  The study of quantum mechanical bound states is as old as quantum theory
itself. Yet, it took many years to realize that three-body borromean systems
that are bound when any two-body subsystem is unbound are abundant in nature.
Here we demonstrate the existence of borromean systems of spin-polarized
(spinless) identical fermions in two spatial dimensions. The ground state with
zero orbital (planar) angular momentum exists in a borromean window between
critical two- and three-body strengths. The doubly degenerate first excited
states of angular momentum one appears only very close to the two-body
threshold. They are the lowest in a possible sequence of so-called super-Efimov
states. While the observation of the super-Efimov scaling could be very
difficult, the borromean ground state should be observable in cold atomic gases
and could be the basis for producing a quantum gas of three-body states in two
dimensions.
