The nonlinear optical (NLO) responses of topological materials are under active research. Most previous works studied the surface and bulk NLO responses separately. Here we develop a generic Green’s function framework to investigate the surface and bulk NLO responses together. We reveal that the topological surface can behave disparately from the bulk under light illumination. Remarkably, the photocurrents on the surface can flow in opposite directions to those in the bulk interior, and the light-induced spin current on the surface can be orders of magnitude stronger than its bulk counterpart on a per-volume basis. We also study the responses under inhomogeneous field and higher-order NLO effect, which are all distinct on the surface. These anomalous surface responses suggest that light can be a valuable tool for probing the surface states of topological materials. Besides, the surface effects should be prudently considered when investigating the optical properties of topological materials.

拓扑材料的非线性光学 (NLO) 响应正在积极研究中。大多数以前的工作分别研究了表面和体 NLO 响应。在这里，我们开发了一个通用的格林函数框架来一起研究表面和体 NLO 响应。我们揭示了拓扑表面在光照下的行为可能与主体不同。值得注意的是，表面上的光电流可以以与体内部相反的方向流动，并且表面上的光诱导自旋电流可以比其在每体积基础上的体对应物强几个数量级。我们还研究了在不均匀场和高阶 NLO 效应下的响应，这些在表面上都是不同的。这些异常的表面响应表明，光可以成为探测拓扑材料表面状态的宝贵工具。此外，在研究拓扑材料的光学特性时，应谨慎考虑表面效应。