Ternary iron selenide K$_{0.8}$Fe$_{1.6}$Se$_2$ is an antiferromagnetic semiconductor

We have studied electronic and magnetic structures of K$_{0.8+x}$Fe$_{1.6}$Se$_2$ by performing the first-principles electronic structure calculations. The ground state of the Fe-vacancies ordered K$_{0.8}$Fe$_{1.6}$Se$_2$ is found to be a quasi-two-dimensional blocked checkerboard antiferromagnetic (AFM) semiconductor with an energy gap of 594 meV and a large ordering magnetic moment of 3.37 $\mu_B$ for each Fe atom, in excellent agreement with the neutron scattering measurement. The underlying mechanism is the chemical-bonding-driven tetramer lattice distortion. K$_{0.8+x}$Fe$_{1.6}$Se$_2$ with finite $x$ is a doped AFM semiconductor with low conducting carrier concentration which is approximately proportional to the excess potassium content, consistent qualitatively with the infrared observation. Our study reveals the importance of the interplay between antiferromagnetism and superconductivity in these materials. This suggests that K$_{0.8}$Fe$_{1.6}$Se$_2$, instead of KFe$_2$Se$_2$, should be regarded as a parent compound from which the superconductivity emerges upon electron or hole doping.