Jacques Friedel and the physics of metals and alloys

TL;DR

This paper introduces the theoretical physics of metals, covering Fermi statistics effects, alloy resistivity, phase shifts, Friedel oscillations, and their derivations, highlighting Friedel's contributions to understanding metallic and alloy behaviors.

Contribution

It provides a comprehensive overview of Friedel's theories on metals and alloys, emphasizing the derivation of resistivity, phase shift sum rules, and Friedel oscillations, integrating various theoretical approaches.

Findings

Friedel derived a theory of alloy resistivity.

Established a sum rule linking phase shifts to impurity electrons.

Described multiple methods to derive Friedel oscillations.

Abstract

This is an introduction to the theoretical physics of metals for students and physicists from other specialities. Certain simple consequences of the Fermi statistics in pure metals are first addressed, namely the Peierls distortion, Kohn anomalies and the Labb\'e-Friedel distortion. Then the physics of dilute alloys is discussed. The analogy with nuclear collisions was a fruitful starting point, which suggested one should analyse the effects of impurities in terms of a scattering problem with the introduction of phase shifts. Starting from these concepts, Friedel derived a theory of the resistivity of alloys, and a celebrated sum rule relating the phase shifts at the Fermi level to the number of electrons in the impurity, which turned out to play a prominent role later in the context of correlated impurities, as for instance in the Kondo effect. Friedel oscillations are also an important result, related to incommensurate magnetic structures. It is shown how they can be derived in various ways: from collision theory, perturbation theory, self-consistent approximations and Green's function methods. While collision theory does not permit to take the crystal structure into account, which is responsible for electronic bands, those effects can be included in other descriptions, using for instance the tight binding approximation.