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

中文翻译：

---

谐波陷阱中相互作用的二维凝聚玻色子-格子系统的拓扑边缘状态表现。

在这封信中，证明了相互作用可以在存在谐波电势的情况下促进量子简并玻色子系统的拓扑边缘状态的出现。通过在合成规范场下由自旋玻色子组成的六边形格子的具体模型证明了这种效果。在铁离子或非相互作用系统中，谐波陷阱的存在会掩盖边缘状态的观察。对于我们在托马斯-费米制中具有弱相互作用的玻色子的系统，我们可以清楚地看到具有带隙的边缘态横穿的拓扑带结构。我们还发现，在存在谐波陷阱的情况下，穿过间隙的边沿状态数量会增加，并且边沿模式在穿越与系统拓扑特性相关的第一个布里渊区时会经历能量转移。