[Paper Review] Programming moiré patterns in 2D materials by bending

Maëlle Kapfer, Bjarke S. Jessen+21 more|arXiv (Cornell University)|Sep 21, 2022

Acoustic Wave Resonator Technologies4 citations

TL;DR

This paper demonstrates a novel method to program moiré patterns in 2D materials by mechanically bending monolayer ribbons using an atomic force microscope (AFM) tip. By inducing controlled in-plane bending, the technique enables continuous, homogeneous tuning of twist angles with ultra-low disorder and minimal random strain, achieving highly tunable moiré superlattices with precise strain engineering for quantum materials research.

ABSTRACT

Moiré superlattices in twisted two-dimensional materials have generated tremendous excitement as a platform for achieving quantum properties on demand. However, the moiré pattern is highly sensitive to the interlayer atomic registry, and current assembly techniques suffer from imprecise control of the average twist angle, spatial inhomogeneity in the local twist angle, and distortions due to random strain. Here, we demonstrate a new way to manipulate the moiré patterns in hetero- and homo-bilayers through in-plane bending of monolayer ribbons, using the tip of an atomic force microscope. This technique achieves continuous variation of twist angles with improved twist-angle homogeneity and reduced random strain, resulting in moiré patterns with highly tunable wavelength and ultra-low disorder. Our results pave the way for detailed studies of ultra-low disorder moiré systems and the realization of precise strain-engineered devices.

Motivation & Objective

• To overcome the limitations of current twist-heterostructure fabrication, including poor twist-angle control and random strain, by introducing a mechanical bending approach.
• To achieve continuous, spatially homogeneous tuning of twist angles in 2D bilayers without relying on manual alignment or fixed-angle stacking.
• To reduce disorder in moiré superlattices by minimizing random strain and strain inhomogeneity during fabrication.
• To enable precise strain-gradient engineering in 2D materials for studying correlated quantum phases.
• To demonstrate a scalable, in-situ method for creating ultra-low disorder moiré systems suitable for detailed quantum transport and spectroscopy studies.

Proposed method

• The authors use the tip of an atomic force microscope to bend suspended monolayer ribbons of graphene or WSe2 on hexagonal boron nitride (hBN), inducing controlled in-plane strain gradients.
• The bending is modeled using classical beam theory, where deflection at the free end produces a spatially varying twist angle across the ribbon, with no fitting parameters.
• Local twist angles and strain are measured using low-frequency microscopy (LFM) and piezoresponse force microscopy (PFM), with fast Fourier transforms (FFTs) of PFM data used to extract moiré wavelength and twist angle.
• Strain is independently quantified using Raman spectroscopy and nano-photoluminescence (nano-PL) mapping, which correlate peak shifts with local strain.
• The method enables real-time, reversible tuning of moiré patterns, with strain and twist-angle gradients mapped across the ribbon with sub-micrometer resolution.
• A non-local means (NLM) denoising algorithm is applied to enhance image quality and reliably detect moiré superlattice sites in noisy PFM data.

Experimental results

Research questions

• RQ1 Can mechanical bending of 2D material ribbons via an AFM tip achieve continuous and homogeneous tuning of twist angles in moiré superlattices?
• RQ2 To what extent does bending reduce random strain and disorder compared to conventional twist-heterostructure fabrication?
• RQ3 How accurately can strain gradients and local twist angles be measured and controlled using PFM and FFT analysis?
• RQ4 Can the observed strain and twist-angle profiles be quantitatively predicted by classical beam bending theory?
• RQ5 What is the impact of strain on moiré superlattice fidelity, especially at low twist angles?

Key findings

• The twist angle varies continuously along the ribbon, with measured values matching theoretical predictions from classical cantilever bending theory with no fitting parameters.
• The maximum relative twist angle reaches up to 2.3° in 2 µm-wide graphene/hBN ribbons under 300 nm deflection, with strain gradients of up to 0.64% per µm.
• Strain gradients are precisely measured via Raman and nano-PL, showing linear strain variation across the ribbon with a 0.33% per µm gradient in 2.4 µm-wide WSe2/hBN ribbons.
• Buckling occurs at a critical strain of ~3%, consistent with theoretical predictions of ~2.5% for graphene on hBN, indicating high mechanical stability.
• Nano-ARPES measurements confirm that the twist angle varies continuously along a 7 µm-wide ribbon, with no significant bandstructure modification due to low overall strain.
• The method enables reversible tuning of moiré patterns, with buckling and recovery observed in real time, demonstrating full control and reversibility.