The prediction and realization of topological insulators have sparked great interest in experimental approaches to the classification of materials^1,2,3. The phase transition between non-trivial and trivial topological states is important, not only for basic materials science but also for next-generation technology, such as dissipation-free electronics⁴. It is therefore crucial to develop advanced probes that are suitable for a wide range of samples and environments. Here we demonstrate that circularly polarized laser-field-driven high-harmonic generation is distinctly sensitive to the non-trivial and trivial topological phases in the prototypical three-dimensional topological insulator bismuth selenide⁵. The phase transition is chemically initiated by reducing the spin–orbit interaction strength through the substitution of bismuth with indium atoms^6,7. We find strikingly different high-harmonic responses of trivial and non-trivial topological surface states that manifest themselves as a conversion efficiency and elliptical dichroism that depend both on the driving laser ellipticity and the crystal orientation. The origins of the anomalous high-harmonic response are corroborated by calculations using the semiconductor optical Bloch equations with pairs of surface and bulk bands. As a purely optical approach, this method offers sensitivity to the electronic structure of the material, including its nonlinear response, and is compatible with a wide range of samples and sample environments.

拓扑绝缘体的预测和实现激发了人们对材料^1,2,3分类的实验方法的极大兴趣。非平凡和平凡拓扑状态之间的相变很重要，不仅对于基础材料科学，而且对于下一代技术，例如无耗散电子⁴。因此，开发适用于各种样品和环境的先进探针至关重要。在这里，我们证明了圆偏振激光场驱动的高谐波产生对原型三维拓扑绝缘体硒化铋^{5中的非平凡和平凡拓扑相明显敏感}. 相变是通过用铟原子取代铋来降低自旋轨道相互作用强度以化学方式引发的^6,7。我们发现平凡和非平凡拓扑表面态的显着不同的高谐波响应表现为转换效率和椭圆二色性，这取决于驱动激光的椭圆率和晶体取向。通过使用具有成对表面和体带对的半导体光学布洛赫方程的计算证实了异常高谐波响应的起源。作为一种纯光学方法，该方法对材料的电子结构（包括其非线性响应）具有敏感性，并且与广泛的样品和样品环境兼容。