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Holographic Superconductors with Higher Curvature Corrections

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.