FROM NEXT NEAREST NEIGHBOR SITE PERCOLATION TO CONTINUUM PERCOLATION: APPLICATION TO HIGH-TcSUPERCONDUCTORS

In high-Tcsuperconductors dopant atoms supply holes or excess electrons, and electric conduction is established in the neighborhood of the dopant. We propose that percolation of these conducting areas leads to global electric conduction. To investigate these processes numerical procedures to simulate continuum percolation are developed. The relation between the concentration of connecting discs and the fraction of the area of the plane covered by all discs is computed in the whole range between next nearest neighbor site percolation and continuum percolation. This method is applied to investigate underdoped copper oxides where small hole or excess electron concentrations are insufficient to establish electric conduction. The results of this study are applied to the model of mobile charge carriers which consist of or are accompanied by diffusingd-electrons. Our investigations show that with increasing doping the Neel temperature of the antiferromagnetism vanishes and spin glass states appear in accordance with experiments. Furthermore, the peaks in the specific heat become very broad. This broadening due to randomness and loss of translation invariance has been observed in nuclear magnetic resonance peaks of doped superconducting cuprates.