Holographic p-wave superconductor with spontaneously broken translation

At the probe level, we investigate the holographic p-wave conductor/superconductor phase transition by both numerical and analytical methods. Especially, due to the nonlinear axion correction, the translational symmetry in superconductor is broken spontaneously. We then study the effects of the axion correction (or disorder) and the mass of vector field on the superconductor phase transition. Concretely, as the disorder parameter and the scaling dimension of vector operator increase, the critical temperature decreases and the stable value of condensate at the low temperature as well as the energy gap increase, which suggests that the larger mass of vector field and the disorder correction inhibit the phase transition, and increase the strength of interaction in superconductor. Near the critical point, the system always undergoes a second-order phase transition, which is independent of the disorder strength and the mass of vector field. According to the behaviors of grand potential and conductivity, the hairy state is verified to be thermodynamical favored and indeed superconducting state. Meanwhile, the analytical results uphold the numerical ones in terms of the critical behavior of condensate.