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Correlation between T_c and the Cu 4s level reveals the mechanism of high-temperature superconductivity

Band structure trends in hole-doped cuprates and correlations with T_c are interpreted within the s--d exchange mechanism of high-T_c superconductivity. The dependence of T_c on the position of the copper 4s level finds a natural explanation in the generic Cu 3d, Cu 4s, O 2p_x and O 2p_y four-band model. The Cu 3d--Cu 4s intra-atomic exchange interaction is incorporated in the standard BCS scheme. This dependence of T_c in the whole interval of 25--125 K has no alternative explanation at present, and possibly this quarter of a century standing puzzle is already solved.