  The multiband nature of iron-pnictide superconductors is one of the keys to
the understanding of their intriguing behavior. The electronic and magnetic
properties heavily rely on the multiband interactions between different
electron and hole pockets near the Fermi level. At the fundamental level,
though many theoretical models were constructed on the basis of the so-called
1-Fe Brillouin zone (BZ) with an emphasis of the basic square lattice of iron
atoms, most electronic structure measurements were interpreted in the 2-Fe BZ.
Whether the 1-Fe BZ is valid in a real system is still an open question. Using
angle-resolved photoemission spectroscopy (ARPES), here we show in an extremely
hole-doped iron-pnictide superconductor CsFe$_2$As$_2$ that the distribution of
electronic spectral weight follows the 1-Fe BZ, and that the emerging band
structure bears some features qualitatively different from theoretical band
structures of the 1-Fe BZ. Our analysis suggests that the interlayer separation
is an important tuning factor for the physics of FeAs layers, the increase of
which can reduce the coupling between Fe and As and lead to the emergence of
the electronic structure in accord with the 1-Fe symmetry of the Fe square
lattice. Our finding puts strong constraints on the theoretical models
constructed on the basis of the 1-Fe BZ.
