POSSIBLE PAIRING WITHOUT SUPERCONDUCTIVITY AT LOW CARRIER CONCENTRATIONS IN BULK AND THIN-FILM SUPERCONDUCTING SEMICONDUCTORS

Simultaneous equations for the BCS parameter Δ and for the Fermi energy in the BCS state are studied at low carrier concentrations in bulk and thin-film superconducting semiconductors at T=0 for large cutoff energies, and solutions are plotted in the form of universal curves. For electron-electron attraction greater than some critical value in bulk material or for any attractive interaction in very thin films, the pair-binding energy tends to a constant limit for low n, and pairing without superconductivity is expected in some temperature range. Solutions of simultaneous equations for Tc as obtained by formal application of the BCS theory, and for the Fermi energy at Tc, are also obtained in bulk material; but it is shown that at low carrier concentrations the temperature Tp at which pairing takes place is given by Tp=2Tc, while it is thought that superconductivity will not set in until a lower temperature, of the order of the Bose-Einstein condensation temperature of the pairs, is reached. By combining the above theory with a previously published model for superconductivity in Zr-doped SrTiO3, predictions for this material in the region of low carrier concentrations are made. © 1969 The American Physical Society.