报告摘要：The Riemannian geometry of optical transition dipoles has become a powerful framework for understanding linear and nonlinear optical responses. In this talk I report that the interacting quantum geometry of optical transitions possesses a rich structure and can be naturally delineated into two types: localized and delocalized particle-hole excitations. The former possesses uniform quantum geometry with flat Hermitian curvature, whereas the latter possess non-uniform quantum geometry with non-vanishing Hermitian curvature. As a striking example, we find that uniform quantum geometry can be produced by electron-hole interactions: even when composed of extended Bloch states in the particle and hole bands, excitons possess uniform and flat quantum geometry. This geometric distinction directly manifests in nonlinear optical responses. Using a many-body time-dependent perturbation theory, we connect the optical transition quantum geometry of localized particle-hole excitations to their nonlinear responses. For second-order response, we find that excitonic excitations possess a quantum shift vector that is independent of light polarization. This strongly constrains their second-order shift current response: in non-centrosymmetric but non-polar materials, excitonic transitions possess zero shift photocurrent; this contrasts with finite and strongly light polarization dependent shift currents for non-interacting free particle-hole excitations. More strikingly, we find that the uniform and flat excitonic quantum geometry forces its third-order circular photoconductivity to vanish non-magnetic materials, in stark contrast to its non-interacting counterparts. These results demonstrate the rich landscape of the non-perturbative effects of electron-hole interactions in the quantum geometry and nonlinear response of excited states.

个人简介：杨栩博士目前是南洋理工大学Justin Song教授课题组的博士后研究员。他2015年于北京大学取得学士学位，2021年于波士顿学院获得博士学位，2021至2024年在俄亥俄州立大学从事博士后研究。杨博士的研究方向为凝聚态理论，主要关注拓扑物相的分类和物理响应。近年来，他进一步将非线性响应理论用于探究相互作用下关联量子物态的拓扑与几何性质。

邀请人：孙孝奇　xqsun@iphy.ac.cn