Fermi surfaces and electronic topological transitions in metallic random alloys. I. The influence on equilibrium properties.

Abstract

In this paper we address the question of how the so-called electronic topological transitions (ETT's) can affect the physical properties of metallic random alloys, extending the existing theory in order to include substitutional disorder. The ETT's, or, as sometimes called, the Lifshitz 21/2 transitions, occur when the chemical potential passes through a Van Hove singularity on changing the thermodynamic state of a metal. That can be easily achieved by alloying. As a consequence, the Fermi-surface topology changes and a number of transport as well as equilibrium properties show anomalies, when studied versus the concentration. We show that these anomalies might be only slightly affected by disorder scattering and/or finite temperatures. Our theoretical results, which hold in a neighborhood of the ETT, predict anomalies in correspondence to such variations of Fermi-surface connectivity for the equilibrium volumes and total energies. In particular, our theory predicts deviations of the alloy lattice parameter from Vegard's rule. These are confirmed by our ab initio Korringa-Kohn-Rostoker--coherent-potential-approximation calculations for the ${\mathrm{Ag}}_{\mathit{c}}$${\mathrm{Pd}}_{1\mathrm{\ensuremath{-}}\mathit{c}}$ system. For this system the largest deviation from Vegard's rule occurs as the d-conduction bands are completely filled. Detailed calculations of the ${\mathrm{Ag}}_{\mathit{c}}$${\mathrm{Pd}}_{1\mathrm{\ensuremath{-}}\mathit{c}}$ Fermi surfaces are presented in a separate paper (II).