Nonlinear optical responses and quantum geometry
by
TDLI Meeting Room N600 (East Wing of Floor 6, North Building)
Nonlinear optical (NLO) responses of materials, e.g., second-harmonic generation and bulk photovoltaic effect (BPVE) [Fig. (a)], have received renewed interests recently due to their promising applications in next generation optoelectronics, photovoltaic solar cells and sensitive THz radiation detection. In the meantime, understanding of responses of materials to static electromagnetic fields, e.g., quantum Hall effect, in terms of geometry of quantum states has become a powerful approach, resulting in such important discoveries as quantum anomalous Hall (Chern) insulator. However, it has been challenging to relate quantum geometry with optical responses. In this talk, I will present the main findings of our recent endeavor along this direction. In particular, we found that in BPVE, injection photocurrent is controlled by quantum metric and Berry curvature while shift photocurrent is governed by Christoffel symbols [1]. Further, by identifying transition dipole moment matrix elements as tangent vectors [Fig. (b)], we constructed a Riemannian geometry theory for NLO processes, and showed that optical responses are the manifestations of Riemannian geometry of quantum states [2]. We also demonstrated that third-order photovoltaic Hall effect in topological materials are caused mainly by Riemannian curvature tensor.
[1] J. Ahn, G.-Y. Guo and N. Nagaosa, Phys. Rev. X 10, 041041 (2020).
[2] J. Ahn, G.-Y. Guo, N. Nagaosa, and A. Vishwanath, Nature Physics 18, 290 (2022).
Guang-Yu Guo is currently an NTU Chair Professor of National Taiwan University (NTU) and also the Director of Physics Division, National Center for Theoretical Sciences. He received his PhD from Cambridge University, UK in 1987. He joined the NTU Physics Faculty in 1998 after working in Daresbury Laboratory, UK for 11 years as a postdoc, higher and senior staff scientist. He also worked in National Chengchi University as a Chair Professor and the founding director of the Graduate Institute of Applied Physics during 2009-2013. He has been vigorously conducting research in condensed matter and materials physics in the past 36 years, publishing over 300 journal papers with nearly 14,000 citations and h-index of 61. He has won several academic awards and honors including the National Science Council Outstanding Research Awards (1998, 2004, 2009) as well as the Ministry of Education 57th Academic Award (2013) and 19th National Chair Professorship (2015). He is an elected Fellow of the PSROC (2005), APS (USA) (2005) and Institute of Physics (UK) (2013).
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