Thickness and strain effects on electronic structures of transition metal dichalcogenides: 2H-MX2semiconductors (M=Mo, W;

Origin of Indirect Optical Transitions in Few-Layer MoS2, WS2, and WSe2

“…Increase in the in-plane lattice constant by ∆a leads to reduction of direct and indirect transition energies at a different rate (Figure 2a and d) in agreement with the previous studies 16,18,19,24,30,31 . The changes are more pronounced for transitions involving the K point.…”

“…This behavior was predicted by calculations 7,[16][17][18][20][21][22] and confirmed in early photoemission experiments on WS 2 monolayer grown by van der Waals epitaxy 23 . Similarly, the conduction band valley at the Λ point (midpoint between K and Γ) shifts downward in the presence of interlayer interaction as indicated by calculations 7,16,17,[20][21][22] . In contrast, the states near the K point are comparatively less susceptible to the number of layers 4,7,9,10 .…”

“…The indirect-to-direct crossover in these MX 2 compounds (M=Mo,W and X=S,Se) results from local shift of valence band hills and conduction band valleys in the Brillouin zone 4,7,9,10,[16][17][18][19] . In single layers, the conduction band minimum (CBM) and valence band minimum (VBM) coinciding at the K point, making them direct gap semiconductors.…”

“…In few-layer MX 2 , the conduction band valleys of the K and Λ points compete in energy. For bilayer MoS 2 and WS 2 , some calculations 16,17,21,22,24 show that the CBM is located at the K point while others 7,16,17,20 show that it is at the Λ point. The discrepancy is partly due to the fact that some calculations neglect spin-orbit interactions.…”

Tuning the electronic structure of monolayer graphene/MoS2van der Waals heterostructures via interlayer twist

“…For a 0° twist angle, charge loss affects the Mo-S bond length; for a 30° twist angle, on the other hand, it is predicted that charge loss of the Mo-S bond is absent because graphene has a different registry with respect to the S atoms for this orientation [21]. Note that comprehensive DFT calculations have shown that band structure of monolayer MoS 2 is significantly affected by bond length variation [40]. Similarly, Wang et al attribute the twist-angle dependence of the MoS 2 band structure to strain, and they too mention the presence of charge redistribution at the interface [22].…”