Origin of the superconducting state in the collapsed tetragonal phase of KFe2As2

Recently, KFe$_2$As$_2$ was shown to exhibit a structural phase transition from a tetragonal to a collapsed tetragonal phase under applied pressure of about $15~\mathrm{GPa}$. Surprisingly, the collapsed tetragonal phase hosts a superconducting state with $T_c \sim 12~\mathrm{K}$, while the tetragonal phase is a $T_c \leq 3.4~\mathrm{K}$ superconductor. We show that the key difference between the previously known non-superconducting collapsed tetragonal phase in AFe$_2$As$_2$ (A= Ba, Ca, Eu, Sr) and the superconducting collapsed tetragonal phase in KFe$_2$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 KFe$_2$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 DFT+DMFT 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.