Galilo Bogdan, Lee Derek K K, Barnett Ryan
Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom.
Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom.
Phys Rev Lett. 2017 Nov 17;119(20):203204. doi: 10.1103/PhysRevLett.119.203204.
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.
在这封信中，研究表明，在存在谐波势的情况下，相互作用可以促进量子简并玻色子系统拓扑边缘态的出现。通过在合成规范场下由自旋为1的玻色子组成的六边形晶格的具体模型，证明了这种效应。在费米子或非相互作用系统中，谐波陷阱的存在可能会掩盖边缘态的观测。对于我们在托马斯-费米区域具有弱相互作用玻色子的系统，我们可以清楚地看到具有由边缘态穿过的带隙的拓扑能带结构。我们还发现，在存在谐波陷阱的情况下，穿过带隙的边缘态数量增加，并且边缘模式在穿越第一布里渊区时会经历能量偏移，这与系统的拓扑性质有关。我们找到了边缘态能量的解析表达式，并且我们与数值计算的比较显示出极好的一致性。
