Broadband measurement of Feibelman's quantum surface response functions

• 成果类型: Article
• 署名作者: Chen, Zeling; Yang, Shu; Xie, Zetao; Hu, Jinbing; Zhang, Xudong; Xia, Yipu; Shen, Yonggen; Su, Huirong; Xie, Maohai; Christensen, Thomas; Yang, Yi
• 署名单位: University of Hong Kong; University of Hong Kong; University of Shanghai for Science & Technology; Technical University of Denmark
• 刊物名称: PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
• ISSN/ISSBN: 0027-13813
• DOI: 10.1073/pnas.2501121122
• 发表日期: 2025-06-10
• 关键词: fresnel optics; nonlocal corrections; plasmon dispersion; metal-surfaces; model-calculations; SUM-RULES; size; ag; electrodynamics; resonance

摘要

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 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.