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Geometry-controlled directional wave-packet transmission in graphene with photonic-crystal-like electrostatic patterns

Kh. Rakhimov1,2,3,*, H. T. Yusupov4,†, M. Yusupov5,6,7, S. M. Vaez Allaei8,9, R. Sepehrinia8, and A. Chaves10

  • *Contact author: kh.rakhimov@gmail.com
  • †Contact author: x.yusupov@kiut.uz
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Phys. Rev. B 114, 245412 – Published 13 October, 2026

DOI: https://doi.org/10.1103/b5bd-z893

Abstract

We investigate electron wave-packet transport in monolayer graphene subjected to photonic-crystal-inspired electrostatic superlattices composed of periodically arranged circular barriers and wells with zero net potential. Using the time-dependent Dirac equation combined with a split-operator propagation method, we systematically examine how lattice geometry, barrier-well ordering, propagation direction, carrier energy, and scatterer radius govern transient dynamics and long-time transmission behavior. Three representative superlattice configurations are analyzed: square, staggered, and triangular superlattices. While all systems exhibit a universal temporal evolution characterized by an initial transient regime followed by transmission saturation, the saturated transmission strongly depends on structural geometry and propagation direction (i.e., forward and backward). In particular, square and triangular lattices display pronounced directional asymmetry, whereas the staggered configuration serves as an isotropic system in both the forward and backward directions. By introducing the normalized asymmetry coefficient η, we demonstrate that both the magnitude and sign of directional preference can be controllably tuned—and even reversed—through variations in electrostatic potential strength and incident wave-packet energy. These findings establish circular electrostatic superlattices as a versatile platform for geometry-programmable Dirac-fermion transport, opening pathways toward graphene-based directional filters, tunable energy-selective transport elements, and advanced electron-optical devices.

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Phys. Rev. B 114, 245412– Published 13 October, 2026
  • Received 18 June 2026
  • Revised 29 August 2026
  • Accepted 14 September 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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