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In this Letter, it is shown that interactions can facilitate the emergence oftopological edge states of quantum-degenerate bosonic systems in the presenceof a harmonic potential. This effect is demonstrated with the concrete model ofa hexagonal lattice populated by spin-one bosons under a synthetic gauge field.In fermionic or noninteracting systems, the presence of a harmonic trap canobscure the observation of edge states. For our system with weakly interactingbosons in the Thomas--Fermi regime, we can clearly see a topological bandstructure with a band gap traversed by edge states. We also find that thenumber of edge states crossing the gap is increased in the presence of aharmonic trap, and the edge modes experience an energy shift while traversingthe first Brillouin zone which is related to the topological properties of thesystem. We find an analytical expression for the edge-state energies and ourcomparison with numerical computation shows excellent agreement.

Topological Edge-State Manifestation of Interacting 2D Condensed Boson-Lattice Systems in a Harmonic Trap