Size dependence in two-dimensional lateral heterostructures of transition metal dichalcogenides

Lateral heterostructures (LHSs) of semiconductors can give rise to novel electronic and optoelectronic properties, which may open up unforeseen opportunities in materials science and device physics. However, due to the high computational cost, previous theoretical studies are usually limited to small size LHSs, which fail to demonstrate the intrinsic features of the large size LHSs. Here, by using state-of-the-art real-space density functional theory, we study the LHSs of two-dimensional (2D) monolayer semiconductors consisting of transition metal dichalcogenides (TMDs) with a length up to 4234 angstrom, which for the first time gives the same order of magnitude as compared with the experiments. The numerical calculation shows that the electronic properties of the LHSs are highly dependent on their size. In particular, for the zigzag boundary we find that the band gap decreases monotonously from 1.70 eV to 0 eV with increasing LHS size. Such behavior can be interpreted by the properties of the size dependent edge states resulting from the deformation gauge field and the corresponding effective pseudo-spin-orbit coupling. Consequently, one may precisely control and design the electronic and optoelectronic properties of 2D TMD LHSs by tuning their size. Our investigation could provide an interesting strategy for designing novel electronic and optoelectronic devices.