  Based on the dynamical mean field theory (DMFT) and angle resolved
photoemission spectroscopy (ARPES), we have investigated the mechanism of high
$T_c$ superconductivity in stoichiometric LiFeAs. The calculated spectrum is in
excellent agreement with the observed ARPES measurement. The Fermi surface (FS)
nesting, which is predicted in the conventional density functional theory
method, is suppressed due to the orbital-dependent correlation effect with the
DMFT method. We have shown that such marginal breakdown of the FS nesting is an
essential condition to the spin-fluctuation mediated superconductivity, while
the good FS nesting in NaFeAs induces a spin density wave ground state. Our
results indicate that fully charge self-consistent description of the
correlation effect is crucial in the description of the FS nesting-driven
instabilities.
