Three-body bound states of two bosonic impurities immersed in a Fermi sea in 2D

TL;DR

This paper investigates three-body bound states of two bosonic impurities in a 2D Fermi sea, revealing medium-induced Borromean-like states and analyzing the effects of particle-hole fluctuations on their stability.

Contribution

It provides a detailed analysis of three-body bound states in 2D Fermi systems, including medium effects and corrections due to particle-hole fluctuations, which is a novel insight.

Findings

Three-body bound states exist below the Fermi energy.

Medium-induced Borromean-like states are identified in 2D.

Particle-hole fluctuations have a small effect on the state stability.

Abstract

We consider two identical impurities immersed in a Fermi sea for a broad range of masses and for both interacting and non-interacting impurities. The interaction between the particles is described through attractive zero-range potentials and the problem is solved in momentum space. The two impurities can attach to a fermion from the sea and form three-body bound states. The energy of these states increase as function of the Fermi momentum $k_F$, leading to three-body bound states below the Fermi energy. The fate of the states depends highly on two- and three-body thresholds and we find evidence of medium-induced Borromean-like states in 2D. The corrections due to particle-hole fluctuations in the Fermi sea are considered in the three-body calculations and we show that in spite of the fact that they strongly affect both the two- and three-body systems, the correction to the point at which the three-body states cease to exist is small.