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arXiv · 2605.23492

Commensuration torques in double-moir\'e twisted trilayer hexagonal boron nitride and graphene heterostructures

Youngju Park·Nicolas Leconte·Prathap Kumar Jharapla·Md Shaifullah·E. H. Hwang·Jeil Jung
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Abstract

We study commensuration-driven torques and angle locking in double-moir\'e trilayer hexagonal boron nitride (hBN) and graphene heterostructures using large-scale atomistic relaxations. In twisted trilayer hBN (t3BN) homostructures, double-moir\'e commensuration ($\theta_{12} = -\theta_{23}$) give rise to local energy minima accompanied by torque sign reversals, signaling a restoring tendency toward the commensurate configuration. The corresponding binding energies are $\sim$0.2-0.3 meV/atom, originating from enhanced overlap of low-energy stacking domains, although the system is globally stable at zero twist. In contrast, in graphene/hBN heterolayers systems the global energy minimum can coincide with the double-moir\'e commensuration angle, particularly near $\sim$0.6$^{\circ}$, reflecting competition between lattice mismatch and interfacial relaxation. Incommensurate atomic structures have reduced stabilization due to suppressed overlap of low-energy stacking and have enhanced superlubricity due to spatial averaging of interfacial energies. These results establish double-moir\'e commensuration as a general, system-dependent mechanism for twist-angle stabilization, whose angular stability is characterized by the torque magnitude and binding energy. Coulomb electrostatic interactions further enhance the stabilization energy without changing the underlying physics.

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Youngju Park, Nicolas Leconte, Prathap Kumar Jharapla, Md Shaifullah, E. H. Hwang, Jeil Jung. 2026-05-22. Commensuration torques in double-moir\'e twisted trilayer hexagonal boron nitride and graphene heterostructures. https://arxiv.org/abs/2605.23492

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