Holographic Lifshitz Superconductors with an Axion Field

We use a Yang-Mills field coupled to an axion as probes of a black hole with arbitrary Lifshitz scaling to investigate, via holography, superconducting phase transitions of the dual theory with a $p_x+i{p}_y$ condensate. In the relativistic case with no axion, this phase is known to be unstable, the stable phase corresponding to condensates of the $p_x$ form. We investigate this stability in theories with non-relativistic scaling. Finally we numerically compute the “Hall” conductivity of these black holes in the non superconducting phase as a function of their Lifshitz scaling.