Holographic s+p superconductors with axion induced translation symmetry breaking

We construct a holographic model for an s+p superconductor with axion induced translation symmetry breaking within the framework of gauge/gravity duality, working in the probe limit. The equations of motion are solved numerically to investigate the influence of the parameter k / T on the competition and coexistence between the s-wave and p-wave orders. We find that increasing k / T suppresses the thermodynamic stability of both the single condensate s-wave and p-wave solutions. With the k-μ k - μ phase diagram and the condensate curves, we see that the region dominated by the single condensate p-wave phase gradually decreases with the increasing of k / T , finally leaving only the single condensate s-wave phase in the large k / T region, which is explained by the grand potential curves showing a slower decreasing of the thermodynamic stability for the s-wave solution than that for the p-wave solution. Furthermore, a larger minimum ratio of the charges qₚ/qₛ q p / q s is required to stabilize the s+p coexistent phase as k / T increases, and we determine the precise dependence of this critical ratio on k / T . Finally, our study of the optical conductivity reveals that the gap frequency increases with k / T . A characteristic kink, associated with the s+p coexistent phase, is identified in the dependence of gap frequency on k / T , which could serve as a potential experimental signature for detecting multi-condensate superconductivity.