When intense lightwaves accelerate electrons through a solid, the emerging high-order harmonic (HH) radiation offers key insights into the material^{1,2,3,4,5,6,7,8,9,10,11}. Sub-optical-cycle dynamics—such as dynamical Bloch oscillations^2,3,4,5, quasiparticle collisions^6,12, valley pseudospin switching¹³ and heating of Dirac gases¹⁰—leave fingerprints in the HH spectra of conventional solids. Topologically non-trivial matter^14,15 with invariants that are robust against imperfections has been predicted to support unconventional HH generation^{16,17,18,19,20}. Here we experimentally demonstrate HH generation in a three-dimensional topological insulator—bismuth telluride. The frequency of the terahertz driving field sharply discriminates between HH generation from the bulk and from the topological surface, where the unique combination of long scattering times owing to spin–momentum locking¹⁷ and the quasi-relativistic dispersion enables unusually efficient HH generation. Intriguingly, all observed orders can be continuously shifted to arbitrary non-integer multiples of the driving frequency by varying the carrier-envelope phase of the driving field—in line with quantum theory. The anomalous Berry curvature warranted by the non-trivial topology enforces meandering ballistic trajectories of the Dirac fermions, causing a hallmark polarization pattern of the HH emission. Our study provides a platform to explore topology and relativistic quantum physics in strong-field control, and could lead to non-dissipative topological electronics at infrared frequencies.

^{当强烈的光波加速电子通过固体时，新兴的高次谐波 (HH) 辐射提供了对材料1,2,3,4,5,6,7,8,9,10,11}的重要见解。亚光学循环动力学——例如动态布洛赫振荡^2,3,4,5、准粒子碰撞^6,12、谷赝自旋切换¹³和狄拉克气体的加热¹⁰ ——在传统固体的 HH 光谱中留下指纹。拓扑非平凡物质^14,15具有对缺陷具有鲁棒性的不变量，预计将支持非常规 HH 生成^{16,17,18,19,20}. 在这里，我们通过实验证明了三维拓扑绝缘体 - 碲化铋中的 HH 生成。太赫兹驱动场的频率明显区分了 HH 的产生是来自本体还是来自拓扑表面，其中由于自旋动量锁定^{17而导致的长散射时间的独特组合}准相对论色散使 HH 生成异常高效。有趣的是，根据量子理论，通过改变驱动场的载流子包络相位，所有观察到的阶次都可以连续移动到驱动频率的任意非整数倍。由非平凡拓扑保证的异常 Berry 曲率强制狄拉克费米子的曲折弹道轨迹，导致 HH 发射的标志性偏振模式。我们的研究为探索强场控制中的拓扑和相对论量子物理提供了一个平台，并可能导致红外频率的非耗散拓扑电子学。