Holographic Superconductors with Higher Curvature Corrections

TL;DR

The paper analyzes (3+1)-dimensional holographic superconductors within 5D Einstein-Gauss-Bonnet gravity in the probe limit and shows that higher curvature corrections hinder scalar condensation by lowering the critical temperature $T_c$. It develops a simple analytic matching method that accurately reproduces $T_c$ and the order-parameter behavior near the transition, corroborated by numerical results. Conductivity calculations reveal a GB-dependent gap frequency $rac{ω_g}{T_c}$, indicating the breakdown of the previously observed universality $rac{ω_g}{T_c}\nobreak ilde= obreak 8$ under stringy corrections. The work also extends the analytic approach to (2+1)-dimensional cases in the appendix, highlighting how curvature corrections shape both the phase transition and transport properties in holographic superconductors.

Abstract

We study (3+1)-dimensional holographic superconductors in Einstein-Gauss-Bonnet gravity both numerically and analytically. It is found that higher curvature corrections make condensation harder. We give an analytic proof of this result, and directly demonstrate an analytic approximation method that explains the qualitative features of superconductors as well as giving quantitatively good numerical results. We also calculate conductivity and $ω_g / T_c $, for $ω_g$ and $T_c$ the gap in the frequency dependent conductivity and the critical temperature respectively. It turns out that the `universal' behaviour of conductivity, $ω_g / T_c \simeq 8$, is not stable to the higher curvature corrections. In the appendix, for completeness, we show our analytic method can also explain (2+1)-dimensional superconductors.

Figures (5)

• Figure 1: The condensate as a function of temperature for various values of $\alpha$. The (lowest) red line is for $\alpha=0.0001$, the middle brown plot is $\alpha=0.1$, the top blue line is $\alpha=0.2$ and the remaining line intersecting the other three in green is the Chern-Simons limit $\alpha=0.25$. Note that while the generic Einstein-Gauss-Bonnet behaviour is to level out for $T \leq T_c/2$, the Chern-Simons limit has a much stronger variation of the condensate with temperature.
• Figure 2: A comparison of analytic and numerical results. The shaded region is that in which the geometry forbids the possibility of a scalar condensate from (\ref{['anbnd']}). The dashed line indicates the analytic approximation of the value of $T_c$ obtained by matching methods, (\ref{['mainTc']}). The data points are the exact numerical results. For simplicity $\rho$ and $L$ have been set to 1.
• Figure 3: Conductivity for $\alpha=0.0001$ case
• Figure 4: Conductivity for $\alpha=0.1$ case
• Figure 5: Conductivity for $\alpha=0.2$ case