MoireStudio: A Universal Twisted Electronic Structure Calculation Package

TL;DR

MoireStudio is presented as a universal Python package for calculating twisted electronic structures of arbitrary 2D material combinations, unifying commensurate geometry with tight-binding and continuum models. It integrates a full relaxation framework so that large moiré supercells can be treated accurately at manageable cost, including the low-energy $k\cdot p$ continuum descriptions and interlayer TB couplings. The main contributions are automated commensurate‑structure search and generation, Wannier90‑based TB parameterization, and relaxation‑enabled Hamiltonians with outputs such as band structures and Chern numbers, all compatible with standard tools. The package is positioned to accelerate twistronics research by enabling parallel computation, visualization, and seamless interfacing with external software.

Abstract

Twistronics is an emerging and captivating field in condensed matter physics and material science. However, accurately and efficiently calculating the electronic structures of twisted systems remains a significant challenge. To address this, we have developed MoireStudio, a universal Python-based computational package for twisted electronic structures. Its functionalities include commensurate structure search, structure generation, parameterization, and construction for tight-binding models and continuum models, and the precise incorporation of full relaxation effects. The package is applicable to arbitrary combinations of two-dimensional materials, including rectangular lattices and heterostructures. User-friendly and easy to use, MoireStudio supports parallel large-scale computations, provides visualization capabilities, and offers interfaces with third-party software. It is poised to become a convenient and powerful tool for researchers in twistronics fields.

Figures (9)

• Figure 1: Workflow of MoireStudio. Starting from an input.json file, the system constructs and analyzes twisted material systems from three perspectives: structural geometry, TB model, and continuum model. It outputs results such as Hamiltonians, band structures, and topological properties. MoireStudio also supports visualization and interfacing with other computational software.
• Figure 2: Example of MoireStudio structural module.(a)-(d) twisted bilayer graphene, twisted black phosphorene, twisted CrPS$_{4}$, and graphene-hexagonal boron nitride (hBN) heterostructures. Here, graphene and hBN have similar lattice vectors essentially, but their lattice constants differ by about 2%. The abscissa represents the angle, while the ordinate represents log$_{10} N_{atom}$, where $N_{atom}$ is the number of atoms in the primitive cell corresponding to the given commensurate angle. (e)-(h) The minimum commensurable structure of each system.
• Figure 3: The influence of relaxation on the structure of tTMD. (a) Unrelaxed structure; (b) relaxed structure.
• Figure 4: Band structure of (a) TBG and (b) twisted MoS$_{2}$ with twist angle $\theta=21.79^{\circ}$ calculated by TB module of MoireStudio.
• Figure 5: Band structure of twisted bilayer CrPS$_{4}$ at a twist angle of $\theta=67.92^{\circ}$: (a) calculated by MoireStudio, (b) calculated by DFT (VASP)kresse_efficient_1996.