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A Model with a Singular Electronic Density of States and Some Properties of High‐Temperature Superconductors

The influence of singularities in the electronic density of states (DOS) on high-temperature superconductors is studied in the framework of the conventional BCS theory. By using a DOS with singularities at two different points we are able to explain the asymmetry in the isotope exponent a with respect to the point where T c is maximum. A DOS with a power law singularity reproduces the vanishingly small values of a and large values of R 2 = ΔC(T c )/C n (T c ), the ratio of the jump in the electronic specific heat to the normal specific heat at T = T c , observed in certain high-T c materials. However, the value of the ratio R 1 = 2Δ 0 /k B T c does not deviate much from its canonical BCS value of 3.53, in agreement with earlier results.