Gauss–Bonnet holographic superconductors in lower dimensions

We disclose the effects of Gauss–Bonnet gravity on the properties of holographic s-wave and p-wave superconductors, with higher-order corrections, in lower-dimensional spacetime. We employ shooting method to solve equations of motion numerically and obtain the effect of different values of mass, nonlinear gauge field and Gauss–Bonnet parameters on the critical temperature and condensation. Based on our results, increasing each of these three parameters leads to lower temperatures and larger values of condensation. This phenomenon is rooted in the fact that conductor/superconductor phase transition faces with difficulty for higher effects of nonlinear and Gauss–Bonnet terms in the presence of a massive field. In addition, we study the electrical conductivity in holographic setup. In four dimension, real and imaginary parts of conductivity in holographic s- and p-wave models behave similarly and follow the same trend as higher dimensions by showing the delta function and divergence behavior at low-frequency regime that Kramers–Kronig relation can connect these two parts of conductivity to each other. We observe the appearance of a gap energy at ωg≈8Tc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega _{\mathrm{g}}\approx 8T_{\mathrm{c}}$$\end{document} which shifts toward higher frequencies by diminishing temperature and increasing the effect of nonlinear and Gauss–Bonnet terms. Conductivity in three dimensions is far different from other dimensions. Even the real and imaginary parts in s- and p-wave modes pursue various trends. For example in ω→0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega \rightarrow 0$$\end{document} limit, imaginary part in holographic s-wave model tends to infinity but in p-wave model approaches to zero. However, the real parts in both models show a delta function behavior. In general, real and imaginary parts of conductivity in all cases that we study tend to a constant value in ω→∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega \rightarrow \infty $$\end{document} regime.