Renormalized band

Fig. 21. Real part of the conductivity of YbFe4St>i2- The symbols on die left axis represent dc values at different temperatures. Below T (fv 50 K), a narrow peak at zero frequency and a gap-like feature at 18 meV gradually develop. Inset Renormalized band structure calculated from die Anderson lattice Hamiltonian. % and f denote bands of free carriers and localized electrons, respectively. At low temperatures a direct gap A opens. The Fermi level, Ep is near die top of die lower band,, resulting in hole-like character and enhanced effective mass of die quasiparticles (Dordevic et al., 2001).

For applications, see Refs. [84-89]. Reference [89] describes the results of relativistic band structure calculations for CeRu2Si2, and also in this case it was found that the topology of the Fermi surface is well described by the LDA, although the T-linear specific heat coefficient is very large, 7 350 mJ/molK. This, and the similar observation made for UPts were explained [85,86] by showing that the Fermi surface topologies derived from renormalized bands and an LDA calculation for this kind of systems... 

Fig. 47. Schematic quasiparticle density of states N (s) as obtained from the mean-field dispersion, eq. (112). They lead to a hybridization gap centered around , = and two peaks in N e) whose width and separation is also of order The Fermi level (0) is pinned in this region. The temperature dependence of the effective hybridization K, given by the function fl T) = rJ(T)/rJ(0, N = 2) as shown in the inset (Coleman 1987). IF is a slightly renormalized band width [a square DOS of width W has been used for the bare A/,(e)].

Fig. 4. Schematic summary of renormalized band calculation for metals with strongly correlated electrons.

The validity of the Fermi liquid picture is concluded from a comparison of the effective masses on the fourth pillow-shaped sheet as given in table 2. From the large linear specific heat the renormalized band scheme deduces a characteristic energy kT 10 K which in turn implies heavy masses of the order of w / w 100. This value was confirmed by experiments (Albessard et al., 1993 Aoki et at, 1993 Tautz et al., 1995) where the ijr orbit vnth m /m 120 was observed. The corresponding Fermi surface cross section is in agreement with estimates from the renormalized band theory. This proves that the heavy quasiparticles... 

Low-temperature values of the critical magnetic fields for the transition into the high-field 5-phase . Comparison with experiment of the renormalized band prediction for the approximate critical magnetic fields for field directions along the tetragonal axis and in the basal plane (Zwicknagl and Pulst, 1993)... 

Fig. 20. Left panel Neutron diffraction intensity in CeCu2Si2 at temperatures above and below the A-phase transition temperature Incommensurate peak corresponds to Q = (0.215,0.215,0.53) (Stockert et al., 2004). Right panel Nesting of heavy FS columns (fig. 18) leads to a peak in the static susceptibility x(

In LDA, the electron correlations are taken into account only by a mean field approximation which utilizes the correlation enei of the uniform electron gas. In the Ce compounds where the 4f electrons are believed to be itinerant in the ground state, such as in CeSns, the topology of the Fermi surface can be described by the band structure calculated in LDA. However, the strong intra-atomic correlation effect between the 4f electrons should be considered for consistent explanations of the Fermi surface, the electronic specific heat coefficient and the cyclotron efifective mass. Beyond LDA, there are two approaches by which the correlation effect between the 4f electrons is taken into account in an explicit way. One is p-f mixing theory and the other is renormalized band theory. 

In section 2, we briefly outline density functional theory and the various approximations employed including the local density approximation (LDA), and discuss generalizations of LDA to incorporate spin (LSDA), orbital, and relativistic effects. We also discuss phenomenological renormalized band schemes based on the slave-boson or Kondo phase-shift methods. 

In section 3 - the main section - we discuss results for many f electron materials, examining where possible comparisons to LDA calculations which treat the f electrons as either band-like (itinerant f) or core-like (local f), and to renormalized band calculations. Although there is some discussion of bonding properties, we concentrate on the general electronic structure, the Fermi-surface related properties, and magnetism (a detailed discussion of bonding properties is given by Johansson and Brooks in this volume). 

There is, however, another school of thought that claims that the f electrons form well-defined Bloch states and very narrow bands at all temperatures (Zwicknagl 1992, Liu 1993, Sheng and Cooper 1995). While there is little quarrel with this view at low temperatures, conventional band theory (using the Local Density Approximation, or LDA) is clearly unable to explain the high-temperature properties as well as the very heavy mass. Renormalized band theories (Strange and Newns 1986, Zwicknagl 1992) may yet prove useful, especially those that incorporate physics similar to the Kondo effect and... 

Various renormalized band approaches (Zwicknagl 1992, Strange and Newns 1986] have succeeded in effectively reproducing the large electron masses in heavy fermions. 

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