The remarkable properties of atomically-thin semiconducting TMD layers include an indirect-to-direct bandgap crossover 1, 2, 9 , field-induced transport with high on-off ratios 16 , 3 valley selective circular dichroism [3][4][5][6] , and strong photovoltaic response 17,18 . Fundamental understanding of the electron/hole quasiparticle band structure and many-body interactions in 2D TMDs, however, is still lacking. Enhanced Coulomb interactions due to low-dimensional effects are expected to increase the quasiparticle bandgap as well as to cause electron-hole pairs to form more strongly bound excitons [10][11][12][13] . Untangling such many-body effects in single-layer TMDs requires measurement of both the electronic bandgap and the optical bandgap, the most fundamental parameters for transport and optoelectronics, respectively. The electronic bandgap (E g ) characterizes single-particle (or quasiparticle) excitations and is defined by the sum of the energies needed to separately tunnel an electron and a hole into monolayer MoSe 2 . The optical bandgap (E opt ), on the other hand, describes the energy required to create an exciton, a correlated two-particle electron-hole pair, via optical absorption. The difference in these energies (E g -E opt ) directly yields the exciton binding energy (E b ) (Fig. 2a). Here we provide evidence for Coulomb driven quasiparticle bandgap renormalization and unusually strong exciton stability in 2D TMD through direct determination of both E g and E opt via STS and PL spectroscopy, respectively. STS and PL measurements were carried out on the same high-quality sub-monolayer MoSe 2 films grown on epitaxial bilayer graphene (BLG) on a 6H-SiC(0001) substrate.Because the MoSe 2 surface coverage for our sample was ~ 0.8 ML, we were able to simultaneously image the MoSe 2 monolayer and the underlying graphene substrate using scanning tunneling microscopy (STM). We experimentally investigated both the electronic structure and the optical transitions in monolayer MoSe 2 /BLG by combining STS and PL spectroscopy. Fig. 2b shows a typical STM dI/dV spectrum acquired on monolayer MoSe 2 /BLG. The observed electronic structure is dominated by a large electronic bandgap surrounded by features labeled V 1-4 in the valence band (VB) and C 1 in the conduction band (CB). The MoSe 2 band edges are best determined by taking the logarithm of dI/dV, as shown in Fig. 2d.There the VB maximum (VBM) for monolayer MoSe 2 is seen to be located at -1.55 ± 0.03 V and the CB minimum (CBM) at 0.63 ± 0.02 V. The relative position of E F (V bias = 0 V) with respect to the band edges reveals n-type doping for our samples, although with 5 a very low carrier concentration. We tentatively attribute the n-doping of our MoSe 2 samples to intrinsic point defects such as vacancies and/or lattice antisites, which have been found to be responsible for n-doping in similar materials 20 . Our STS measurements yield a value for the single-particle electronic bandgap of E g = E CBM -E VBM = 2.18 eV ± 0.04 eV. The uncertainty ...