1. Broadband measurement of Feibelman's quantum surface response functions
- Author
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Chen, Zeling, Yang, Shu, Xie, Zetao, Hu, Jinbing, Zhang, Xudong, Xia, Yipu, Shen, Yonggen, Su, Huirong, Xie, Maohai, Christensen, Thomas, and Yang, Yi
- Subjects
Physics - Optics ,Condensed Matter - Mesoscale and Nanoscale Physics ,Condensed Matter - Materials Science - Abstract
The Feibelman $d$-parameter, a mesoscopic complement to the local bulk permittivity, describes quantum optical surface responses for interfaces, including nonlocality, spill-in and-out, and surface-enabled Landau damping. It has been incorporated into the macroscopic Maxwellian framework for convenient modeling and understanding of nanoscale electromagnetic phenomena, calling for the compilation of a $d$-parameter database for interfaces of interest in nano-optics. However, accurate first-principles calculations of $d$-parameters face computational challenges, whereas existing measurements of $d$-parameters are scarce and restricted to narrow spectral windows. We demonstrate a general broadband ellipsometric approach to measure $d$-parameters at a gold--air interface across the visible--ultraviolet regimes. Gold is found to spill in and spill out at different frequencies. We also observe gold's Bennett mode, a surface-dipole resonance associated with a pole of the $d$-parameter, around 2.5 eV. Our measurements give rise to and are further validated by the passivity and Kramers--Kronig causality analysis of $d$-parameters. Our work advances the understanding of quantum surface response and may enable applications like enhanced electron field emission.
- Published
- 2024