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Understanding quasiparticle band structures of transition metaldichalcogenides (TMDs) is critical for technological advances of thesematerials for atomic layer electronics and photonics. Although theoreticalcalculations to date have shown qualitatively similar features, there existsubtle differences which can lead to important consequences in the devicecharacteristics. For example, most calculations have shown that all singlelayer (SL) TMDs have direct band gaps, while some have shown that $SL-WSe_2$have an indirect gap. Moreover, there are large variations in the reportedquasiparticle gaps, corresponding to large variations in exciton bindingenergies. By using a comprehensive form of scanning tunneling spectroscopy, wehave revealed detailed quasiparticle electronic structures in TMDs, includingthe quasi-particle gaps, critical point energy locations and their origins inthe Brillouin Zones (BZs). We show that $SL-WSe_2$ actually has an indirectquasi-particle gap with the conduction band minimum located at the Q point(instead of K), albeit the two states are nearly degenerate. Its implicationson optical properties are discussed. We have further observed richquasi-particle electronic structures of TMDs as a function of atomic structuresand spin-orbital couplings.

Probing critical point energies of transition metal dichalcogenides: surprising indirect gap of single layer $SL-WSe_2$