Probing critical point energies of transition metal dichalcogenides: surprising indirect gap of single layer $SL-WS{e}_2$

Abstract

Understanding quasiparticle band structures of transition metal dichalcogenides (TMDs) is critical for technological advances of these materials for atomic layer electronics and photonics. Although theoretical calculations to date have shown qualitatively similar features, there exist subtle differences which can lead to important consequences in the device characteristics. For example, most calculations have shown that all single layer (SL) TMDs have direct band gaps, while some have shown that $SL-WS{e}_2$ have an indirect gap. Moreover, there are large variations in the reported quasiparticle gaps, corresponding to large variations in exciton binding energies. By using a comprehensive form of scanning tunneling spectroscopy, we have revealed detailed quasiparticle electronic structures in TMDs, including the quasi-particle gaps, critical point energy locations and their origins in the Brillouin Zones (BZs). We show that $SL-WS{e}_2$ actually has an indirect quasi-particle gap with the conduction band minimum located at the Q point (instead of K), albeit the two states are nearly degenerate. Its implications on optical properties are discussed. We have further observed rich quasi-particle electronic structures of TMDs as a function of atomic structures and spin-orbital couplings.

27 pages, 4 figures and one table, supplementary information appended

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