[Jacques Friedel et la théorie des métaux et alliages]
Cet article est une introduction à la théorie électronique des métaux. Il s'adresse aux étudiants et aux physiciens non spécialistes. On commence par décrire certaines conséquences simples de la statistique de Fermi–Dirac dans les métaux purs, comme la distorsion de Peierls, les anomalies de Kohn et la distorsion de Labbé–Friedel. On discute ensuite la physique des alliages dilués. L'analogie avec le problème des collisions nucléaires fut un point de départ fructueux, qui amena à considérer l'effet des impuretés comme un problème de diffusion, dans lequel apparaissent les déphasages de l'onde électronique diffusée. Friedel élabora ainsi une théorie de la résistivité des alliages, et établit une règle de somme qui relie les déphasages au niveau de Fermi à la charge de l'impureté. Cette règle de somme joua plus tard un rôle essentiel dans le cas d'électrons fortement corrélés, notamment dans l'effet Kondo. Une autre découverte importante fut celle des oscillations de Friedel, responsables par exemple de la formation de structures magnétiques incommensurables. On montre comment elles peuvent être déduites de diverses méthodes : de la théorie des collisions, de la théorie des perturbations, d'approximations self-consistentes ou de la méthode des fonctions de Green. Si la théorie des collisions ne tient pas compte de la structure électronique, et par conséquent de la structure de bandes, ces effets peuvent facilement être inclus dans d'autres théories, par exemple en faisant appel à l'approximation des liaisons fortes.
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 Labbé–Friedel distortion. Then the physics of dilute alloys is discussed. The analogy with nuclear collisions was a fruitful starting point, which suggested one should analyze 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.
Mot clés : Electrons dans les métaux, Effet d'écran, Oscillations de Friedel, Anomalies de Kohn, Effet Kondo, Approximation des liaisons fortes
Jacques Villain 1 ; Mireille Lavagna 2, 3 ; Patrick Bruno 4
@article{CRPHYS_2016__17_3-4_276_0,
author = {Jacques Villain and Mireille Lavagna and Patrick Bruno},
title = {Jacques {Friedel} and the physics of metals and alloys},
journal = {Comptes Rendus. Physique},
pages = {276--290},
publisher = {Elsevier},
volume = {17},
number = {3-4},
year = {2016},
doi = {10.1016/j.crhy.2015.12.010},
language = {en},
}
Jacques Villain; Mireille Lavagna; Patrick Bruno. Jacques Friedel and the physics of metals and alloys. Comptes Rendus. Physique, Volume 17 (2016) no. 3-4, pp. 276-290. doi : 10.1016/j.crhy.2015.12.010. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2015.12.010/
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