  Screening due to surrounding dielectric medium reshapes the electron-hole
interaction potential and plays a pivotal role in deciding the binding energies
of strongly bound exciton complexes in quantum confined monolayers of
transition metal dichalcogenides (TMDs). However, owing to strong
quasi-particle bandgap renormalization in such systems, a direct quantification
of estimated shifts in binding energy in different dielectric media remains
elusive using optical studies. In this work, by changing the dielectric
environment, we show a conspicuous photoluminescence (PL) peak shift at low
temperature for higher energy excitons (2s, 3s, 4s, 5s) in monolayer MoSe$_2$,
while the 1s exciton peak position remains unaltered - a direct evidence of
varying compensation between screening induced exciton binding energy
modulation and quasi-particle bandgap renormalization. The estimated modulation
of binding energy for the 1s exciton is found to be 58.6% (70.5% for 2s, 78.9%
for 3s, 85% for 4s) by coating an Al$_2$O$_3$ layer on top, while the
corresponding reduction in quasi-particle bandgap is estimated to be 248 meV.
Such a direct evidence of large tunability of the binding energy of exciton
complexes as well as the bandgap in monolayer TMDs holds promise of novel
device applications.
