# Polaron in a $p+ip$ Fermi topological superfluid

## TL;DR

This paper investigates how an impurity interacts with a two-dimensional $p+ip$ Fermi superfluid, revealing topological phase transitions and many-body state competitions through polaron and trimer behaviors.

## Contribution

It demonstrates the impact of topological phase transitions on polaron energies and identifies a polaron-trimer crossover in a $p+ip$ Fermi superfluid, highlighting impurity as a probe for topological phases.

## Key findings

- Discontinuity in second derivative of polaron energy at topological transition
- Polaron to trimer crossover in strongly interacting regime
- Pairing interactions facilitate impurity-fermion binding

## Abstract

We study polaron excitations induced by an impurity interacting with a two-dimensional $p+ip$ Fermi superfluid. As the Fermi-Fermi pairing interaction is tuned, the background Fermi superfluid undergoes a topological phase transition. We show that such a transition is accompanied by a discontinuity in the second derivative of the polaron energy, regardless of the impurity-fermion interaction. We also identify a polaron to trimer crossover when the Fermi superfluid is in the strongly interacting, thus topologically trivial, regime. However, the trimer state is metastable against the molecular state where the impurity binds a Bogoliubov quasiparticle from the Fermi superfluid. By comparing the polaron to molecule transition in our system with that of an impurity in a noninteracting Fermi sea, we find that pairing interactions in the background Fermi superfluid effectively facilitate the impurity-fermion binding. Our results suggest the possibility of using the impurity as a probe for detecting topological phase transitions in the background; they also reveal interesting competitions between various many-body states in the system.