normal state a peak evolves in the B1g Raman spectrum at a frequency of about (3/2)Eg , which corresponds to the frequency di erence between the peaks in the density of states. The continuous evolution of the B1g Raman peak with decreasing T as shown in Fig. 3.44b for Eg = 0.15t is similar to the observed evolution of the peak in slightly underdoped Bi2212 [178]. We note that the position of the peak at about ω 0.25t 62 meV for t = 250 meV is of the order of magnitude of the observed resonance at 75 meV [178]. The increase of the normal–state peak with decreasing T is accompanied by a suppression of the low–frequency spectral weight, as is seen in the experiments (see Fig. 3.45b) [178].

Next we discuss the interesting question of whether the pseudogap can also explain the normal–state data for B2g Raman spectra of YBCO and Bi2212 in the underdoped regime, where a reduction of spectral weight with decreasing temperature is observed [179]. We find indeed that spectral weight is lost at higher Raman shifts, while the slope at ω = 0 is increased with decreasing temperature T (see Fig. 3.45c for Eg = 0.15t). The broad peak arising below the pair-breaking threshold 2Eg is much less pronounced than the sharp peak occurring in the B1g Raman spectrum (see Fig. 3.45b). In the superconducting state, the slope at ω = 0 decreases with decreasing T in agreement with the experimental data for the B2g channel; however, our pair–breaking maximum (see Fig. 3.25) is much less pronounced than the experimental one [179]. This deserves further investigation. In particular, a frequency–dependent pseudogap would be required.

3.5.3 Brief Summary of the Consequences of the Pseudogap

In this section, we have investigated the influence of a d–wave pseudogap on many physical quantities in the underdoped regime of hole–doped superconductors. The general equations were derived in Sect. 2.2.1. The resulting neutron scattering intensity, spin–lattice relaxation rate 1/T1, Knight shift, resistivity, and photoemission intensity are in qualitative agreement with the data on underdoped high-Tc cuprates. The value of Tc for superconductivity and also that of Tc decrease and the crossover temperature T for 1/T1T increases with increasing pseudogap amplitude of φc, which is in qualitative agreement with the phase diagram for underdoped cuprates. We consider this as an important step towards an understanding of the whole phase diagram within one microscopic theory. Furthermore, we find that the pseudogap leads, with decreasing temperature, to the development of a d–wave gap structure in the density of states, which merges continuously into the superconducting spectrum. A corresponding pair-breaking peak evolves continuously in the B1g Raman spectrum as T decreases in the normal state and below Tc. We have also calculated the c-axis infrared conductivity σc(ω) in underdoped cuprate superconductors and find, below a temperature T Eg /2, that a gap develops in σc (ω) for ω < 2Eg in the incoherent (di use) transmission limit. The corresponding resistivity shows “semiconducting” behavior, i.e. it increases