Polarons and Molecules in a Two-Dimensional Fermi Gas

TL;DR

This paper investigates impurity behavior in a two-dimensional Fermi gas, revealing that polaron states are always energetically favored over dimers, and highlights the importance of particle-hole pairs in lower dimensions.

Contribution

It demonstrates that simple variational approaches are unreliable in 2D Fermi gases and emphasizes the significance of particle-hole excitations in impurity states.

Findings

Polaron always has lower energy than dimer in 2D.

Exact solutions show both bound states and Fermi sea distortions are important.

Variational methods are insufficient for accurate impurity energy predictions.

Abstract

We study an impurity atom in a two-dimensional Fermi gas using variational wave functions for (i) an impurity dressed by particle-hole excitations (polaron) and (ii) a dimer consisting of the impurity and a majority atom. In contrast to three dimensions, where similar calculations predict a sharp transition to a dimer state with increasing interspecies attraction, we show that the polaron ansatz always gives a lower energy. However, the exact solution for a heavy impurity reveals that both a two-body bound state and distortions of the Fermi sea are crucial. This reflects the importance of particle-hole pairs in lower dimensions and makes simple variational calculations unreliable. We show that the energy of an impurity gives important information about its dressing cloud, for which both ans\"atze give inaccurate results.