We study the structural relaxation and electronic properties of a one-dimensional (1D) moiré system composed of a zigzag graphene nanoribbon (GNR) placed on a hexagonal boron nitride $\left(h\text{−}\mathrm{BN}\right)$ substrate. Using an effective grid model derived from continuum elasticity theory, we calculate the relaxed atomic structure of the GNR/$h$-BN system for various twist angles and ribbon widths. The relaxation gives rise to a characteristic 1D domain structure consisting of alternating commensurate ${\mathrm{AB}}^{\prime }$ regions and two distinct types of domain boundaries. At finite twist angles, the ribbon adopts a wavy shape, locally tracing the $h$-BN zigzag direction but occasionally sliding to adjacent atomic rows. The resulting moiré potential strongly modulates the electronic structure: the zero-energy zigzag edge states are modulated by the local stacking, leading to densely packed subbands in the ${\mathrm{AB}}^{\prime }$ domains and sharply localized domain-wall states in the energy gaps between the domain subbands, which together realize gate-tunable one-dimensional arrays of quantum-confined electronic states. Our results demonstrate that moiré modulation in GNR/$h$-BN heterostructures provides a versatile platform for electronic structure engineering and the design of 1D moiré nanodevices.

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• Elasticity
• Electrical properties
• Graphene
• Hexagonal boron nitride
• Nanoribbon