Mass enhancement factors

Fig. 2 Inverse of the polaron mass enhancement factor, m/m, as a function of for the T (8) a (HP Holstein polaron) and the (8) e JT polaron. In the latter, the result in the infinite chain d = 1) is compared with that in the two-site system as weU as the analytic result in (26). The anti-adiabatic condition of (Uo// = 5 is assumed...

Fig. 3 Inverse of the mass enhancement factor, mim, as a function of g

Physically the polaron mass enhancement is brought about by the virtual excitation of phonons. In the H (g a Holstein model no restriction is imposed on exciting multiple phonons, implying that all the terms in Fig. lb for the vertex function contribute, while in the g e JT model, there is a severe restriction due to the existence of the conservation law intimately related to the 50(2) rotational symmetry in the pseudospin space. Actually, among the first- and second-order terms for the vertex function, only the term T2/ contributes, leading to the smaller polaron mass enhancement factor m jm than that in the Holstein model in which the correction r 1 is known to enhances m /m very much. In this way, the applicable range of the Migdal s approximation [48] becomes much wider in the g e JT system [63]. 

Mass enhancement due to the electron-magnon interaction in magnetically ordered compounds is large compared to the one due to the electron-phonon interaction. The mass enhancement factor is in the range of 1-2. 

As for an appropriate band theory for the localized 4f-electron system, an attractive approach based on the p-f mixing model was proposed, and was plied to CeSb. A future problem is to refine the approach so as to carry out quantitative calculations in a self-consistent way. The anomalously large enhancement factors for the cyclotron effective masses and the y values observed in the Ce compounds cannot be explained by band structure alone. Quantitative analysis of the mass enhancement factor is a problem challenging to many-body theory. There is still much room for improvement for a complete understanding of the electronic structures of lanthanide compoimds. 

Fig. 5. (top) Optical conductivity spectra, bottom) Absorption maximum, comaxy n/m ( Neff), and mass enhancement factor, X, of Bai xKxBi03 for various x [136]... 

The upper band is qualitatively the same as the simple two-band model discussed in section 3.1.2, but the band mass at zero temperature is enhanced by roughly a factor of 5 for fi 0) = 13r], where /r(0) is the Fermi level as temperature T=0 (Liu 1987, 1988). This factor plus the correlation effect due to Uk could put the mass enhancement factor to within the measured range of 20-30. When there are many f levels and many broad bands as in a real LDA calculation, there should be a one-to-one correspondence between the model bands and the LDA bands at the Fermi level. On the other hand, until the f hole screening dynamics can be calculated from realistic band eigenvalues and eigenstates, the present theory should only be considered qualitative or at most semi-quantitative. The quantity /r(0) cannot be determined with certainty, and we will treat it as a parameter in the model calculation. 

Of great interest are specific-heat data, since the obtained y-value for CeAs (17mJ/molK ) is nearly the same as those for CeSb and CeBi (Kwon et al. 1991), although CeSb and CeBi have carrier concentrations of about 0.02 electron/Ce-atom (determined by the dHvA effect), with a mass enhancement factor of about 25. Thus, the mass enhancement for CeAs must be very large, and one can consider it as a heavy-fermion system with an extremely low carrier concentration. 

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