---
title: 1D Moiré Channels in 2D Materials
url: https://www.emergentmind.com/topics/1d-moire-channel
type: topic
---

# 1D Moiré Channels in 2D Materials

A one-dimensional (1D) moiré channel is a spatially confined region, typically arising within van der Waals heterostructures or modulated low-dimensional superlattices, where the interplay of lattice mismatch, relative twist, or strain between two atomically thin layers induces a periodic potential that is essentially unidirectional. This moiré modulation leads to new phenomena not present in the constitutive materials, including gate-tunable arrays of quantum-confined states, flat-band physics, and sensitive control over topological and correlated electronic phases. 1D moiré channels can be engineered via various routes, including controlled stacking of nanoribbons on incommensurate substrates, undulation-induced registry modulation in bilayers, twist-angle-induced stripes in non-hexagonal systems, or domain-wall engineering in moiré superlattices.

## 1. Structural Formation and Continuum Modeling of 1D Moiré Channels

The archetype of a 1D moiré channel is realized by placing a zigzag graphene nanoribbon (GNR) on hexagonal boron nitride (hBN) with a finite twist angle and carefully controlled registry [2510.21166]. Atomic relaxation in this composite is accurately described within a continuum elasticity theory, where the total energy is the sum of elastic deformation and moiré-induced interlayer binding. In the continuum limit, the in-plane elastic energy for each layer is
\[
U_E = \sum_{l=1,2}\!\int d^2r\,\left\{\frac{\lambda^{(l)}+\mu^{(l)}}{2}(u_{xx}^{(l)}+u_{yy}^{(l)})^2 
+ \frac{\mu^{(l)}}{2}\left[(u_{xx}^{(l)}-u_{yy}^{(l)})^2+4u_{xy}^{(l)\,2}\right]\right\}
\]
where \(\lambda^{(l)}, \mu^{(l)}\) are Lamé parameters for each material. Minimization of this energy, given the moiré potential from lattice mismatch and/or orientation, yields a periodic domain pattern with alternating commensurate AB′ stacking and domain walls. The resulting atomic-scale relaxation causes the GNR to adopt a locally wavy trajectory, tracing the hBN crystal axes but featuring discrete stacking slips.

Analogous 1D moiré channels can also be produced via undulatory deformation of van der Waals bilayers (e.g., hBN or TMDs) [2410.17548]. A sinusoidal height profile along x,
\[
h(x) = A \sin \Bigl(2\pi x

Source: https://www.emergentmind.com/topics/1d-moire-channel