EFFECTS OF SADDLE-POINT SINGULARITIES ON THE ELECTRON LIFETIME

We calculate the imaginary part of the response function (Imchi) and the imaginary part of the electron self-energy (ImSIGMA) for a two-dimensional energy band with a saddle point close to the Fermi energy E(F), using lowest-order perturbation theory in the screened Coulomb interaction. We find that Imchi(q,omega) remains finite for arbitrarily small frequencies omega for certain directions of q if the saddle point is at E(F), leading to a rich behavior of IMSIGMA. For an electron far from the saddle point, ImSIGMA(k, E(k)) approximately [E(k) - E(F)]1.5, except in specific directions of k where the power is only 4/3. For an electron close to a saddle point, a linear dependence on the energy is obtained. These results are compared with numerical calculations for the Emery model of the CuO2 planes in high-T(c) superconductors.