Using the first-principles calculations, we explore the electronic structures of 2H-MX2 (M = Mo, W; X = S, Se, Te). When the number of layers reduces to a single layer, the indirect gap of bulk becomes a direct gap with larger gap and the band curvatures are found to lead to the drastic changes of effective masses. On the other hand, when the strain is applied on the single layer, the direct gap becomes an indirect gap and the effective masses vary. Especially, the tensile strain reduces the gap energy and effective masses while the compressive strain enhances them. Furthermore, the much larger tensile stress leads to become metallic.

We have investigated the electronic structures of single- and double-layered MoS${}_2$, composing of heterojunction structures such as graphene, MoS${}_2$, and SiO${}_2$ and MoS${}_2$ and SiO${}_2$, using scanning photoelectron microscopy. Negative shifts of both core levels and valence bands toward the Fermi energy have been observed. In connection with first-principles calculations, we have confirmed that the direct gap of single-layer MoS${}_2$ is changed to an indirect gap by stacking additional layers via van der Waals interlayer interactions.

The stacking order in layered transition-metal dichalcogenides (TMDCs) induces variations in the electronic and interlayer couplings. Therefore, controlling the stacking orientations when synthesizing TMDCs is desirable but remains a significant challenge. Here, we developed and showed the growth kinetics of different shapes and stacking orders in as-grown multi-stacked MoS₂ crystals and revealed the stacking-order-induced interlayer separations, spin–orbit couplings (SOCs), and symmetry variations. Raman spectra in AA(A…)-stacked crystals demonstrated blueshifted out-of-plane (A_1g) and in-plane (E_2g¹) phonon frequencies, representing a greater reduction of the van der Waals gap compared to conventional AB(A…)-stacking. Our observations, together with first-principles calculations, revealed distinct excitonic phenomena due to various stacking orientations. As a result, the photoluminescence emission was improved in the AA(A…)-stacking configuration. Additionally, calculations showed that the valence-band maxima (VBM) at the K point of the AA(A…)-stacking configuration was separated into multiple sub-bands, indicating the presence of stronger SOC. We demonstrated that AA(A…)-stacking emitted an intense second-harmonic signal (SHG) as a fingerprint of the more augmented non-centrosymmetric stacking and enabled SOC-induced splitting at the VBM. We further highlighted the superiority of four-wave mixing-correlated SHG microscopy to quickly resolve the symmetries and multi-domain crystalline phases of differently shaped crystals. Our study based on crystals with different shapes and multiple stacking configurations provides a new avenue for development of future optoelectronic devices.

We report the effective methods to induce weak ferromagnetism in pristine ${\mathrm{MoS}}_2$ persisting up to room temperature with the improved transport property, which would lead to new spintronics devices. The hydrogenation of ${\mathrm{MoS}}_2$ by heating at $300°\mathrm{C}$ for 1 h leads to the easy axis out of plane, while the irradiation of proton with a dose of $1\times {10}^{13}\mathrm{P}/{\mathrm{cm}}^2$ leads to the easy axis in plane. The theoretical modeling supports such magnetic easy axes.