Topological insulators are bulk semiconductors that manifest in-gap surface states with massless Dirac-like dispersion due to the topological bulk-boundary correspondence principle^1,2,3. These surface states can be manipulated by the interface environment to display various emergent phenomena^{4,5,6,7,8,9,10,11}. Here, we use angle-resolved photoemission spectroscopy and scanning tunnelling microscopy to investigate the interplay of crystallographic inhomogeneity with the topologically ordered band structure in a model topological insulator. We develop quantitative analysis methods to obtain spectroscopic information, in spite of a limited dwell time on each measured point. We find that the band energies vary on the scale of 50 meV across the sample surface, and this enables single sample measurements that are analogous to a multi-sample doping series. By focusing separately on the bulk and surface electrons we reveal a hybridization-like interplay between fluctuations in the surface and bulk state energetics.

^{拓扑绝缘体是体半导体，由于拓扑体边界对应原理1,2,3}，具有无质量 Dirac 样色散的间隙内表面状态。这些表面状态可以通过界面环境进行操作，以显示各种突发现象^{4、5、6、7、8、9、10、11}. 在这里，我们使用角分辨光电子能谱和扫描隧道显微镜来研究晶体学不均匀性与模型拓扑绝缘体中拓扑有序能带结构的相互作用。尽管每个测量点的停留时间有限，但我们开发了定量分析方法来获取光谱信息。我们发现，带能量在整个样品表面的 50 meV 范围内变化，这使得单个样品测量类似于多样品掺杂系列。通过分别关注体电子和表面电子，我们揭示了表面波动和体态能量学之间的类似杂交的相互作用。