  We demonstrate the reduction of the inhomogeneous linewidth of the free
excitons in atomically thin transition metal dichalcogenides (TMDCs)
MoSe$_{2}$, WSe$_{2}$ and MoS$_{2}$ by encapsulation within few nanometer thick
hBN. Encapsulation is shown to result in a significant reduction of the 10K
excitonic linewidths down to $\sim3.5 \text{ meV}$ for n-MoSe$_{2}$, $\sim5.0
\text{ meV}$ for p-WSe$_{2}$ and $\sim4.8 \text{ meV}$ for n-MoS$_{2}$.
Evidence is obtained that the hBN environment effectively lowers the Fermi
level since the relative spectral weight shifts towards the neutral exciton
emission in n-doped TMDCs and towards charged exciton emission in p-doped
TMDCs. Moreover, we find that fully encapsulated MoS$_{2}$ shows resolvable
exciton and trion emission even after high power density excitation in contrast
to non-encapsulated materials. Our findings suggest that encapsulation of
mechanically exfoliated few-monolayer TMDCs within nanometer thick hBN
dramatically enhances optical quality, producing ultra-narrow linewidths that
approach the homogeneous limit.
