Excitonic condensation of strongly correlated electrons: the case of Pr$_{0.5}$Ca$_{0.5}$CoO$_3$

We use a combination of dynamical mean-field model calculations and LDA+U material specific calculations to investigate the low temperature phase transition in the compounds from the (Pr$_{1-y}$R$_y$)$_x$Ca$_{1-x}$CoO$_3$ (R=Nd, Sm, Eu, Gd, Tb, Y) family (PCCO). The transition, marked by a sharp peak in the specific heat, leads to an exponential increase of dc resistivity and a drop of the magnetic susceptibility, but no order parameter has been identified yet. We show that condensation of spin-triplet, atomic-size excitons provides a consistent explanation of the observed physics. In particular, it explains the exchange splitting on the Pr sites and the simultaneous Pr valence transition. The excitonic condensation in PCCO is an example of a general behavior expected in certain systems in the proximity of a spin-state transition.