  It has long been a challenging task to find compounds with similar crystal
and electronic structures as cuprate superconductors with low dimensionality
and strong antiferromagnetic fluctuations. The parent compounds of cuprate
superconductors are Mott insulators with strong in-plane antiferromagnetic
exchange interactions between Cu moments. Here we show, based on
first-principles density functional calculations, that AFeSe2 (A=Tl, K, Rb, or
Cs) exhibit many of the physical properties common to the cuprate parent
compounds: (1) the FeSe2 layer in AFeSe2 is similar in crystalline and
electronic structures to the CuO2 plane in cuprates, although Se atoms are not
coplanar to the square Fe-lattice; (2) they are antiferromagnetic insulators,
but with relatively small charge excitation gaps; (3) their ground states are
Neel antiferromagnetic ordered, similar as in cuprates; and (4) the
antiferromagnetic exchange interactions between Fe moments are larger than in
other iron-based superconducting materials, but comparable to those in
cuprates. Like cuprates, these compounds may become high-Tc superconductors
upon doping of charge carriers either by chemical substitution or intercalation
or by liquid or solid gating.
