Band Unfolding for Moiré Systems

Author: Hsu Quinn Date: April 2025

This project implements band unfolding for honeycomb lattices, specifically designed for Moiré superlattices. The code is written in Julia and supports sparse matrix computations and band structure visualization.

Features

• Band unfolding for honeycomb lattices.
• Efficient sparse matrix handling.
• Visualization of energy bands along the K->Γ->M path.

Requirements

Install the following Julia packages:

using Pkg
Pkg.add(["DelimitedFiles", "LinearAlgebra", "JSON", "HDF5", "ArgParse", "SparseArrays", "Pardiso", "Arpack", "LinearMaps", "JLD", "PyPlot", "Statistics"])

Usage

1. Prepare Input Data: Place required files (rlat.dat, orbital_types.dat, site_positions.dat, etc.) in the input directory.
2. Run the Script:

   julia src/band_unfolding.jl --input_dir ./test/deephdata --output_dir ./output

3. View Results: The output directory will contain BandUnFolDing.png, showing the unfolded band structure.

Input Files

• rlat.dat: Reciprocal lattice vectors.
• orbital_types.dat: Orbital types for each site.
• site_positions.dat: Atomic positions.
• hamiltonians_pred.h5: Predicted Hamiltonians.
• overlaps.h5: Overlap matrices.

Output

• BandUnFolDing.png: Band structure visualization.

Notes

• Ensure OMP_NUM_THREADS and JULIA_NUM_THREADS are set for optimal performance.
• The code currently supports honeycomb lattices but can be adapted for other lattice types.