Multiband, Strong coupling and Strong Correlations in Ba$_{1-x}$K$_{x}$Fe$_{2}$As$_{2}$ single crystals. Mind the (nodal) gap!

We report an exhaustive thermodynamic study (heat capacity, magnetization, thermal expansion) of the normal- and superconducting-state properties of the entire Ba$_{1-x}$K$_{x}$Fe$_{2}$As$_{2}$ series. We show that strong correlations develop with increasing hole concentration indicating the possible proximity to an orbital-selective Mott transition predicted by theory. In the superconducting state, these single crystals exhibit strong multiband and paramagnetic effects and we give evidence of a strong-to-weak-coupling crossover that occur near the concentration where the electron sheets disappear. Our data show no evidence for a symmetry change, from {\it s} to {\it d}-wave, of the superconducting state. Dissimilarities with the Ba(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$ series are emphasized.