Charge-charge, current-current, and Raman correlation functions are derived in a consistent way using the unified response theory. The theory is based on the improved description of the conduction electron coupling to the external electromagnetic fields, distinguishing further the direct and indirect ͑assisted͒ scattering on the quasistatic disorder. The two scattering channels are distinguished in terms of the energy and momentum conservation laws. The theory is illustrated on the Emery three-band model for the normal state of the underdoped high-T c cuprates which includes the incoherent electron scattering on the disorder associated with the quasistatic fluctuations around the static antiferromagnetic ͑AF͒ ordering. It is shown, for the first time consistently, that the incoherent indirect processes dominate the low-frequency part of the Raman spectra, while the long-range screening which is dynamic removes the long-range forces in the A 1g channel. In the mid-infrared frequency range the coherent AF processes are dominant. In contrast to the nonresonant B 1g response, which is large by itself, the resonant interband transitions enhance both the A 1g and B 1g Raman spectra to comparable values, in good agreement with experimental observation. It is further argued that the AF correlations give rise to the mid-infrared peak in the B 1g Raman spectrum, accompanied by a similar peak in the optical conductivity. The doping behavior of these peaks is shown to be correlated with the linear doping dependence of the Hall number, as observed in all underdoped high-T c compounds.
The dynamical conductivity of interacting multiband electronic systems derived in Ref. 1 is shown to be consistent with the general form of the Ward identity. Using the semiphenomenological form of this conductivity formula, we have demonstrated that the relaxation-time approximation can be used to describe the damping effects in weakly interacting multiband systems only if local charge conservation in the system and gauge invariance of the response theory are properly treated. Such a gauge-invariant response theory is illustrated on the common tight-binding model for conduction electrons in hole-doped graphene. The model predicts two distinctly resolved maxima in the energyloss-function spectra. The first one corresponds to the intraband plasmons (usually called the Dirac plasmons). On the other hand, the second maximum (π plasmon structure) is simply a consequence of the van Hove singularity in the single-electron density of states. The dc resistivity and the real part of the dynamical conductivity are found to be well described by the relaxationtime approximation, but only in the parametric space in which the damping is dominated by the direct scattering processes. The ballistic transport and the damping of Dirac plasmons are thus the questions that require abandoning the relaxation-time approximation.
An approach to microwave measurements is used in order to determine both, the in-plane and out-of-plane conductivity of the high-T c superconductor HgBa 2 CuO 4+␦ near optimal doping. Unlike the ab-plane conductivity, the c-axis conductivity is highly sensitive to superconducting fluctuations. From a single c-axis data set, we can clearly discern the opening of the pseudogap at T ء = 185͑15͒ K, the appearance of the superconducting fluctuations at a much lower temperature TЈ = 105͑2͒ K, and the full transition to the superconducting state at the critical temperature T c = 94.3 K. Thus, with the present high sensitivity, we establish that the extent of the superconducting fluctuations is only about 10 K above T c .
The frequency and wave-vector-dependent memory function in the longitudinal conductivity tensor of weakly interacting electronic systems is calculated by using an approach based on quantum transport equations. In this paper, we show that there is a close relation between the single-electron self-energy, the electron-hole pair self-energy, and the memory function. It is also shown in which way singular long-range Coulomb interactions, together with other q ≈ 0 scattering processes, drop out of both the memory function and the related transport equations. The theory is illustrated on heavily doped graphene, which is the prototype of weakly interacting single-band electron-phonon systems. A steplike increase of the width of the quasiparticle peak in angle-resolved photoemission spectra at frequencies of the order of the frequency of in-plane optical phonons is shown to be consistent with the behavior of an intraband plasmon peak in the energy loss spectroscopy spectra. Both anomalies can be understood as a direct consequence of weak electron scattering from in-plane optical phonons.
A systematic method of calculating the dynamical conductivity tensor in a general multiband electronic model with strong boson-mediated electron-electron interactions is described. The theory is based on the exact semiclassical expression for the coupling between valence electrons and electromagnetic fields and on the self-consistent Bethe-Salpeter equations for the electron-hole propagators. The general diagrammatic perturbation expressions for the intraband and interband singleparticle conductivity are determined. The relations between the intraband Bethe-Salpeter equation, the quantum transport equation and the ordinary transport equation are briefly discussed within the memory-function approximation. The effects of the Lorentz dipole-dipole interactions on the dynamical conductivity of low-dimensional spα models are described in the same approximation. Such formalism proves useful in studies of different (pseudo)gapped states of quasi-one-dimensional systems with the metal-to-insulator phase transitions and can be easily extended to underdoped two-dimensional high-Tc superconductors.
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