p-wave superconductors in dilaton gravity

In this paper, we study peculiar properties of p-wave superconductors in dilaton gravity. The scale invariance of the bulk geometry is effectively broken due to the existence of dilaton. By coupling the dilaton to the non-Abelian gauge field, i.e., $-\frac14 e^{-\beta \Phi} F^a_{\mu\nu}F^{a\mu\nu}$, we find that the dissipative conductivity of the normal phase decreases and approaches zero at the zero frequency as $\beta$ increases. Intuitively, the system behaves more and more like an insulator. When the hairy solution is turned on, the system crosses a critical point to the superconducting phase. We find that the critical chemical potential decreases with the increasing of $\beta$ and the maximum height of the conductivity is suppressed gradually which are consistent with our intuition for insulator/supercondutor transition.