On self-protecting singlets in cuprate superconductors

The basal area (Cu-Cu grid) of the cuprate superconductors not only tends to shrink on hole doping, as expected from single-electron quantum chemistry, but exhibits also an electronically incompressible "hump" around optimum doping n(opt)similar or equal to0.16. The hump collapses near critical doping n(crit)similar or equal to0.19.We analyze the origin of the hump in terms of a classical liquid of interacting incompressible particles in a container with antiferromagnetic walls. Oxygen holes interacting with the wall form singlets, protect themselves against other holes by an incompressible "spin fence," and thus interact also with the lattice. Occupation of the CuO2 lattice with holes must therefore follow a non-double-occupant constraint also for the oxygen cage enclosing the copper hole. Closest packing of self-protecting singlets is found to occur around critical doping; closest packing of paired self-protecting singlets around optimum doping. These singlet states are bosonic, but are not magnetic polarons.