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The interplay of high and low-energy mass renormalizations with band-shiftsreflected by the positions of van Hove singularities (VHS) in the normal statespectra of the highest hole-overdoped and strongly correlated AFe$_2$As$_2$(A122) with A = K, Cs is discussed phenomenologically based on ARPES data andGGA band-structure calculations with full spin-orbit coupling. The big increaseof the Sommerfeld coefficient $\gamma$ from K122 to Cs122 is ascribed to anenhanced coupling to low-energy bosons in the vicinity of a quantum criticalpoint to an unknown, yet incommensurate phase different from the commensurateMott one. We find no sizeable increase in correlations for Cs122 in contrast toF. Eilers et al., PRL v. 116, 237003 (2016) [3]. The empirical (ARPES) VHSpositions as compared with GGA-predictions point even to slightly weakercorrelations in Cs122 in accord with low-$T$ magnetic susceptibility $\chi(T)$data and a decreasing Wilson ratio $\propto \chi(0)/\gamma$.

Mass enhancements and band shifts in strongly hole overdoped Fe-based pnictide superconductors: KFe$_2$As$_2$ and CsFe$_2$As$_2$