Fermi liquid theory

Note that the exchange term is of the form / y(r,r ) h(r )dr instead of the y (r) (r) type. Equation (1.12), known as the Hartree-Fock equation, is intractable except for the free-electron gas case. Hence the interest in sticking to the conceptually simple free-electron case as the basis for solving the more realistic case of electrons in periodic potentials. The question is how far can this approximation be driven. Landau s approach, known as the Fermi liquid theory, establishes that the electron-electron interactions do not appear to invalidate the one-electron picture, even when such interactions are strong, provided that the levels involved are located within kBT of Ep. For metals, electrons are distributed close to Ep according to the Fermi function f E) ... 

Before the discovery, in 1986, by Bednorz and Muller [1] of high-Tc superconductivity, there was a rather widespread belief that Solid State Theory was satisfactorily built so as to allow the comprehension of any solid state problem, provided the computations to be carried out were feasible. Nourishing this believe there was, on the free quasi-particle side, the Fermi Liquid Theory and tools as Green Functions and Diagrammatic Perturbation Theory, which allowed to study most of the band-theoretic-based solid-state properties. Namely, Diagrammatic Perturbation Theory has... 

Specific heat. In the Fermi liquid theory, the expression for the electronic contribution to the specific heat is linear in temperature CXT) = yT, where the Sommerfeld constant is... 

Key features of both the non-interacting and the interacting Fermi liquid theory can be illustrated through the retarded one-particle Green function, which can be defined from the following Fourier transform... 

This conversion procedure must be attempted for the longitudinal as well as for the transverse transport. The results for p (7) in (TMTSFljPF at ambient pressure is given in Fig. 14 where a cross-over from a superlinear to a linear (or sublinear) power law temperature dependence is observed in the vicinity of 80 K. A detailed analysis based on the Fermi liquid theory shows that a law is apparently well satisfied below 50 K down to the vicinity of the spin density-wave transition where the resistivity is dominated by critical scattering effects [75]. 

N may be as crude as the Fermi liquid theory for nucleons, plus classical estimates of electromagnetic energy density, and P(SC C) N). may have such broad support that it places essentially no restriction on stellar nucleosynthesis. For this reason, we introduce Hoyle s posterior observation of estimated carbon abundances. 

In the previous Section we analysed the normal-state properties of high-7) superconductors, based on the Fermi-liquid picture. In this Section we discuss some aspects which seemingly contradict the Fermi liquid theory, in particular... 

Fermi liquid theory is valid for the set of Fermions. The validity of this is an... 

Once the Landau Fermi-liquid theory is set up and the assumption (22) made about the density of states, explicit calculaiions of M(H) and C (H) can be made. Quantitative agreement is found with all of the experimental results including not only (19), (20), and (21), but the full field dependence of M(H) and C (H) once cA is fixed. These are striking successes, and one would like to have a deeper microscopic understanding of what is going on than is afforded by the assumptions 7. and 8. 

The most important experimental quantity with which to recognize heavy-carrier masses is the Sommerfeld coefficient y of the electronic specific heat. In Fermi-liquid theory (Abrikosov et al. 1963, Nozieres 1964, Baym and Pethick... 

Due to Anderson s compensation theorem (Anderson 1961), which holds for sufficiently structureless bands, may be identified with the number of electrons residing in the partially filled shell of the impurity. The phase shift 8 in Fermi-liquid theory is given by... 

Typically, is near to one for Ce systems with the bare f-level well below Ep. Note that the Anderson width A is much smaller than that conduction-band width, so that N (Ep) is indeed large when compared with the bare conduction-band DOS. On the other hand, it should be clear that singlet formation via an indirect exchange coupling cannot transfer much spectral weight from the bare local level up to Ep. Thus, a narrow resonance near the Fermi level of maximum height (jrAY and width k Tp < A arises. It should be emphasized that the local DOS considered here is not the quasiparticle DOS that is used in Fermi-liquid theory to express thermodynamic quantities via free-particle for-... 

It is important to mention one serious deficiency of the extended Drude analysis. This formalism is based on an isotropic version of Fermi-liquid theory which is highly questionable in cuprates where the electronic structure is in fact very anisotropic in the ab-plane. One approach that addresses this problem is to first calculate the conductivity, using a proper anisotropic theory with A -dependent Fermi velocity and scattering rate 1/r, and then use the real and imaginary parts of the calculated conductivity to find the effective scattering rates l/r(co) and m. Some steps in that direction have been made by Stojkovic and Pines (1996) and Branch and Carbotte (1998). 

Miyake, K., Fermi-liquid theory of dilute submonolayer He on thin He film—dimer bound state and Cooper pairs, Progr. Theor. Phys., 69, 1794, 1983. 

Any temperature dependence of the CEF halfwidth can be attributed to either s-f interaction or the interaction of f states with phonons, s-f line broadening for simple metals has been attributed to the effects of the carrier spin dynamics on the CEF-state lifetimes and has been described by the Fermi liquid theory, introduced by Becker et al. (1977). The s-f interaction Hamiltonian describing the coupling between the 4f electrons and the conduction electrons can be written as... 

The kernel is a well known quantity that appears in several branches of theoretical physics. For example, evaluated for the electron gas, /xc is, up to a factor, the local field correction . To emphasize the correspondence to the effective interaction of Landau s Fermi-liquid theory, to which it reduces in the appropriate limit, /xc plus the bare Coulomb interaction is sometimes called the effective interaction , while in the theory of classical liquids the same quantity is referred to as the Ornstein-Zernicke function. 

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