  While the interaction potential between two dipoles residing in a single
plane is repulsive, in a system of two vertically adjacent layers of dipoles it
changes from repulsive interaction in the long range to attractive interaction
in the short range. Here we show that for dipolar excitons in semiconductor
heterostructures, such a potential may give rise to bound states if two such
excitons are excited in two separate layers, leading to the formation of
vertically coupled dipolar exciton molecules. Our calculations prove the
existence of such bound states and predict their binding energy as a function
of the layers separation as well as their thermal distributions. We show that
these molecules should be observed in realistic systems such as semiconductor
coupled quantum well structures and the more recent van-der-Waals bound
heterostructures. Formation of such molecules can lead to new effects such as a
collective dipolar drag between layers and new forms of multi-particle
correlations, as well as to the study of dipolar molecular dynamics in a
controlled system.
