GREENS-FUNCTION AND A GENERALIZED LLOYD FORMULA FOR THE DENSITY OF STATES IN DISORDERED MUFFIN-TIN ALLOYS

We consider the Korringa-Kohn-Rostoker coherent-potential-approximation Greens function for a disordered system of muffin-tin potentials and evaluate its integral over the Wigner-Seitz cell rigorously throughout the complex energy plane. The resulting expression is shown to possess a perfect derivative form, provided the angular-momentum summations are extended to infinity; for a finite angular-momentum cutoff this result is valid to a good approximation. For real energies our expression constitutes a generalization of the Lloyd formula for the density of states. The conventional Lloyd formula contains unphysical singularities that are not only unsatisfactory from a formal viewpoint, but also make its use increasingly cumbersome in multicomponent alloys as the number of atoms in the unit cell becomes larger. Our expression, on the other hand, is free from such singularities, and thus provides a useful basis for evaluating density of states and its energy integral in muffin-tin systems. © 1990 The American Physical Society.