By Jenö Sólyom
This e-book is the 3rd of a three-volume sequence written via an identical writer that goals to convey a complete and self-contained account of the sizeable box of solid-state physics. It is going a ways past such a lot vintage texts within the presentation of the homes of solids and experimentally saw phenomena, in addition to the elemental options and theoretical tools used to appreciate them and the fundamental good points of varied experimental techniques.
The first quantity bargains with the atomic and magnetic constitution and dynamics of solids, the second one with these digital houses that may be understood within the one-particle approximation, and the 3rd with the consequences as a result of interactions and correlations among electrons.
In the current quantity the electron—electron interplay is handled first within the Hartree—Fock approximation. The density-functional concept is brought to account for correlation results. The reaction to exterior perturbations is mentioned within the framework of linear reaction idea. Landau’s Fermi-liquid thought is via the speculation of Luttinger drinks. the next chapters are dedicated to digital levels with damaged symmetry: to itinerant magnetism, to spin- and charge-density waves and their realizations in quasi-one-dimensional fabrics, in addition to to the microscopic concept of superconductivity. an outline is given of the physics of strongly correlated platforms. The final bankruptcy covers chosen difficulties within the physics of disordered platforms.
The textual content offers fabric for upper-level undergraduate and graduate classes. it is going to even be a beneficial reference for researchers within the box of condensed topic physics.
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Extra resources for Fundamentals of the Physics of Solids: Volume 3 - Normal, Broken-Symmetry, and Correlated Systems
18) dr dr U (r − r ) n(r) n(r ) for the mean-ﬁeld Hamiltonian. 4). The physical 22 28 Electron–Electron Interaction and Correlations meaning of the constant correction term will be discussed later. 11) or, more precisely, an expression where self-interaction is omitted. 21) σσ − dr dr U (r − r ) ψˆσ† (r )ψˆσ (r ) ψˆσ† (r)ψˆσ (r) . 22) σσ with the one-particle Hamiltonian (1) HH (r) = − 2 2me dr U (r − r ) ψˆσ† (r )ψˆσ (r ) . 23) The Hamiltonian takes an even simpler form when it is written in terms of the creation and annihilation operators of the one-particle states φλσ (r).
In what follows we will often make this simpliﬁcation and the band index ni will be neglected. We remark that such a simpliﬁed model cannot be valid for transition metals. Their physical properties are determined not solely by the electrons in the 4s (5s) bands. The 3d (4d) bands may play an equally important role. 42) has to be satisﬁed. This can be checked simply by using the Bloch theorem valid for the single-particle wavefunctions ψnkσ (r). To see this the interaction is written in Fourier representation and the integral over the volume of the sample is replaced by a sum over the primitive cells and the integral is performed within the cells.
The existence of a sharp Fermi edge and the Luttinger theorem stating the conservation of the volume enclosed by the Fermi surface can be proven quite generally, provided that perturbation theory is applicable and the perturbation series converges. Fermi systems for which this assumption is valid are called normal Fermi systems. Their perturbed ground state can be obtained from the noninteracting ground state by turning on the interaction adiabatically. This is the case for ordinary metals. There are systems, however, in which the interaction cannot be treated in perturbation theory.