Perfect nesting

The Fermi surface departs from perfect nesting when the second harmonic contribution in Eq. (27) becomes a relevant contribution, namely if t[ T0. Thus the nesting of the Fermi surface is frustrated and the susceptibility Xo(logarithmic divergence at q = Q, as T —> 0 but only a relative (nondivergent as T —> 0) maximum at a... 

At complete filling, n = 1, in the case of undoped LaMnOs, the Fermi surfaces become straight lines, flat . Also, at n = 1, there is a perfect nesting. The energies of two bands coincide, ei (p -l- Q) = 2 (p), with a shift by the wave vector Q = (jT, n). In three dimensions (3D), for the ferromagnetic case, a similar nesting takes place with the 3D-vector, Q = it, it, n). 

Extraction of metal cations Me from the sofid can also lead to creation of surface hydroxyls, with n OH groups created per Me species removed, in agreement with the rule of charge preservation. Typically, this chemistry can be formulated as an exchange reaction. However, more comphcated situations are also encoimtered. For example, extraction of framework Al ions from zeolites leads to the formation of so-called silanol nests (Figure 2.2). A perfect nest should consist of four Si—OH groups (26). 

Fig. 7. Left panel Cooper pairs (—k, k) and electron-hole (Peierls) pairs (—k, —k + Q) for the n.n. tight binding Fermi surface (thick line) with perfect nesting vector Q. Saddle points (S) of 6(k) at (0, .7t) and ( 7T, 0) lead to DOS peak at the Fermi energy. Therefore unconventional pair states can only have nodes away from S, i.e., at the Dirac points D ( j, j) where the quasiparticle spectrum takes the form of eq. (54). This is the case for a

Finite frequency probes Finally we discuss finite freqnency probes for d-DW states like optical conductivity (Yang and Nayak, 2002). It exhibits non-Drade like behaviomat low frequencies because of arbitrary low excitation energies for q = 0 interband E- Efr) transitiorrs at the nodal (Dirac) points. For perfect nesting Ep = Q) at low temperatures one obtairrs (for (WT 1, r = quasiparticle lifetime)... 

The contrast between this behavior and the perfect nesting case is illustrated in fig. 3.67. In real metals one only finds gentle peaks in x(q) rather than divergences. 

Fig. 3.67. The generalized susceptibility functions for the perfect nesting model and the imperfect nesting model.

Fig. 3.74. The effect of magnetic ordering on the generalized susceptibility function of the perfect nesting model (Evenson and Liu, 1969).

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