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  • Open Access

Tunable two-dimensional energy orbital angular momentum synthetic lattices with free electrons

Jing Li1, Yuhan Jiang1, Wu Wen1, Dixuan Wu1, and Yunquan Liu1,2,3,*

  • 1State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
  • 2Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
  • 3Peking University Yangtze Delta Institute of Optoelectronics, Nantong, Jiangsu 226010, China

  • *Contact author: Yunquan.liu@pku.edu.cn
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Phys. Rev. Research 8, 033355 – Published 23 September, 2026

DOI: https://doi.org/10.1103/rpst-tkh7

Abstract

Free-electron interactions with optical near fields are conventionally described as one-dimensional energy ladders, in which multicolor photon-exchange pathways can become spectrally degenerate. In this work, we show that coupling a single free electron to commensurate two-color optical vortices can unfold this degeneracy, realizing a tunable synthetic lattice spanned by the electron energy and orbital angular momentum (OAM). The resulting single-particle dynamics map the free-electron light interaction onto an effective tight-binding Hamiltonian whose primitive hopping vectors and coupling anisotropy are controlled by the optical OAM charges and near-field amplitudes. We use this construction to emulate a Lifshitz transition in the synthetic quasienergy band structure, identified by a topological reconnection of the zero-quasienergy contour and the associated Van Hove singularity in the density of states. We further show that the generated electron state exhibits tunable intraparticle energy-OAM mode nonseparability, which serves as a diagnostic of the synthetic-lattice geometry. These results establish free electrons as a tunable platform for synthetic-band engineering, combining electron-wavefunction control with ultrafast electron-microscopy and nanoscale near-field techniques.

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Phys. Rev. Research 8, 033355– Published 23 September, 2026
  • Received 24 February 2026
  • Revised 30 April 2026
  • Accepted 8 September 2026
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