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We investigate the physical effects of translational symmetry breaking inFe-based high-temperature superconductors due to alternating anion positions.In the representative parent compounds, including the newly discoveredFe-vacancy-ordered $\mathrm{K_{0.8}Fe_{1.6}Se_2}$, an unusual change of orbitalcharacter is found across the one-Fe Brillouin zone upon unfolding thefirst-principles band structure and Fermi surfaces, suggesting that covering alarger one-Fe Brillouin zone is necessary in experiments. Most significantly,the electron pockets (critical to the magnetism and superconductivity) arefound only created with the broken symmetry, advocating strongly its fullinclusion in future studies, particularly on the debated nodal structures ofthe superconducting order parameter.

One-Fe versus Two-Fe Brillouin Zone of Fe-Based Superconductors: Creation of the Electron Pockets via Translational Symmetry Breaking