A theory for doping in high-temperature superconductors

We present a continuum model for the doping of high-temperature superconductors. It is shown that, because of a constraint which follows from the equations of motion, skyrmion topological defects are introduced on the antiferromagnetic background coinciding with the dopant positions. The energy of the quantum skyrmions is evaluated as a function of the doping at zero temperature. The destruction of the antiferromagnetically ordered Neel ground state occurs for a critical value be of the doping parameter for which the skyrmion energy vanishes. The model predicts a value of the critical doping given by delta (C) = 0.39 +/- 0.03 for YBCO, which agrees with the experimental value delta (exp)(C) = 0.41 +/- 0.02.