Fermi-surface harmonics

It is often useful to explicitly account for the crystalline symmetry of the material in the Raman scattering cross-section by expanding the Raman scattering vertex y in terms of Fermi surface harmonics [Pg.519]

To motivate our next step recall that the LOFF spectrum can be view as a dipole [oc Pi (a )] perturbation of the spherically symmetrical BCS spectrum, where Pi(x) are the Legendre polynomials, and x is the cosine of the angle between the particle momentum and the total momentum of the Cooper pair. The l = 1 term in the expansion about the spherically symmetric form of Fermi surface corresponds to a translation of the whole system, therefore it preserves the spherical shapes of the Fermi surfaces. We now relax the assumption that the Fermi surfaces are spherical and describe their deformations by expanding the spectrum in spherical harmonics [17, 18]... 

There seems to be a growing consensus that the superconductivity is d-wave [97], more specifically, dx2 y2 type. Recent microwave measurements [98] would indicate that the penetration depth is linear in temperature, a sign that the gap has zeros. As pointed out in Ref. 99, this does not exclude 5-wave pairing since harmonics of the basic combinations [Eq. (38)] can also lead to zeros of the gap on the Fermi surface. It is interesting to note that d-wave pairing is quite in line with the extrapolations of the two-dimensional Hubbard and t-J models (Section V.B) and the observed competition with AFM. This would point to a spin-exchange mechanism. The parallel with the quasi-one-dimensional superconductors is striking. 

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... 

The Fourier spectrum of these oscillations (H a ), shown in Fig. 2, consists of a sharp symmetric peak centered at a frequency of about 600 T, and a smaller peak at around 1200 T, obviously the second harmonic in the spectrum of an anharmonic oscillation. The oscillations being thus periodic in 1/H, we are confident that we observe in fact the Shubnikov-de Haas effect. An observed frequency F is then related to an extremal cross-section S of the Fermi Surface normal to the magnetic field direction by S=(2iTe/tic)F /13/, and thus geometric information about the Fermi Surface can be obtained from the angular dependence F(0). The result for the fundamental peak frequency in ET2Cu(NCS)2 is shown in Fig. 3. 

The amount of splitting between the majority and minority Fermi surfaces corresponds to a band splitting of 0.95 eV, quite close to the value 0.8 eV calculated by Harmon and Freeman (1974). Together with the calculated density of states for Gd, this gives a spin moment of 0.78 Bohr magneton per atom, somewhat larger than the measured value of 0.63. 

The strong d-like character of large sections of the Fermi surface of the rare earths (Harmon and Freeman 1974) results in a relatively low conduction electron mobility. Furthermore, even in the purest material available, presiduai-describing the temperature independent scattering by non-magnetic impurities and lattice defects-is some 3x 10 flm (Jordan et al. 1974). Thus the electron mean free path is presently limited to a value several orders of magnitude lower than has been achieved for other metals. 

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