  Recently, new FeAs based high-temperature superconductors CaAFe4As4 (A=K, Rb,
Cs) with a layered tetragonal crystal structure were synthesized (TC ~ 30 K).
In this Letter, we report for the first time the band structures, Fermi surface
topology, total and partial densities of electronic states and interatomic
interactions for CaAFe4As4 as estimated by means of the first-principles
FLAPW-GGA calculations. The interatomic bonding picture can be represented as a
highly anisotropic mixture of metallic, covalent, and ionic contributions,
which are realized inside Fe4As4 layered blocks and between these blocks and
Ca, A atomic sheets. The Fermi surfaces of these systems have a multisheet
character and are compiled of a large number of cylinders at the edges and in
the central part of the Brillouin zone. It is established that the
high-temperature superconductivity in CaAFe4As4 compounds as in other related
systems correlates well with such structure parameters as bond angles and anion
height.
