To investigate the band structure is one of the key approaches to study the fundamental properties of a novel material. We report here the precision band mapping of a 2-dimensional (2D) spin-orbit (SO) coupling in an optical lattice. By applying the microwave spin-injection spectroscopy, the band structure and spin-polarization distribution are achieved simultaneously. The band topology is also addressed with observing the band gap close and re-open at the Dirac points. Furthermore, the lattice depth and the Raman coupling strength are precisely calibrated with relative errors in the order of ${10}^{-3}$. Our approach could also be applied for exploring the exotic topological phases with even higher dimensional system.

研究能带结构是研究新材料基本性质的关键方法之一。我们在这里报告光学晶格中二维 (2D) 自旋轨道 (SO) 耦合的精确带映射。通过应用微波自旋注入光谱，能带结构和自旋极化分布同时实现。带拓扑还通过观察带隙在狄拉克点处关闭和重新打开来解决。此外，晶格深度和拉曼耦合强度精确校准，相对误差为${10}^{-\mathrm{3个}}$. 我们的方法也可用于探索具有更高维系统的奇异拓扑相。