How can we engineer electronic transitions through twisting and stacking in TMDC bilayers and heterostructures? a first-principles approach.

Layered two-dimensional (2D) materials exhibit unique properties not found in their individual forms, opening new avenues for material exploration. This study examines MX transition metal dichalcogenides (TMDCs), where M is Mo or W, and X is S, Se or Te. These materials are foundational for the creation of hetero- and homo-bilayers with various stacking configurations. Recent interest has focused on twisted homogeneous bilayers, as critical twist angles can significantly alter material properties. This work highlights MX TMDC bilayers with twisted angles that form Moiré patterns, essential to understanding the behaviors of these materials. We performed first-principles calculations using Density Functional Theory (DFT) with range-separated hybrid functionals on 30 combinations of six MX materials with two stacking configurations, revealing that the building blocks and stacking arrangements influence the stability of the heterostructure and the band gap energy ( ). In particular, the MoTe/WSe heterostructure, shifted by 60°, exhibits a direct band gap, indicating potential for novel applications. Our investigation of homobilayers included fully relaxed and low-strain scenarios, examining various stacking styles and twisting angles. Under low-strain conditions, MoS, WS, and WSe can exhibit direct or indirect band gaps at specific twist angles. Additionally, MoS can transition between semiconductor and conductor states, showcasing diverse electronic properties. Critical twist angles, specifically 17.9° and its corresponding angles (42.1°, 77.9° and 102.1°), in twisted WS and WSe bilayers create symmetric Moiré patterns, leading to direct band gaps. The magnitude of the band gap energy can be tuned by varying the twist angles, which also affect the flatness of the electronic band. Like conventional stacking, most twisted TMDC bilayers exhibit favorable interlayer interactions but with more tailorable characteristics. Using heterostructures and controlled twist angles is a powerful approach in material engineering, enabling the manipulation of various electronic behaviors in advanced materials.