Quantum Skyrmions and the Destruction of Antiferromagnetic Order in High-Temperature Superconductors

A continuous field theory which describes the process of doping in high-T$_c$ superconductors of the YBCO-type is presented. It is shown that the introduction of dopants produces the creation of skyrmion topological excitations on the antiferromagnetic background. The energy of these excitations is evaluated. Destruction of the N\'eel ground state occurs for a critical value $\delta_C$ of the doping parameter for which the skyrmion energy vanishes. We evaluate this at zero temperature, obtaining $\delta_C = 0.39 \pm 0.03$ which agrees with the experimental value $\delta_C^{exp} = 0.41 \pm 0.02$.