The chemical control of high-T_c superconductivity: Metal-superconductor-insulator transition in (Tl_1-yPb_y)Sr₂(Ca_1-xY_x)Cu₂O₇

We have carried out a detailed study of the relationship between the semiconducting, the superconducting, and the metallic region in the system (Tl_0.5Pb_0.5)Sr₂(Ca_1-xY_x)Cu₂O₇. The critical density (or concentration), n_c, derived from Hall measurement of the titled series compounds at which the transition from insulator to metal place can be given by the well-known Mott formula: n_c ^1/3a_H ^*=0.26 where a_H ^* is the effective Bohr orbit radius of the isolated donor or acceptor state wavefunction. We propose that the insulator-metal transition in the cuprates generally occurs at a very high hole density (n_c∼10²⁰-10²¹cm^-3) as compared to conventional doped semiconductors (n_c∼10¹⁷-10¹⁸cm^-3) but rather lower than the critical densities for elemental metals (n_c>10²¹cm^-3).