Avoided Quantum Criticality near Optimally Doped High Temperature   Superconductors
  We study the crossover from the underdoped to the overdoped regime in the t-J model.The underdoped regime is dominated by the superexchange interaction, locking the spins into singlets which weakly perturbe coherent charge carriers. 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 superexchange and Kondo interaction balance each other, bringing the system close to a local quantum critical point near the point of maximal superconducting transition temperature. At this point, particle hole symmetry is dynamically restored and physical quantities such as the optical conductivity, exhibit power law behaviour at intermediate frequencies as observed experimentally. Quantum criticality is avoided by the onset of superconductivity. 
Kristjan Haule and Gabriel Kotliar