Abstract

We study commensuration-driven torques and angle locking in double-moiré trilayer hexagonal boron nitride (hBN) and graphene heterostructures using large-scale atomistic relaxations. In twisted trilayer hBN (t3BN) homostructures, double-moiré commensuration (θ12 = −θ23) gives rise to local energy minima accompanied by torque sign reversals, signaling a restoring tendency toward the commensurate configuration. The corresponding binding energies are ∼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-moiré commensuration angle, particularly near ∼0.6°, 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-moiré 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.

Abstract

We study commensuration-driven torques and angle locking in double-moiré trilayer hexagonal boron nitride (hBN) and graphene heterostructures using large-scale atomistic relaxations. In twisted trilayer hBN (t3BN) homostructures, double-moiré commensuration (θ12 = −θ23) gives rise to local energy minima accompanied by torque sign reversals, signaling a restoring tendency toward the commensurate configuration. The corresponding binding energies are ∼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-moiré commensuration angle, particularly near ∼0.6°, 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-moiré 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.

Abstract

We study commensuration-driven torques and angle locking in double-moiré trilayer hexagonal boron nitride (hBN) and graphene heterostructures using large-scale atomistic relaxations. In twisted trilayer hBN (t3BN) homostructures, double-moiré commensuration (θ12 = −θ23) gives rise to local energy minima accompanied by torque sign reversals, signaling a restoring tendency toward the commensurate configuration. The corresponding binding energies are ∼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-moiré commensuration angle, particularly near ∼0.6°, 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-moiré 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.

Abstract

We study commensuration-driven torques and angle locking in double-moiré trilayer hexagonal boron nitride (hBN) and graphene heterostructures using large-scale atomistic relaxations. In twisted trilayer hBN (t3BN) homostructures, double-moiré commensuration (θ12 = −θ23) gives rise to local energy minima accompanied by torque sign reversals, signaling a restoring tendency toward the commensurate configuration. The corresponding binding energies are ∼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-moiré commensuration angle, particularly near ∼0.6°, 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-moiré 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.