Holographic s+p superconductors with nonlinear electrodynamics

Abstract We investigate a holographic s+p superconductor model coupled to nonlinear electrodynamics in the probe limit. The equations of motion are solved numerically, and the condensates as well as the grand potential curves for phase transitions at different values of the nonlinear parameter b are illustrated. It is confirmed that as b increases, both the pure s-wave and p-wave condensates are suppressed. From the $$b-T$$ b - T phase diagram involving the s+p phases, we observe that the region of the pure s-wave phase gradually shrinks with increasing b , which is attributed to the stronger suppression on the s-wave condensate compared to that on the p-wave. Moreover, a smaller charge ratio $$q_p/q_s$$ q p / q s is sufficient for the s+p coexistent phase to appear as b grows. A particularly interesting feature is that, due to the nonlinear self-interaction of the electromagnetic field, charge accumulates spontaneously outside the event horizon from the bulk perspective even in the absence of scalar and vector condensates, thereby invalidating the conventional formula for the superconducting charge density. We improve the definition of the superconducting charge density as the background-subtracted value of the accumulated charge outside the horizon with respect to that in the normal phase. Finally, the optical conductivity in the normal phase is also modified by this accumulated charge for a finite b , and its imaginary part develops a minimum at a finite frequency. This minimum persists in the superconducting phase near the critical point, confusing the extraction of the gap frequency.