Nookiin: Python software to build commensurable multilayer heterostructures

• Portable and efficient Python software. • Construction of periodic multilayered structures with laminated materials and slabs. • Twist and strain towards the formation of three-dimensional heterostructures. • Real and reciprocal space visualization of moiré patterns. Many first-principles packages employ periodic and symmetry conditions to reduce the computational time and cost. The supercell (SC) method is useful to address periodic systems with different physical perturbations; however, the theoretical definition of a specific SC is a real challenge in Crystallography and Solid State Physics studies. In particular, whether the system is commensurable and made of several two-dimensional (2D) layers with different Bravais lattice, initial local stacking, and interlayer relative orientation. This work presents Nookiin (from the junction of Yucatec Maya words, Nook: ’ knit ’ or ’ wave ’; and iin: ’ me ’), an open-source Python code, designed for the efficient generation of commensurable SCs using geometric methods. Nookiin has an efficient algorithm that minimizes structural distortions at a geometric level, providing an optimized approach for representing 2D heterostructures with a reduced number of atoms. Its modular architecture facilitates adaptation to different problems. Its use through both an interactive console interface and programmatic implementation allows seamless integration into scientific workflows. Additionally, Nookiin offers tools for structural visualization and export of configurations compatible with first-principles codes such as the Vienna ab initio Simulation Package (VASP) code [17]. This report presents the theoretical foundations of the method, the computational implementation of the algorithm, and the results obtained that validate its effectiveness in generating commensurable SCs. With these characteristics, Nookiin establishes itself as a versatile and alternative resource for research in Solid State Physics and Materials Science. The software is openly available at github.com/OssielAg/Nook-iin , with a citable release archived at doi.org/10.5281/zenodo.15706528 . Program Summary Program Title: Nookiin CPC Library link to program files: https://doi.org/10.17632/yvxpwg8sx6.1 Developer’s repository link: https://github.com/OssielAg/Nook-iin , https://doi.org/10.5281/zenodo.14257396 Licensing provisions: GPL-3.0 Programming language: Python External routines/libraries: numpy, matplotlib Nature of problem: Van der Waals heterostructures usually comprise many layers with different composition, initial local stacking, Bravais lattices and relative interlayer orientation due to weak dispersion forces. The definition of a periodic and commensurable common cell is a challenge, if physical properties are studied by first principles calculations within the supercell method. Solution method: Nookiin is designed for the efficient generation of unrestricted commensurable multilayer heterostructures using geometric methods and symmetry-guided strain optimization based on transformation matrices. In addition, Nookiin performs a calculation of the diffraction pattern in two-dimensions to guide microscopy experimentalists. Additional comments: Even for large input systems, memory usage remains remarkably low, making Nookiin suitable for use on standard desktop machines.