Abstract
We investigate the neutral AdS black-hole solution in the consistent D → 4 Einstein-Gauss-Bonnet gravity proposed in [K. Aoki, M.A. Gorji, and S. Mukohyama, Phys. Lett. B810 (2020) 135843] and construct the gravity duals of (2 + 1)-dimensional superconductors with Gauss-Bonnet corrections in the probe limit. We find that the curvature correction has a more subtle effect on the scalar condensates in the s-wave superconductor in (2 + 1)-dimensions, which is different from the finding in the higher-dimensional superconductors that the higher curvature correction makes the scalar hair more difficult to be developed in the full parameter space. However, in the p-wave case, we observe that the higher curvature correction always makes it harder for the vector condensates to form in various dimensions. Moreover, we note that the higher curvature correction results in the larger deviation from the expected relation in the gap frequency ωg/Tc ≈ 8 in both (2 + 1)-dimensional s-wave and p-wave models.
Highlights
It was observed that the higher curvature correction makes the scalar condensates harder to form and causes the behavior of the claimed universal ratio ω/Tc ≈ 8 [15] unstable
We find that the curvature correction has a more subtle effect on the scalar condensates in the s-wave superconductor in (2 + 1)-dimensions, which is different from the finding in the higher-dimensional superconductors that the higher curvature correction makes the scalar hair more difficult to be developed in the full parameter space
All the studies mentioned above concerning the holographic dual models with the curvature correction are based on the Einstein-Gauss-Bonnet gravity in dimensions D ≥ 5, where we find that the higher curvature corrections make it harder for the scalar [14, 16,17,18,19,20,21,22,23,24,25,26,27,28,29] or vector [30,31,32,33,34,35,36] hair to form
Summary
We consider a Maxwell field and a charged complex scalar field coupled via the action d4x√−g. We give in figure 3 the condensates of the scalar operator O− as a function of temperature with various Gauss-Bonnet parameters α for the fixed masses m2L2 = −2 and m2L2eff = −2, which will diverge at low temperatures, similar to that for the standard holographic superconductor model in the probe limit neglecting backreaction of the spacetime [8]. Considering the correct consistent influence due to the Gauss-Bonnet parameter in various condensates for all dimensions [16, 31] and the pure effect of the curvature correction on the critical temperature Tc for the fixed mass m2L2 = m2L2eff = 0, i.e., the increase of α results in the decrease of Tc, we argue that it is more appropriate to choose the mass of the scalar field by selecting the values of m2L2eff for the Gauss-Bonnet superconductors even in (2 + 1)-dimensions. The higher curvature corrections make it harder for the condensate of the scalar operator O− to form
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