A Mobile Impurity in the Kitaev Chain: Phase Diagram and Signatures of Topology

Abstract

We study the physics of a mobile impurity immersed in a $1d$ topological superconductor. We discuss the system's phase diagram obtained with exact diagonalization. We argue that the character of the transition from a weak to strong coupling regime depends on the phase of the host superconductor. A smooth crossover between a weakly coupled polaron and a molecular state is observed in the topological phase. In contrast, the impurity undergoes a sharp phase transition in a topologically trivial background.