  Monolayer FeSe films grown on SrTiO3 (STO) substrate show superconducting
gap-opening temperatures (Tc) which are almost an order of magnitude higher
than those of the bulk FeSe and are highest among all known Fe-based
superconductors. Angle-resolved photoemission spectroscopy (ARPES) observed
"replica bands" suggesting the importance of the interaction between FeSe
electrons and STO phonons. These facts rejuvenated the quest for Tc enhancement
mechanisms in iron-based, especially iron-chalcogenide, superconductors. Here,
we perform the first numerically-exact sign-problem-free quantum Monte Carlo
simulations to iron-based superconductors. We (i) study the electronic pairing
mechanism intrinsic to heavily electron doped FeSe films, and (ii) examine the
effects of electron-phonon interaction between FeSe and STO as well as nematic
fluctuations on Tc. Armed with these results, we return to the question "what
makes the Tc of monolayer FeSe on SrTiO3 so high?" in the conclusion and
discussions.
