Complete Phase Diagrams for a Holographic Superconductor/Insulator System

TL;DR

This work extends holographic superconductor/insulator models by including backreaction and presenting complete $T$–$\mu$ phase diagrams for the Einstein–Maxwell–scalar system in five dimensions. By analyzing both AdS soliton and AdS black hole backgrounds with scalar hair, the authors uncover a four‑phase structure and, for small scalar charge $q$, a novel sequence where a conductor becomes a superconductor and then an insulator as $T$ decreases, including a new first‑order superconductor/insulator boundary. A neutral scalar limit yields boson‑star–type solutions interpreted as a Bose–Einstein condensate of glueballs, illustrating a gravitational dual to confinement physics. The results highlight intricate phase competition and potential routes to stabilizing ground states via backreaction and higher‑order interactions, with implications for both holographic condensed matter and confining gauge theories.

Abstract

The gravitational dual of an insulator/superconductor transition driven by increasing the chemical potential has recently been constructed. However, the system was studied in a probe limit and only a part of the phase diagram was obtained. We include the backreaction and construct the complete phase diagram for this system. For fixed chemical potential there are typically two phase transitions as the temperature is lowered. Surprisingly, for a certain range of parameters, the system first becomes a superconductor and then becomes an insulator as the temperature approaches zero. As a byproduct of our analysis, we also construct the gravitational dual of a Bose-Einstein condensate of glueballs in a confining gauge theory.

Figures (7)

• Figure 1: The value of the condensate (left), and the charge density (right) as a function of chemical potential, for the soliton with $q=2$.
• Figure 2: The free energy densities of the soliton with scalar (solid purple), and the soliton without scalar (dashed blue), against chemical potential with $q=1.2$ (top left), $q=1.15$ (top right), $q=1.1$ (bottom left), and $q=1$ (bottom right). Here, we have scaled $\gamma=\pi$. The $q=1.2$ plot shows the typical secord-order phase transition seen in the probe limit. The $q=1.15$ and $q=1.1$ plots have second order phase transitions, but a discontinuity within the superconducting phase. The $q=1$ plot shows a first order phase transition.
• Figure 3: The value of the condensate (left plots), and the charge density (right plots) as a function of chemical potential, for the AdS soliton with $q=1.15$ (top plots) and $q=1$ (bottom plots). Here, we have scaled $\gamma=\pi$. Note that the $q=1.15$ plots have a second order phase transition into the superconducting phase (at $\mu\approx1.71$), but within the superconducting phase (at $\mu\approx 1.8$), there's a discontinuity in the charged density and condensate. The $q=1$ plots give a first order phase transition.
• Figure 4: The energy density (left), and the condensate (right) as a function of scalar field at the tip, for the AdS soliton with neutral scalar field excited. Here, we have scaled the period of the $\eta$ coordinate to be $\gamma=\pi$. These solutions have a maximum mass and condensate.
• Figure 5: The value of the condensate (left), and the charge density (right) as a function of chemical potential, for the AdS black hole with $q=2$.