Compressed tetragonal phase in $X{\mathrm{Fe}}_2{\mathrm{As}}_2$ ($X=\mathrm{Na}$, K, Rb, Cs) and in the alloy ${\mathrm{Na}}_{0.5}{\mathrm{K}}_{0.5}{\mathrm{Fe}}_2{\mathrm{As}}_2$

Motivated by the recent discovery of a high-temperature superconducting phase in ${\mathrm{KFe}}_2{\mathrm{As}}_2$ at 16 GPa accompanied by an isostructural phase transition from the tetragonal to the compressed tetragonal phase, we extend the study of pressure effects to the whole $X{\mathrm{Fe}}_2{\mathrm{As}}_2$ family ($X=\mathrm{Na}$, K, Rb, Cs). We demonstrate that the ionic radius of the $X$ atom determines the transition to the compressed phase which induces relevant changes in electronic properties and the Fermi surface which can enhance the superconducting pairing. Based on these results and in analogy with ${\mathrm{KFe}}_2{\mathrm{As}}_2$, we theoretically propose ${\mathrm{Na}}_{0.5}{\mathrm{K}}_{0.5}{\mathrm{Fe}}_2{\mathrm{As}}_2$ as a possible new superconductor material in its compressed tetragonal phase which we predict to happen above 6 GPa.

Figure 1

Lattice parameters as a function of the pressure for ${\mathrm{KFe}}_2{\mathrm{As}}_2$. On the left (right) axis we report the $a\left(c\right)$ lattice constant. Both theoretical (this work, solid symbols) and experimental values [22] (open symbols) are shown.

Figure 2

Band structures for ${\mathrm{KFe}}_2{\mathrm{As}}_2$ at the equilibrium volume [panel (a)] and in the CT phase at 22.6 GPa [panel (b)]. The size of the circles is proportional to the As $p_z$ character of the eigenvalues. Fermi energy was set to zero.

Figure 3

Fermi surface for ${\mathrm{KFe}}_2{\mathrm{As}}_2$ in the CT phase.

Figure 4

Out-of-plane $c$ lattice parameter as a function of applied pressure for Na-, K-, Rb-, and Cs-${\mathrm{Fe}}_2{\mathrm{As}}_2$.

Figure 5

Band structures for $X$-122 at the tetragonal conditions and in the CT phase. The As $p_z$ character of the bands is proportional to the radius of the black circles. In panel $h$, Cs $p_z$ character in ${\mathrm{CsFe}}_2{\mathrm{As}}_2$ is indicated with grey (yellow on-line) circles. The Fermi energy was set to zero.

Figure 6

Fermi surfaces for $X{\mathrm{Fe}}_2{\mathrm{As}}_2$ in the CT phase.

Figure 7

Out-of-plane lattice parameter as a function of applied pressure for ${\mathrm{Na}}_{0.5}{\mathrm{K}}_{0.5}{\mathrm{Fe}}_2{\mathrm{As}}_2$.

Figure 8

Band structure for ${\mathrm{Na}}_{0.5}{\mathrm{K}}_{0.5}{\mathrm{Fe}}_2{\mathrm{As}}_2$ at equilibrium (upper panel) and in the CT phase at $P\sim 9$ GPa (lower panel). The gray scale indicates the unfolding weight of the Kohn-Sham eigenvalues [46]. The Fermi energy was set to zero.