Electronic structure of vacancy-ordered iron-selenide K$_0.5$Fe$_1.75$Se$_2$

The electronic structure of the vacancy-ordered K$_0.5$Fe$_1.75$Se$_2$ iron-selenide compound (278 phase) is studied using the first-principles density functional method. The bare electron susceptibility of the 278 phase is featureless, suggesting a paramagnetic ground state for the phase. Near Fermi level, the density of states are dominated by the Fe-3d orbitals, and both electron-like and hole-like Fermi surfaces appear in the Brillouin zone. Unfolded band structure shows limited similarities to a hole doped 122 phase. With 0.1e electron doping, the two-dimensionality of the electron-like Fermi surfaces are greatly enhanced, resulting in a better nesting behavior. Our study should be relevant to the recently reported superconducting phase K$_0.5+x$Fe$_1.75+y$Se$_2$ with both x and y very tiny.