Effect of alloying on the Fermi surface

Abstract

We obtain a theoretical expression for the change in Fermi-surface areas when dilute impurities are introduced in a nearly-free-electron-like host metal or in a $d$-band host metal having no resonances in the immediate vicinity of the Fermi energy. Following Stern, we obtain the Fermi surface from the real part of the self-energy. The self-energy is derived within a pseudopotential $T$-matrix formalism which is developed as an extension of usual scattering theory. We approximate the crystal lattice Green's function by a free-electron propagator in the $T$-matrix equation. The final expression for Fermi-surface changes involves impurity scattering phase shifts and pseudo-wave-function angular momentum expansion coefficients. These are the same parameters which enter the expression for the electron lifetime. The theoretical results are in agreement with recent de Haas-van Alphen measurements in dilute lead and magnesium based alloys.