  Heavy long-lived multi-charged leptons (MCLs) are predicted by various new
physics models. These hypothetical MCLs can form bound states, due to their
high electric charges and long life times. In this work, we propose a novel
strategy of searching for MCLs through their bound state productions and
decays. By utilizing LHC-8 TeV data in searching for resonances in the diphoton
channel, we exclude the masses of isospin singlet heavy leptons with electric
charge $|q|\geq 6$ (in units of electron charge) lower than $\sim$1.2 TeV,
which are much stronger than the corresponding 8 TeV LHC bounds from analysing
the high ionisation and the long time-of-flight of MCLs. By utilising the
current 13 TeV LHC diphoton channel measurements the bound can further exclude
MCL masses up to $\sim$1.6 TeV for $|q|\geq 6$. Also, we demonstrate that the
conventional LHC limits from searching for MCLs produced via Drell-Yan
processes can be enhanced by including the contribution of photon fusion
processes.
