Transition metal dichalcogenides have attracted much attention recently due to their potential applications in spintronics and photonics as a result of the indirect to direct band gap transition and the emergence of the spin-valley coupling phenomenon upon moving from the bulk to monolayer limit. Here, we report high-resolution angle-resolved photoemission spectroscopy on MoSe2 (molybdenum diselenide) single crystals and monolayer films of MoS2 grown on Highly Ordered Pyrolytic Graphite

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... e. Our experimental results, for the first time, resolve the two distinct bands at the Brillouin zone corner of the bulk MoSe2, and provide evidence for the critically important spin-orbit split bands of the monolayer MoS2. Moreover, by depositing potassium on cleaved surfaces of these materials, the process through which quantum well states form on the surfaces of transition metal dichalcogenides is systematically imaged. We present a theoretical model to account for the observed spin-orbit splitting and the rich spectrum of the quantum well states observed in our experiments. Our findings taken together provide important insights into future applications of transition metal dichalcogenides in nanoelectronics, spintronics, and photonics devices as they critically depend on the spin-orbit physics of these materials.