Eur. Phys. J. B (2026) 99: 50
https://doi.org/10.1140/epjb/s10051-026-01158-7

Research - Condensed Matter

Tunable quantum oscillations in graphene nanoribbons: from single-mode Fabry–Pérot interference to multi-mode transport

School of Physics and New Energy, Xuzhou University of Technology, 221018, Xuzhou, Jiangsu, China

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Received: 8 September 2025
Accepted: 23 March 2026
Published online: 12 April 2026

Abstract

Using the Keldysh Green function formalism, we compute the bond-resolved current on the hexagonal honeycomb lattice of graphene, including next- and third-nearest neighbor hopping, and establish a direct one-to-one correspondence between the spatial patterns of local current oscillations and the oscillatory conductance observed for both electron and hole carriers. At $t^{\prime }=0.05t$, the $p=\pm 2,\pm 1,0$ conduction subbands lie above the Fermi level of $E_F=2.5\text{eV}$, supporting five electron-type quantum channels. Applying a potential barrier $U>0$ reduces the number of accessible subbands inside the barrier region. Each propagating mode acts as a Fabry-Pérot interferometer, giving rise to decaying periodic oscillations in the conductance, $G=(2e^2/h){\sum }_i{|t_{\mathit{ii}}|}^2$. In contrast, applying a well potential $U>0$ increases the number of accessible subbands, activating interband transitions. The conductance follows the multimode Landauer formula $G=(2e^2/h){\sum }_i{\sum }_j{|t_{\mathit{ji}}|}^2$, where $t_{\mathit{ji}}$ is the transmission amplitude from incident mode i to outgoing mode j. The resulting sum over paths with incommensurate phase factors $e^{i(k_m-k_l)}$ yields irregular conductance oscillations, accompanied by local current profiles with distinct periods inside and outside the well. By contrast, for $t^{\prime }=0.20t$, only the lowest $p=0$ conduction subband lies above the Fermi level. Although a quantum well activates additional subbands inside the well, the total transmission can be reorganized into an effective single-mode Fabry–Pérot form, $G=(2e^2/h){\sum }_i{|t_{00}|}^2$, yielding periodic conductance oscillations with the local current confined to the well. A similar picture holds for hole-type carriers at $t^{\prime }=0.15t$ at $E_F=-1.5\text{eV}$. Finally, we note that, the next nearest-neighbor hopping breaks band symmetry, producing a convex region in the band structure. This asymmetry leads to a non-uniform local current distribution. When the Fermi level intersects the convex region, both electron- and hole-carriers contribute to transport, which is then dominated by edge conduction, analogous to chiral edge channel transport in quantum Hall systems.