Experimental determination of the massive Dirac-fermion parameters in MoS$_{2}$, MoSe$_{2}$, WS$_{2}$, and WSe$_{2}$

The physics associated with group 6 transition metal dichalcogenides (TMDs) MX$_{2}$ (M $=$ Mo, W; X $=$ S, Se) is one of the most intriguing issues in condensed matter physics. These materials have several interesting aspects, especially the direct to indirect band gap transition and spin-orbit interaction (SOI) induced spin band splitting at the K point. Recently, one reported a minimal band model, called massive Dirac-fermion model, for K point of the monolayer MX$_{2}$ Brillouin zone. There are several parameters in this model obtained by calculations, not by experiment, until now. Here we report the parametric studies on MX$_{2}$ using angle resolved photoemission spectroscopy (ARPES). We factor out the massive Dirac-Fermion parameters from the bulk MX$_{2}$, not monolayer. For confirming the accurate experimental values, we performed the photon energy dependence experiment to find the exact $\Gamma $ point and in-situ potassium-dosing experiment were performed for each MX$_{2}$.