---
_id: '67146'
abstract:
- lang: eng
  text: "<jats:p>\r\n                    High-harmonic generation in solids enables
    probing of strong-field electron dynamics in condensed matter and the development
    of compact ultrafast light sources. Whereas most studies have focused on above-bandgap
    high-order harmonics, which are usually interpreted through short electron-hole
    trajectories that recombine within one optical cycle, the microscopic origin of
    low-order emission near the bandgap remains poorly understood. Here, we investigate
    near-bandgap harmonic generation in ZnO by combining semiconductor Bloch equations with
    a complex-time quantum-trajectory analysis. Our results indicate that these harmonics
    are not a continuation of the short trajectory. Rather, they originate from multiple-scattering
    trajectories, in which the electron-hole pair undergoes repeated Bragg scattering
    at the Brillouin-zone boundary and electron-hole reencounter near the\r\n                    <a:math
    xmlns:a=\"http://www.w3.org/1998/Math/MathML\">\r\n                      <a:mi
    mathvariant=\"normal\">Γ</a:mi>\r\n                    </a:math>\r\n                    point
    before the actual recombination occurs. We identify that the imaginary part of
    the electron-hole displacement provides a practical diagnostic of the residual
    tunneling memory. Real-space electron-hole overlap alone does not imply coherent
    recombination unless the full complex displacement vanishes. These results clarify
    the microscopic picture of near-bandgap harmonic emission in ZnO and offer a framework
    for interpreting phase-resolved strong-field dynamics in solids.\r\n                  </jats:p>"
article_number: '033303'
author:
- first_name: Xunqin
  full_name: Huo, Xunqin
  last_name: Huo
- first_name: Xiwang
  full_name: Liu, Xiwang
  last_name: Liu
- first_name: Shidong
  full_name: Yang, Shidong
  last_name: Yang
- first_name: Xiaohong
  full_name: Song, Xiaohong
  last_name: Song
- first_name: Torsten
  full_name: Meier, Torsten
  id: '344'
  last_name: Meier
  orcid: 0000-0001-8864-2072
- first_name: Weifeng
  full_name: Yang, Weifeng
  last_name: Yang
citation:
  ama: Huo X, Liu X, Yang S, Song X, Meier T, Yang W. Near-bandgap harmonic generation
    in solids from multiple scattering revealed by complex quantum trajectories. <i>Physical
    Review Research</i>. 2026;8(3). doi:<a href="https://doi.org/10.1103/l939-jglf">10.1103/l939-jglf</a>
  apa: Huo, X., Liu, X., Yang, S., Song, X., Meier, T., &#38; Yang, W. (2026). Near-bandgap
    harmonic generation in solids from multiple scattering revealed by complex quantum
    trajectories. <i>Physical Review Research</i>, <i>8</i>(3), Article 033303. <a
    href="https://doi.org/10.1103/l939-jglf">https://doi.org/10.1103/l939-jglf</a>
  bibtex: '@article{Huo_Liu_Yang_Song_Meier_Yang_2026, title={Near-bandgap harmonic
    generation in solids from multiple scattering revealed by complex quantum trajectories},
    volume={8}, DOI={<a href="https://doi.org/10.1103/l939-jglf">10.1103/l939-jglf</a>},
    number={3033303}, journal={Physical Review Research}, publisher={American Physical
    Society (APS)}, author={Huo, Xunqin and Liu, Xiwang and Yang, Shidong and Song,
    Xiaohong and Meier, Torsten and Yang, Weifeng}, year={2026} }'
  chicago: Huo, Xunqin, Xiwang Liu, Shidong Yang, Xiaohong Song, Torsten Meier, and
    Weifeng Yang. “Near-Bandgap Harmonic Generation in Solids from Multiple Scattering
    Revealed by Complex Quantum Trajectories.” <i>Physical Review Research</i> 8,
    no. 3 (2026). <a href="https://doi.org/10.1103/l939-jglf">https://doi.org/10.1103/l939-jglf</a>.
  ieee: 'X. Huo, X. Liu, S. Yang, X. Song, T. Meier, and W. Yang, “Near-bandgap harmonic
    generation in solids from multiple scattering revealed by complex quantum trajectories,”
    <i>Physical Review Research</i>, vol. 8, no. 3, Art. no. 033303, 2026, doi: <a
    href="https://doi.org/10.1103/l939-jglf">10.1103/l939-jglf</a>.'
  mla: Huo, Xunqin, et al. “Near-Bandgap Harmonic Generation in Solids from Multiple
    Scattering Revealed by Complex Quantum Trajectories.” <i>Physical Review Research</i>,
    vol. 8, no. 3, 033303, American Physical Society (APS), 2026, doi:<a href="https://doi.org/10.1103/l939-jglf">10.1103/l939-jglf</a>.
  short: X. Huo, X. Liu, S. Yang, X. Song, T. Meier, W. Yang, Physical Review Research
    8 (2026).
date_created: 2026-09-15T06:50:14Z
date_updated: 2026-09-15T06:51:05Z
department:
- _id: '15'
- _id: '170'
- _id: '293'
- _id: '230'
- _id: '623'
doi: 10.1103/l939-jglf
intvolume: '         8'
issue: '3'
language:
- iso: eng
publication: Physical Review Research
publication_identifier:
  issn:
  - 2643-1564
publication_status: published
publisher: American Physical Society (APS)
status: public
title: Near-bandgap harmonic generation in solids from multiple scattering revealed
  by complex quantum trajectories
type: journal_article
user_id: '16199'
volume: 8
year: '2026'
...