Polaron-molecule transitions in a two-dimensional Fermi gas

TL;DR

This paper investigates the transition between polaron and molecule states of a single impurity in a two-dimensional Fermi gas, revealing a transition and validating a variational approach for such systems.

Contribution

It demonstrates the existence of a polaron-molecule transition in 2D Fermi gases and validates a variational method against exact solutions for large impurity mass.

Findings

Identification of a polaron-molecule transition in 2D

Variational wave function matches exact solutions at high impurity mass

Provides a reliable variational approach for 2D impurity problems

Abstract

We address the problem of a single "spin-down" impurity atom interacting attractively with a spin-up Fermi gas in two dimensions (2D). We consider the case where the mass of the impurity is greater than or equal to the mass of a spin-up fermion. Using a variational approach, we resolve the questions raised by previous studies and we show that there is, in fact, a transition between polaron and molecule (dimer) ground states in 2D. For the molecule state, we use a variational wave function with a single particle-hole excitation on the Fermi sea and we find that its energy matches that of the exact solution in the limit of infinite impurity mass. Thus, we expect the variational approach to provide a reliable tool for investigating 2D systems.