Quasiparticle dispersions

There are two quasiparticle states per spin channel. Defining , = , -I- A as the renormalized f level one obtains the quasiparticle dispersion... 

Due to this repulsion and the expected weak quasiparticle dispersion, anisotropic superconducting phases and reduced coherence lengths seem probable, which is in accord with experiments. On the other hand, there does not really exist any conclusive correlation between an enhanced tendency towards magnetism and the occurrence of such superconductivity, see sect. 3. The conventional deformation-potential coupling mechanism, applied to the itinerant states alone, however, can apparantly not account for pairing between heavy fermions (Entel et al. 1985, Pickett et al. 1986, Fenton 1987, Normal 1988). 

In conclusion, the spin fluctuation models have gone a long way beyond their He counterparts. On the other hand, the theories do not give a gap function with which one is totally happy (see table 3), and the theories are still probably too simplistic for real heavy-fermion metals. First, they replace the complicated quasiparticle matrix elements, of the form , by a simplistic V k — k ) as used above (in fact, the ambiguities discussed above about the momentum dependence of the pair potential are all due to this simple replacement). Second, the vertex is treated as a product of Pauli (spin) matrices, as in He, and completely ignores any orbital or spin-orbital contributions (in fact, the only thing included at this stage is the directional anisotropy terms in x). Finally, the frequency dependences of the pair interaction, the quasiparticle dispersions, and the gap function have been treated in... 

Phenomenological quasiparticle model. Taking into account only the dominant contributions in (7), namely the quasiparticle contributions of the transverse gluons as well as the quark particle-excitations for Nj / 0, we arrive at the quasiparticle model [8], The dispersion relations can be even further simplified by their form at hard momenta, u2 h2 -rnf, where m.t gT are the asymptotic masses. With this approximation of the self-energies, the pressure reads in analogy to the scalar case... 

As follows from (15.14), the obtained quasiparticles have acoustic dispersion for k -C i/47ra/Vo and for k 3> y/4naNo become free particles with... 

Of course, it is an approximation to regard quasiparticles as particles, and this approximation can be expected to break down in several ways. First, core holes always have a finite lifetime, i.e. they are broadened, and disperse on a short timescale. The effects of core-hole broadening will be discussed in chapters 8 and 11. Secondly, the very concept of a core hole may become inapplicable, i.e. it may prove impossible to identify a single structure in the spectrum as the result of exciting a quasiparticle. This form of breakdown is discussed in chapter 7. Experience shows that well-characterised holes tend to be the deepest ones, which are fully screened, while vacancies in the subvalence shells cannot always be described in this way. Thus, the concept of core holes is most useful in X-ray spectroscopy, but can sometimes break down quite severely at lower excitation energies. 

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)].

The funnel approach restricts the number of the possible pathways. Kinematically, it means that for n local rotations — no matter which path down the funnel has been taken by the molecule — there appears the constraint of small n. This constraint comes from the spectroscopic data on the poorly dimensionally sensitive dispersion laws of the internal quasiparticle excitations [9,10], which stem the same order of magnitude for the two time intervals, for the molecular conformational transition (t), as well as for the (average) time of the local segmental rotations (t,), while bearing t = otj in mind. Certainly, this might be a serious restriction, in principle, for the large molecules conformational transitions in the still (semi-)classical funnel approach. 

The quasiparticle energies reflect the interaction among the fermions and therefore may be altered when the overall configuration is changed. A characteristic featnre of interacting Fermi liquids is that the energy dispersion (k) depends on how many other qnasiparticles are present,... 

Here E (k) denotes the energy dispersion of a dilute gas of qnasiparticles. In systems with strong correlations it cannot be calcnlated from the overlap of single-electron wave functions. The interactions among the quasiparticles are characterized by the matrix k ). The... 

The vast majority of recent photoemission experiments on the cuprates have focussed on the narrow, dispersive features found near the Fermi level, first observed by Arko et al, (1989), These states arise in a small foot in the lowest 1 eV below Ep, and grow more prominent as the doping level approaches the optimal value. Careful measurement of the amplitude and peak position of these quasiparticle features allows reconstruction of the band structure and the two-dimensional Fermi surface topology, and can reveal the presence and magnitude of a superconducting gap. Transport, optical, and electrical properties in the cuprate superconductors all manifest anomalous behavior these also must be closely linked to the spectrum of low-energy excitations, since the relevant states lie within a few k T of Ep. 

Fig. 17. Eneigy dispersion of quasiparticles along the FX symmetry line.

The measured band dispersions clearly reveal two plane-derived quasiparticle states, one with a binding energy of 0.22 eV at T, and the other with 0.53 eV which are associated with the antibonding and bonding bilayer bands. The former disperses upward to form a van Hove singularity with a binding energy of 0.13 eV at X, while the latter is weakly... 

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