Amplifying Optical Response 

NLO effects in topological materials are particularly intriguing. Certain NLO responses are closely related to some topological quantities such as the Berry curvature and quantum metric tensors, thus NLO effects can be a direct probe of these bulk topological properties. 

We reveal another facet of the interplay between topology and optical effects: both linear and nonlinear optical responses can be significantly enhanced in topological materials. This is because topological materials have the so-called "band inversion" around the bandgap (see the figure above), so the wavefunctions of the valence bands and the conduction bands get substantially hybridized. Consequently, the inter-band transitions can be accelerated. We also point out that upon band inversion, some topological materials develop the "Mexican-hat" band structure, resulting in a larger joint density of states, and further enhancing optical responses. Compared with normal (topologically trivial) materials, the optical responses can be ~10 stronger in topological materials. The extraordinary optical properties of topological materials make them ideal platforms for e.g., photodetection in the terahertz range. 

We also proposed several rules of thumb for designing materials with strong NLO responses, including 1) non-trivial topology (band inversion), 2) strong inversion-symmetry breaking, 3) small bandgaps, and 4) strong covalent bondings (or equivalent, large electron band velocities).

Related publications:

• Haowei Xu, Jian Zhou, Hua Wang, and Ju Li, J. Giant Photonic Response of Mexican-Hat Topological Semiconductors for Mid-infrared to Terahertz Applications. J. Phys. Chem. Lett. 11, 6119–6126 (2020).

• Haowei Xu, Hua Wang, Jian Zhou, Yunfan Guo, Jing Kong and Ju Li, Colossal switchable photocurrents in topological Janus transition metal dichalcogenides. npj Comput. Mater. 7, 1–9 (2021).

These predictions on the topologial enhancement in optical responses have been verified by our experimental collaborators

• Mark J Polking, Haowei Xu, Raman Sankar, Kevin Grossklaus, Ju Li, Strong long-wave infrared optical response in a topological semiconductor with a Mexican-hat band structure, Phys. Rev. B 111, 085101 (2025)

• Jiaojian Shi*, Haowei Xu*, Christian Heide, Changan HuangFu, Chenyi Xia, Felipe de Quesada, Hongzhi Shen, Tianyi Zhang, Leo Yu, Amalya Johnson, Fang Liu, Enzheng Shi, Liying Jiao, Tony Heinz, Shambhu Ghimire, Ju Li, Jing Kong, Yunfan Guo and Aaron M. Lindenberg, Giant room-temperature nonlinearities in a monolayer Janus topological semiconductor. Nature Commun. 14, 4953 (2023)