Two-dimensional (2D) materials, exemplified by graphene and transition metal dichalcogenides (TMDs), offer unique properties for nanoelectronic and optoelectronic devices. TMDs, particularly, exhibit tunable band gaps, strong light-matter interaction, and high carrier mobility. Furthermore, diverse phenomena like piezoelectricity, valleytronics, superconductivity, and charge density waves have been observed in TMDs. Van der Waals heterostructures (vdWHs), formed by vertically stacking different 2D monolayers (MLs), expand the possibilities even further. The weak van der Waals forces allow for almost arbitrary combinations of MLs, creating a vast compositional and configurational space. However, this vast space poses a challenge for high-throughput electronic structure calculations, as traditional DFT methods, particularly those aiming for accurate band gaps (e.g., hybrid functionals and GW), are computationally expensive. The combinatorial complexity of vdWHs, compounded by lattice mismatch and multiple polymorphs, necessitates a novel approach. This research presents a high-throughput method to calculate vdWH band structures with minimal computational resources. The approach focuses on a library of hexagonal XY₂ compounds and rests on the assumption that interlayer interaction primarily involves electrostatic screening. The study aims to systematically explore the compositional space of vdWHs to identify structures with desirable electronic properties, complementing existing databases like C2DB, which provides band alignment and gap information but lacks the detailed band structure data crucial for understanding many properties.

The isolation of graphene and the subsequent discovery of transition metal dichalcogenides (TMDs) spurred significant research into 2D materials and their potential applications in optoelectronics and nanoelectronics. The inherent tunability of TMD band gaps and their strong light-matter interactions make them attractive candidates. The formation of van der Waals heterostructures (vdWHs) by stacking different 2D monolayers further enhances this potential, offering a nearly limitless number of combinations with potentially novel properties. While vdWHs based on graphene, h-BN, MoS₂, MoSe₂, WS₂, and WSe₂ have been extensively investigated, the full exploration of the vast compositional space remains challenging due to the high computational cost of accurate electronic structure calculations. Existing databases such as C2DB have made significant strides in compiling computed properties of 2D materials, but they often lack the detailed band structure information essential for a comprehensive understanding of vdWH behavior. This work aims to address this gap by developing a method capable of providing high-throughput band structure calculations for vdWHs.

The study constructs a database of 93 hexagonal XY₂ 2D compounds, encompassing both 1T and 2H polytypes, selected from the MaterialsCloud 2D materials database. DFT calculations, using both GGA-PBE (with vdW corrections) and the hybrid HSE06 functional, are employed to determine mechanical and electronic properties. These include binding energy (Eb), elastic modulus (as), band gaps (Eg and Ed), magnetic moments (μ), and effective masses. The GGA is used for initial structural optimization, including vdW corrections, while HSE06, including spin-orbit coupling, provides a more accurate description of the electronic structure. The effective mass tensor is determined by numerically differentiating the HSE06 band structure. The strain coefficient (k) describing band edge response to strain is also calculated. A subset of 38 non-magnetic, non-metallic MLs is selected to generate over 700 bilayer vdWHs using the coincidence lattice method, which minimizes the supercell size while keeping strain below 2%. The electronic structure of the vdWHs is then calculated. The method's foundation relies on the near-independence of monolayer band edges when forming heterostructures, with deviations attributed to dielectric screening. The band structure of the bilayers is approximated by superimposing and folding the band structures of the individual monolayers. This high-throughput approach allows for a systematic exploration of the vast vdWH compositional space, identifying different types of band alignment (Type-I, Type-II, Type-III). The detailed computational parameters involved in the DFT calculations using FHI-AIMS code, including basis set, k-point mesh, and vacuum spacing are specified. The coincidence lattice method is thoroughly described, detailing the algorithm for finding the smallest possible supercell compatible with low strain for each vdWH combination.

The research generated a database of 93 hexagonal XY₂ 2D materials, including both 1T and 2H structures. The analysis of these materials revealed a range of binding energies, elastic moduli, and band gaps. From these, 38 non-magnetic, non-metallic MLs were selected to construct 703 bilayer vdWHs using a high-throughput method based on DFT calculations and a non-interacting model. The study identified a large number of vdWHs with various band gaps (0.1 to 5.5 eV) and band alignments (Type I, Type II, and Type III). A detailed analysis focused on Type II vdWHs with direct band gaps and those with primitive unit cells revealed a variety of structures with diverse band offsets. Specifically, 13 direct-band-gap type-II vdWHs with primitive unit cells, including well-known Mo- and W-based dichalcogenides and ten transition-metal-halide combinations, were identified. The method efficiently maps the vast compositional space of vdWHs, unveiling ten previously unseen transition-metal-halide combinations with promising properties for optoelectronics. The effective masses were calculated, revealing potential for high carrier mobility in certain structures. The effect of strain on the band edges was investigated, providing insights into electron-phonon coupling. The analysis systematically categorized the vdWHs based on band gap type (direct or indirect) and unit cell size, leading to the identification of several promising structures for various applications, including those based on previously unexplored 1T transition metal halides. Specific examples of promising vdWHs, including their band gaps and band offsets, are detailed, highlighting their potential for optoelectronic applications. The database of 703 bilayer vdWHs, with their electronic properties, is provided as supplementary material.

The findings demonstrate the effectiveness of the developed high-throughput method for characterizing the electronic properties of vdWHs. The assumption of limited interlayer interaction beyond electrostatic screening, coupled with the coincidence lattice method for supercell construction, significantly reduces the computational cost without sacrificing accuracy for the band-edge properties. The identification of numerous vdWHs with diverse band gaps and band alignments, including those with direct band gaps and primitive unit cells, underscores the potential of this approach in guiding the design and discovery of novel materials. The discovery of several promising vdWHs composed of transition-metal halides highlights the potential of exploring less-studied materials in the creation of vdWHs. The detailed analysis of effective masses and strain coefficients provides crucial information for understanding and predicting the performance of these materials in devices. The limitations of the study, such as the use of a non-interacting model, are acknowledged, and future work could explore more advanced methods to further refine the accuracy of the band structure calculations.

This study presents a computationally efficient method for high-throughput band structure simulations of vdWHs, successfully mapping a significant portion of the vast compositional space. The approach has identified a large number of vdWH bilayers with diverse band gaps and alignments, highlighting previously unexplored materials combinations. The results provide a valuable resource for materials design and device engineering, paving the way for the exploration of novel vdWHs with tailored properties for various applications. Future work can focus on refining the model to account for more complex interlayer interactions, expanding the database to include more diverse 2D materials, and experimentally verifying the predicted properties of the most promising candidates.

The study's non-interacting model, while computationally efficient, may not capture all aspects of interlayer coupling in vdWHs. The accuracy of the predicted band gaps could be improved by incorporating more sophisticated DFT methods, but this would significantly increase computational cost. The analysis focused primarily on bilayers, and future studies could explore multi-layer vdWHs. Experimental validation of the predicted properties is crucial for fully assessing the reliability of the model.