moire-metrology 0.8.0

Atomic relaxation, strain extraction, and multi-layer analysis for twisted 2D van der Waals heterostructures

moire-metrology

Atomic relaxation, strain extraction, and multi-layer analysis for twisted 2D van der Waals heterostructures.

This is a Python re-implementation of the modeling tools developed for the papers listed under References. The goal is to make the methodology accessible as a pip-installable package, instead of a private collection of MATLAB scripts.

Documentation -- full user guide, theory background, API reference, and examples.

Status

Beta. The single-interface relaxation, strain extraction, multi-layer stack, and finite-mesh point-pinning APIs are all in place and covered by 70+ fast tests plus integration tests gated behind a slow marker.

Features

• Single-interface relaxation of twisted bilayer systems on a periodic triangular FEM mesh, with three solver options: damped Newton, implicit pseudo-time-stepping, and L-BFGS-B.
• Multi-layer stack API (LayerStack) for heterostructures with any number of layers per flake, including fix_top / fix_bottom clamps to approximate semi-infinite substrates.
• Materials database with bundled GSFE parameterizations for graphene, hBN (AA, AA'), MoSe2/WSe2, and graphene/hBN heterointerfaces.
• Strain extraction from measured moire patterns, implementing the closed-form inversion of Halbertal et al., ACS Nano (2022).
• Constrained relaxation on a finite domain via PinningMap.
• Plotting helpers for stacking-energy maps, elastic-energy maps, local twist angle, and displacement fields.

Installation

pip install moire-metrology

Or install from source for development:

git clone https://github.com/dorrih/moire_metrology.git
cd moire_metrology
python3.11 -m venv .venv
.venv/bin/pip install -e '.[dev]'

Requires Python 3.10+. Dependencies: numpy, scipy, matplotlib.

Quick start

from moire_metrology import GRAPHENE_GRAPHENE, RelaxationSolver, SolverConfig

solver = RelaxationSolver(SolverConfig(pixel_size=1.0, max_iter=200))
result = solver.solve(
    moire_interface=GRAPHENE_GRAPHENE,
    theta_twist=1.05,  # degrees
)

print(f"Moire wavelength: {result.geometry.wavelength:.1f} nm")
print(f"Energy reduction: {100 * result.energy_reduction:.1f}%")

result.plot_stacking(n_tile=2)        # AB/BA triangular domains
result.plot_elastic_energy(n_tile=2)  # SDW network
result.plot_local_twist(n_tile=2)     # AA vortex map

All bundled examples are CLI-configurable:

python examples/bilayer_relaxation.py                    # TBG default
python examples/bilayer_relaxation.py --preset hbn       # graphene/hBN
python examples/bilayer_relaxation.py --preset tmd       # MoSe2/WSe2
python examples/bilayer_relaxation.py --list-interfaces  # show all bundled interfaces

See the documentation for the full quick-start guide, multi-layer stacks, strain extraction, constrained relaxation, custom materials via TOML, and the API reference.

References

Capability	Reference
Single-interface relaxation, GSFE-based continuum model	[1]
Multi-layer (LayerStack) relaxation	[2]
Strain matrix and twist-angle extraction from moire vectors	[3]
Spatially-varying / point-pinned constrained relaxation	[4]

1. Halbertal, D. et al. Moire metrology of energy landscapes in van der Waals heterostructures. Nat. Commun. 12, 242 (2021). doi:10.1038/s41467-020-20428-1 -- arXiv:2008.04835

2. Halbertal, D. et al. Multilayered Atomic Relaxation in van der Waals Heterostructures. Phys. Rev. X 13, 011026 (2023). doi:10.1103/PhysRevX.13.011026 -- arXiv:2206.06395

3. Halbertal, D., Shabani, S., Pasupathy, A. N. & Basov, D. N. Extracting the Strain Matrix and Twist Angle from the Moire Superlattice in van der Waals Heterostructures. ACS Nano 16, 1471--1476 (2022). doi:10.1021/acsnano.1c09789

4. Shabani, S., Halbertal, D., Wu, W., Chen, M., Liu, S., Hone, J., Yao, W., Basov, D. N., Zhu, X. & Pasupathy, A. N. Deep moire potentials in twisted transition metal dichalcogenide bilayers. Nature Physics 17, 720--725 (2021). doi:10.1038/s41567-021-01174-7 -- arXiv:2008.07696

Citing the software itself

The package is archived on Zenodo with a concept DOI that always resolves to the latest version:

• DOI (always-latest): 10.5281/zenodo.19468557

A machine-readable citation file is provided as CITATION.cff; GitHub surfaces it via the "Cite this repository" button.

License

MIT. See LICENSE.