Zeroth Order Phase Transition in a Holographic Superconductor with Single Impurity

TL;DR

This paper uses holographic methods to study how a single impurity affects a superconductor, revealing a zeroth order phase transition at critical impurity strength, and confirming known robustness for small impurities.

Contribution

It demonstrates a holographic model capturing impurity effects in superconductors, including a novel zeroth order phase transition at critical impurity strength.

Findings

Robustness of s-wave superconductor to small impurities

Decreasing critical temperature with increasing impurity size

Zeroth order phase transition at critical impurity strength

Abstract

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 $T_c$ 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.