We have performed high-resolution angle-resolved photoemission spectroscopy on heavily overdoped KFe_2As_2 (transition temperature (Tc = 3 K). We observed several renormalized bands near the Fermi level with a renormalization factor of 2-4. While the Fermi surface (FS) around the Brillouin-zone center is qualitatively similar to that of optimally-doped Ba_{1-x}K_xFe_2As_2 (x = 0.4; Tc = 37 K), the FS topology around the zone corner (M point) is markedly different: the two electron FS pockets are completely absent due to excess of hole doping. This result indicates that the electronic states around the M point play an important role in the high-Tc superconductivity of Ba$_{1-x}$K$_x$Fe$_2$As$_2$ and suggests that the interband scattering via the antiferromagnetic wave vector essentially controls the Tc value in the overdoped region.
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