Competing s-wave orders from Einstein-Gauss-Bonnet gravity

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In this paper, the holographic superconductor model with two s-wave orders from 4+1 dimensional Einstein-Gauss-Bonnet gravity is explored in the probe limit.

• At different values of the Gauss-Bonnet coefficient $\alpha$, we study the influence of tuning the mass and charge parameters of the bulk scalar field on the free energy curve of condensed solution with signal s-wave order, and compare the difference of tuning the two different parameters while the changes of the critical temperature are the same.
• Based on the above results, it is indicated that the two free energy curves of different s-wave orders can have one or two intersection points, where two typical phase transition behaviors of the s+s coexistent phase, including the reentrant phase transition near the Chern-Simons limit $\alpha=0.25$, can be found.
• We also give an explanation to the nontrivial behavior of the $T_c-\alpha$ curves near the Chern-Simons limit, which might be heuristic to understand the origin of the reentrant behavior near the Chern-Simons limit.