One-dimensional moir\'e engineering in zigzag graphene nanoribbons on hBN

TL;DR

This paper investigates how moiré patterns in zigzag graphene nanoribbons on hBN substrates influence their atomic relaxation and electronic properties, revealing potential for designing 1D quantum-confined electronic devices.

Contribution

It introduces a continuum elasticity-based model to analyze the atomic relaxation and electronic modulation in GNR/hBN moiré systems, highlighting the formation of 1D domain structures and localized states.

Findings

Relaxation leads to a 1D domain structure with AB' regions and domain boundaries.

Moiré potential modulates edge states, creating subbands and localized domain-wall states.

The system enables gate-tunable 1D quantum-confined electronic states.

Abstract

We study the structural relaxation and electronic properties of a one-dimensional (1D) moir\'e system composed of a zigzag graphene nanoribbon (GNR) placed on a hexagonal boron nitride (hBN) substrate. Using an effective grid model derived from continuum elasticity theory, we calculate the relaxed atomic structure of the GNR/hBN system for various twist angles and ribbon widths. The relaxation gives rise to a characteristic 1D domain structure consisting of alternating commensurate AB$'$ regions and two distinct types of domain boundaries. At finite twist angles, the ribbon adopts a wavy shape, locally tracing the hBN zigzag direction but occasionally sliding to adjacent atomic rows. The resulting moir\'e 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 AB$'$ domains and sharply localized domain-wall states in the energy gaps between domain plateaus, which together realize gate-tunable one-dimensional arrays of quantum-confined electronic states. Our results demonstrate that moir\'e modulation in GNR/hBN heterostructures provides a versatile platform for electronic structure engineering and the design of 1D moir\'e nanodevices.