© David Pines.

The red and blue shaded regions are those in which one finds, respectively, local moment antiferromagnetic order, and quasiparticle superconducting d-wave order. T_{max} is the temperature at which the temperature-dependent uniform spin susceptibility reaches its maximum value, T* is the temperature at which the pseudogap phase emerges, T_{N} is the Neel transition temperature for local moment AF ordering, T_{C} is the quasiparticle superconducting transition temperature, T_{L} is the temperature below which the quasiparticle Fermi liquid (FL) displays Landau FL behavior (which will appear in the superconducting region if magnetic fields strong enough to destroy superconductivity are applied) while above T_{L} (and T*) one finds the anomalous Fermi liquid (AFL) transport behavior expected for quasiparticles being scattered against quantum critical fluctuations emanating from the quantum critical point, shown here at a doping level ~0.22, although its precise location may be at a somewhat lower doping level. To the left of the QCP, local moments and quasiparticles can co-exist over the entire region of doping (x < 0.22), while to its right, no local moments are present below a temperature that has not yet been determined. Above T_{max} the local moments form a spin liquid that exhibits the mean field scaling behavior expected for a two-dimensional Heisenberg antiferromagnet at high temperatures, while below it they display the behavior expected for a two-dimensional Heisenberg antiferromagnet in the quantum critical regime, hence the notation, quantum critical spin liquid (QCSL). Below T* (and above T_{C}) both the local moments and the quasiparticles change their behavior as the pseudogap state of matter emerges, with antinodal quasiparticles forming an insulating state with an energy gap that displays d-wave behavior, while nodal quasiparticles may display Landau Fermi liquid behavior before making the transition into the superconducting state at T_{C}. (Unit: 8)