Oriented gap opening in the magnetically ordered state of Iron-pnicitides: an impact of intrinsic unit cell doubling on the $Fe$ square lattice by $As$ atoms

We show that the complicated band reconstruction near Fermi surfaces in the magnetically ordered state of iron-pnictides observed by angle-resolved photoemission spectroscopies (ARPES) can be understood in a meanfield level if the \emph{intrinsic unit cell doubling} due to As atoms is properly considered as shown in the recently constructed S${}_4$ microscopic effective model. The (0,$\pi$) or ($\pi$,0) col-linear antiferromagnetic (C-AFM) order does not open gaps between two points at Fermi surfaces linked by the ordered wave vector but forces a band reconstruction involving four points in unfolded Brillouin zone (BZ) and gives rise to small pockets or hot spots. The S${}_4$ symmetry naturally chooses a staggered orbital order over a ferro-orbital order to coexist with the C-AFM order. These results strongly suggest that the kinematics based on the S${}_4$ symmetry captures the essential low energy physics of iron-based superconductors.