Occurrence conditions for two-dimensional Borromean systems

In quantum mechanics, 2 particles in 3 spatial dimensions (3D) can attract each other without forming a bound state. However, adding a third particle can make a 3-body system bound. Such bound 3-body structures, where each pair of particles is unbound, are called Borromean states. We search for Borromean three-body systems of identical bosons in two dimensional geometry, i.e. we search for bound three-boson system without bound two-body subsystems. Unlike three spatial dimensions, in two-dimensional geometry the two- and three-body thresholds often coincide ruling out Borromean systems. We show that Borromean states can only appear for potentials with substantial attractive and repulsive parts. Borromean states are most easily found when a barrier is present outside an attractive pocket. Extensive numerical search did not reveal Borromean states for potentials without an outside barrier. We outline possible experimental setups to observe Borromean systems in two spatial dimensions. (authors)