Origin of the superconducting state in the collapsed tetragonal phase of KFe₂ As₂

Recently, KFe₂ As₂ 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 ∼ 12 K, while the tetragonal phase is a T_c ≤ 3.4 K superconductor. We show that the key difference between the previously known nonsuperconducting collapsed tetragonal phase in AFe₂ As₂ (A = Ba, Ca, Eu, Sr) and the superconducting collapsed tetragonal phase in KFe₂ As₂ 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 KFe₂ As₂ 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_± (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.