Three-Boson Bound States in Two 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 ${\epsilon }_b^{(3)}$ for wide ranges of the scattering lengths, and found a universal curve of ${\epsilon }_b^{(3)}/{\epsilon }_b^{(2)}$ 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.

14 pages, 7 figures, references added

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Cited by in corpus (3)

• Few-body bound states of two-dimensional bosons
• Stable p-wave resonant two-dimensional Fermi-Bose dimers
• Controllable fusion of electromagnetic bosons in two-dimensional semiconductors