Pseudogap and strong pairing induced by incipient and shallow bands in quasi-two-dimensional KCa2Fe4As4F2

The optical properties of KCa2Fe4As4F2 (K12442, T-c = 33.5 K) and KCa2(Fe0.95Ni0.05)(4)As4F2 (Ni-K12442, T-c = 29 K) have been examined at a large number of temperatures. For both samples, a nodeless supercon-ducting gap is clearly observed in the optical conductivity at 5 K. The superconducting gap Delta similar or equal to 8.7 meV (2 Delta/k(B)T(c) similar or equal to 6.03) in K12442, pointing towards strong-coupling Cooper pairs, but in sharp contrast, Delta similar or equal to 4.6 meV (2 Delta/k(B)T(c) similar or equal to 3.68) in Ni-K12442, which agrees with the BCS weak-coupling pairing state. More intriguingly, below T* similar or equal to 75 K, the optical conductivity of K12442 reveals a pseudogap that smoothly evolves into the superconducting gap below T-c, while no such behavior is detected in the electron-doped Ni-K12442. The comparison between the two samples suggests that the pseudogap and strong-coupling Cooper pairs in K12442 may be intimately related to the shallow and incipient bands. We provide arguments supporting a preformed pairing mechanism of the pseudogap, but at the moment a magnetic scenario cannot yet be excluded.