Three-Boson Bound States in Two Dimensions

TL;DR

This paper explores the existence and properties of three-boson bound states in two dimensions with specific interaction patterns, revealing a universal energy ratio independent of microscopic details, contrasting with three-dimensional Efimov physics.

Contribution

It introduces an efficient computational method and uncovers a universal energy ratio for three-boson bound states in two dimensions, differing from Efimov effect characteristics.

Findings

Found three-boson bound state energies for various scattering lengths.

Discovered a universal ratio of three- to two-body binding energies.

Contrasted two-dimensional results with Efimov physics in three dimensions.

Abstract

We investigate the possible existence of the bound state in the system of three bosons interacting with each other via zero-radius potentials in two dimensions (it can be atoms confined in two dimensions or tri-exciton states in heterostructures or dihalogenated materials). The bosons are classified in two species (a,b) such that a-a and b-b pairs repel each other and a-b attract each other, forming the two-particle bound state with binding energy $\epsilon_b^{(2)}$ (such as bi-exciton). We developed an efficient routine based on the proper choice of basis for analytic and numerical calculations. For zero-angular momentum we found the energies of the three-particle bound states $\epsilon^{(3)}_b$ for wide ranges of the scattering lengths, and found a universal curve of $\epsilon^{(3)}_b/\epsilon^{(2)}_b$ which depends only on the scattering lengths but not the microscopic details of the interactions, this is in contrast to the three-dimensional Efimov effect, where a non-universal three-body parameter is needed.