Fermi surfaces and electronic topological transitions in metallic solid solutions

Abstract

Notwithstanding the substitutional disorder, the Fermi surface of metallic alloys can be measured and computed. We show that, from the theoretical point of view, it is defined as the locus of the peaks of the Bloch Spectral Function (BSF). Such Fermi surfaces, on varying the atomic concentrations, may undergo changes of their topology, known as Electronic Topological Transitions (ETT). Thus, for instance, pockets of electrons or holes may appear or disappear, necks may open or close. ETTs cause anomalous behaviours of thermodynamic, transport and elastic properties of metals and constitute a fascinating field in the study of Fermi liquid systems. Although ETTs could be studied on pure systems as a function of the thermodynamic variables, nevertheless such a study would often require extreme conditions, and would lead to experimental difficulties. On the other hand, it is possible to explore the variations of atomic concentration, i.e. the valence electron per atom ratio, in metallic solid solutions with a relative experimental ease. In this paper we review the theoretical techniques for the determination of Fermi surfaces in metallic solid solutions and discuss some examples of ETTs, namely LiMg, ZrNb, NbMo, MoRe, AgPd, CdMg, NiW and NiTi alloys, also in connection with experimental data as thermoelectric power, resistivity, elastic constants and electron-phonon coupling and with the determinations of the electron momentum distribution function from Compton scattering and positron annihilation experiments. We show that the ab initio calculations of the electronic structure for the quoted systems, together with a careful determination of the BSF, are able to predict quantitatively ETTs at those concentrations where physical quantities display anomalies, so confirming directly ETT theory. Although it is not the purpose of the present review to give a full account of electronic structure calculation schemes, however, we briefly discuss the ideas and the main physical approximations underlying theories of substitutional disorder in alloys. We shall pay some more attention to the Coherent Potential Approximation (CPA) in the Korringa-Kohn-Rostoker (KKR) multiple scattering framework and the Hohenberg and Kohn Density Functional Theory in the Local Density Approximation (LDA) for the exchange-correlation potential. The above choice is supported by the numerical versatility of the LDAKKRCPA theory, and, more important, by the a fortiori evidence that essentially equivalent results are obtained from different theoretical frameworks, provided the same basic physical approximations are used. Accordingly, when convenient, we present new LDAKKRCPA determinations of the Fermi surfaces, as for the ZrNbMoRe series.