Thermally activated charge carriers and mid-infrared optical excitations in quarter-filled CDW systems

The optical properties of the quarter-filled single-band CDW systems have been reexamined in the model with the electron-phonon coupling related to the variations of electron site energies. It appears that the indirect, electron-mediated coupling between phase phonons and external electromagnetic fields vanishes for symmetry reasons, at variance with the infrared selection rules used in the generally accepted microscopic theory. It is shown that the phase phonon modes and the electric fields couple directly, with the coupling constant proportional to the magnitude of the charge-density wave. The single-particle contributions to the optical conductivity tensor are determined for the ordered CDW state and the related weakly doped metallic state by means of the Bethe--Salpeter equations for elementary electron-hole excitations. It turns out that this gauge-invariant approach establishes a clear connection between the effective numbers of residual, thermally activated and bound charge carriers. Finally, the relation between these numbers and the activation energy of dc conductivity and the optical CDW gap scale is explained in the way consistent with the conductivity sum rules.Comment: 12 pages, 9 figure

Effective numbers of charge carriers in doped graphene: The generalized Fermi liquid approach

The single-band current-dipole Kubo formula for the dynamical conductivity of heavily doped graphene from Kup\v{c}i\'{c} [Phys. Rev. B 91, 205428 (2015)] is extended to a two-band model for conduction $\pi$ electrons in lightly doped graphene. Using a posteriori relaxation-time approximation in the two-band quantum transport equations, with two different relaxation rates and one quasi-particle lifetime, we explain a seemingly inconsistent dependence of the dc conductivity $\sigma^{\rm dc}_{\alpha \alpha}$ of ultraclean and dirty lightly doped graphene samples on electron doping, in a way consistent with the charge continuity equation. It is also shown that the intraband contribution to the effective number of conduction electrons in $\sigma^{\rm dc}_{\alpha \alpha}$ vanishes at $T=0$ K in the ultraclean regime, but it remains finite in the dirty regime. The present model is shown to be consistent with a picture in which the intraband and interband contributions to $\sigma^{\rm dc}_{\alpha \alpha}$ are characterized by two different mobilities of conduction electrons, the values of which are well below the widely accepted value of mobility in ultraclean graphene. The dispersions of Dirac and $\pi$ plasmon resonances are reexamined to show that the present, relatively simple expression for the dynamical conductivity tensor can be used to study simultaneously single-particle excitations in the dc and optical conductivity and collective excitations in energy loss spectroscopy experiments.Comment: 13 pages, 11 figure

Electronic Raman scattering in a multiband model for cuprate superconductors

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 (assisted) scattering on the quasi-static 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 quasi-static fluctuations around the static antiferromagnetic (AF) 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.Comment: 18 pages, 14 figures; to appear in Phys. Rev.

Transport, magnetic and superconducting properties of RuSr2RCu2O8 (R= Eu, Gd) doped with Sn

Ru{1-x}Sn{x}Sr2EuCu2O8 and Ru{1-x}Sn{x}Sr2GdCu2O8 have been comprehensively studied by microwave and dc resistivity and magnetoresistivity and by the dc Hall measurements. The magnetic ordering temperature T_m is considerably reduced with increasing Sn content. However, doping with Sn leads to only slight reduction of the superconducting critical temperature T_c accompanied with the increase of the upper critical field B_c2, indicating an increased disorder in the system and a reduced scattering length of the conducting holes in CuO2 layers. In spite of the increased scattering rate, the normal state resistivity and the Hall resistivity are reduced with respect to the pure compound, due to the increased number of itinerant holes in CuO2 layers, which represent the main conductivity channel. Most of the electrons in RuO2 layers are presumably localized, but the observed negative magnetoresistance and the extraordinary Hall effect lead to the conclusion that there exists a small number of itinerant electrons in RuO$_2$ layers that exhibit colossal magnetoresistance.Comment: 10 pages, 9 figure