An arXiv preprint reports that tunneling and scattering of valley Hall modes in modeled Bernal bilayer graphene were associated with island spacing, in-gap energy and finite-size effects. It also reports that resonant tunneling via an impurity enhanced overlap between superlattice islands and that topological protection was retained under gate-pattern misalignment, alongside more backscattering and inter-valley scattering in the conclusion, especially at shorter domain-wall spacing.
What the model compared
The study asks whether valley Hall modes around gate-defined bilayer-graphene islands could host quantum walks or weakly coupled systems, and how in-gap impurities and gate-pattern misalignment affect tunneling between islands. In ordinary terms, the paper treats these modes around the islands as possible building blocks for those arrangements.
It uses tight-binding simulations of gate-defined islands in Bernal bilayer graphene. The simulated devices included impurity-free and impurity-containing scattering geometries, plus a separate two-island geometry for examining level splitting.
Spacing and finite-size effects
One part of the model focused on localization, meaning how tightly the modes were confined. Higher interlayer bias corresponded to stronger localization, while smoother electrostatic domain walls corresponded to longer evanescent decay lengths - the distance over which a mode's fading tail extends.
In the clean geometry, shorter domain-wall separation was associated with higher tunneling probability. Tunneling probabilities also varied among the available modes as in-gap energy varied.
That pattern was oscillatory rather than a simple, steady change. The analysis associated oscillatory scattering with finite-size quantization and reported suppression and reappearance of tunneling, including parameter choices with fully prohibited scattering.
A resonant impurity
Another calculation used a single circular impurity potential with radius R = 5a and examined in-gap bound states as resonant tunneling channels. The paper reports that resonant tunneling through the impurity enhanced overlap between superlattice islands.
At impurity-bound-state resonance, tunneling depended strongly on domain-wall spacing and on whether the mode had an inner or outer flavor. The model reported preservation of the valley index, while inter-valley scattering was suppressed in the model.
Misalignment and two islands
The results under gate-pattern misalignment were mixed. The simulations reported retained topological protection across the studied parameter range. The conclusion also reports more backscattering and inter-valley scattering with misalignment, particularly at shorter spacing between domain walls.
In the separate two-island geometry, nearby islands showed level splitting associated with peaks in inter-island scattering. For islands of radius 100a, however, suppressed scattering around E = -0.06 eV showed no level splitting despite high local density of states, or LDOS, at each island. Here, LDOS is the model's measure of the states concentrated locally at an island.
A numerical scale-up estimate
The authors give a numerical estimate for scaling up the setup. They estimate that the modeled effects could extend to systems five to 10 times larger by lowering the gap to the 1 to 5 meV scale. The base simulated square was about 80 by 80 nm, with an island radius of approximately 25 nm.
The paper keeps its quantum-walk and weak-coupling discussion at the level of possibilities it examines. It presents the larger-device proposal as a numerical scaling estimate.
The document is an arXiv preprint, version 1, dated 26 Aug 2026. It reports that code and generated data for all simulations are available through the cited repository information.
Paper data and sources
Original title: Size and Impurity Effects on Scattering of Valley Hall Modes in Gate-Defined Bilayer Graphene Superlattices
Authors: Marcus N. Kanestrøm, Antonio L. R. Manesco, D. O. Oriekhov
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text