Abstract
A continuum model for the process of doping in high-temperature superconductors is presented. It is shown that the introduction of dopants produces the creation of skyrmion topological excitations on the antiferromagnetic background as has been proposed before. In the present model, this happens because the equations of motion produce a constraint identifying the dopant and skyrmion positions. The quantum skyrmion energy as a function of doping is obtained from the large distance behavior of the quantum skyrmion correlation function which is evaluated at zero temperature. The destruction of the antiferromagnetically ordered Néel ground state occurs for a critical value δ C of the doping parameter for which the skyrmion energy vanishes. The model predicts a value of the critical doping given by δ C=0.39±0.03 for YBCO, which agrees with the experimental value δ C exp=0.41±0.02.
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