Electrical control of truly two-dimensional neutral and charged excitons in monolayer MoSe$_2$

Monolayer transition metal dichalcogenides (TMDs) have emerged as ideal 2D semiconductors with valley and spin polarized excitations expected to enable true valley-tronics. Here we investigate MoSe$_{2}$, a TMD which has yet to be characterized in the monolayer limit. Specifically, we examine excitons and trions (their singly charged counterparts) in the ultimate 2D limit. Utilizing high quality exfoliated MoSe$_{2}$ monolayers, we report the observation and electrostatic tunability of positively charged (X$+)$, neutral (Xo), and negatively charged (X-) excitons via photoluminescence in FETs. The trion charging energy is large (30 meV), enhanced by strong confinement and heavy effective masses, while the linewidth is narrow (5 meV) at temperatures below 55 K. This is greater spectral contrast than in any known quasi-2D system. Further, the charging energies for X$+$ and X- to are nearly identical implying the same effective mass for electrons and holes, which supports their recent description as massive Dirac fermions. This work demonstrates that monolayer MoSe$_{2}$ is an ultimate 2D semiconductor opening the door for the investigation of truly 2D exciton physics while laying the ground work necessary to begin valley-spin polarization studies.