Origin of the superconducting state in the collapsed tetragonal phase of ${\mathrm{KFe}}_2{\mathrm{As}}_2$

Recently, ${\mathrm{KFe}}_2{\mathrm{As}}_2$ was shown to exhibit a structural phase transition from a tetragonal to a collapsed tetragonal phase under an applied pressure of about 15 GPa. Surprisingly, the collapsed tetragonal phase hosts a superconducting state with $T_c\sim 12\mathrm{K}$, while the tetragonal phase is a $T_c\le 3.4\mathrm{K}$ superconductor. We show that the key difference between the previously known nonsuperconducting collapsed tetragonal phase in $A{\mathrm{Fe}}_2{\mathrm{As}}_2(A=\text{Ba},\mathrm{Ca},\mathrm{Eu},\mathrm{Sr})$ and the superconducting collapsed tetragonal phase in ${\mathrm{KFe}}_2{\mathrm{As}}_2$ is the qualitatively distinct electronic structure. While the collapsed phase in the former compounds features only electron pockets at the Brillouin zone boundary and no hole pockets are present in the Brillouin zone center, the collapsed phase in ${\mathrm{KFe}}_2{\mathrm{As}}_2$ has almost nested electron and hole pockets. Within a random phase approximation spin fluctuation approach we calculate the superconducting order parameter in the collapsed tetragonal phase. We propose that a Lifshitz transition associated with the structural collapse changes the pairing symmetry from $d$ wave (tetragonal) to $s_{\pm }$ (collapsed tetragonal). Our density functional theory combined with dynamical mean-field theory calculations show that effects of correlations on the electronic structure of the collapsed tetragonal phase are minimal. Finally, we argue that our results are compatible with a change of sign of the Hall coefficient with pressure, as observed experimentally.

Figure 1

Crystal structure, schematic Fermi surface (dashed lines), and schematic superconducting gap function (background color) of ${\mathrm{KFe}}_2{\mathrm{As}}_2$ in the one-Fe Brillouin zone before and after the volume collapse. The Lifshitz transition associated with the formation of As $4p_z$-As $4p_z$ bonds in the CT phase changes the superconducting pairing symmetry from $d_{xy}$ to $s_{\pm }$.

Figure 2

Electronic band structure of the collapsed tetragonal phase in (a) ${\mathrm{CaFe}}_2{\mathrm{As}}_2$ and (b) ${\mathrm{KFe}}_2{\mathrm{As}}_2$. The path is chosen in the one-Fe equivalent Brillouin zone. The colors indicate the weights of Fe $3d$ states.

Figure 3

Fermi surface of the collapsed tetragonal phase in (a) ${\mathrm{CaFe}}_2{\mathrm{As}}_2$ and (b) ${\mathrm{KFe}}_2{\mathrm{As}}_2$ at $k_z=0$. The full plot spans the one-Fe equivalent Brillouin zone, while the area enclosed by the gray lines is the two-Fe equivalent Brillouin zone. The colors indicate the weights of Fe $3d$ states.

Figure 4

Summed static susceptibility (top) and its diagonal components ${\chi }_{aa}^{aa}$ (bottom) in the eight-band tight-binding model for (a), (c) ${\mathrm{CaFe}}_2{\mathrm{As}}_2$ and (b), (d) ${\mathrm{KFe}}_2{\mathrm{As}}_2$ in the one-Fe Brillouin zone. The colors identify the Fe $3d$ states.

Figure 5

Leading superconducting gap function ($s_{\pm }$) of the eight-band model in the one-Fe Brillouin zone of ${\mathrm{KFe}}_2{\mathrm{As}}_2$ in the CT phase at (a) $k_z=0$ and (b) $k_z=\pi$.