Abstract
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 nonrelativistic scaling. Finally we numerically compute the ``Hall'' conductivity of these black holes in the nonsuperconducting phase as a function of their Lifshitz scaling.
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