  Using density functional theory calculations, we establish that the
half-metallicity of bulk Ba2FeReO6 survives down to 1 nm thickness in
BaTiO3/Ba2FeReO6/BaTiO3 heterostructures grown along the (001) and (111)
directions. The confinement of the two-dimensional (2D) electron gas in this
quantum well structure arises from the suppressed hybridization between Re/Fe d
states and unoccupied Ti d states, and it is further strengthened by polar
fields for the (111) direction. This mechanism, distinct from the polar
catastrophe, leads to an order of magnitude stronger confinement of the 2D
electron gas than that at the LaAlO3/SrTiO3 interface. We further show
low-energy bands of (111) heterostructure display nontrivial topological
character. Our work opens up the possibility of realizing ultrathin spintronic
devices.
