Zeroth order phase transition in a holographic superconductor with single impurity

We investigate the single normal impurity effect in a superconductor by the holographic method. When the size of impurity is much smaller than the host superconductor, we can reproduce the Anderson theorem, which states that a conventional s-wave superconductor is robust to a normal (non-magnetic) impurity with small impurity strength. However, by increasing the size of the impurity in a fixed-size host superconductor, we find a decreasing critical temperature Tc of the host superconductor, which agrees with the results in condensed matter literatures. More importantly, the phase transition at the critical impurity strength (or the critical temperature) is of zeroth order.