic insulator/superconductor and metal/superconductor. The problem is solved by the variational method for the Sturm-Liouville eigenvalue problem in the theory with dark matter sector of U(1)-gauge field coupled to the Maxwell field. Additionally in the probe limit we investigate the marginally stable modes of scalar perturbations in the AdS solitonic background, connected with magnetic field in the dark matter sector. We have found that even with dark matter sector the superconducting transition temperature $T_c$ is proportional to charge density $\rho$ in power 1/3. This value seem to be strong coupling modification of the exponent 2/3 known from the Bose - Einstein condensation of charged local pair bosons in narrow band superconductors. The holographic droplet solution is affected by the coupling to the dark matter. Interestingly in the probe limit the critical chemical potential increases with the decreasing coupling to dark matter making the condensation transition harder to appear.