  Superconductors close to quantum phase transitions often exhibit a
simultaneous increase of electronic correlations and superconducting transition
temperatures. Typical examples are given by the recently discovered iron-based
superconductors. We investigated the band-specific quasiparticle masses of
AFe2As2 single crystals with A = K, Rb, and Cs and determined their pressure
dependence. The evolution of electronic correlations could be tracked as a
function of volume and hole doping. The results indicate that with increasing
alkali-metal ion radius a quantum critical point is approached. The critical
fluctuations responsible for the enhancement of the quasiparticle masses appear
to suppress the superconductivity.
