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

TL;DR

This paper investigates how a mobile impurity behaves in a one-dimensional topological superconductor, revealing different transition types depending on the host phase, with a smooth crossover in the topological phase and a sharp transition in the trivial phase.

Contribution

It provides the first detailed phase diagram of a mobile impurity in a 1D topological superconductor, highlighting the dependence of transition nature on the superconductor's topology.

Findings

Smooth crossover between polaron and molecular state in topological phase

Sharp phase transition in trivial phase

Transition character depends on the superconductor's topological state

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.