Avoided criticality in near-optimally doped high-temperature superconductors

We study the crossover from the underdoped to the overdoped regime of the t-J model within a plaquette dynamical mean field approach. We find that the shortest electron lifetime occurs near optimal doping where the superconducting critical temperature is maximal. The mean field theory provides a simple physical picture of this effect. In the underdoped regime, the charge carriers propagate coherently among spin singlets, formed by the superexchange interaction. In the overdoped, large carrier concentration regime, the Kondo effect dominates resulting in spin-charge composite quasiparticles which are also coherent. Separating these two Fermi liquid regimes, there is a critical doping where the superexchange and the Kondo interaction balance each other. At this point, the normal phase is highly incoherent and the optical conductivity exhibits power law behavior at intermediate frequencies. The onset of superconductivity restores coherence, causing the appearance of a resonance in the spin channel.