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.
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