Dispersion relations and density of states of the collective oscillations of the electronic dipoles in high-Tc superconductors.

Abstract

Previously we have suggested the collective oscillations of the crystal-field-generated electronic dipoles on oxygen ions as a possible excitation responsible for the electron-electron (or hole-hole) pairing mechanism in high-${\mathit{T}}_{\mathit{c}}$ superconductivity. These self-sustained collective dipole excitations are expected to exist in the high-${\mathit{T}}_{\mathit{c}}$ superconductors. We have investigated these excitations by performing first-principles calculations of the dispersion relations and the density of states associated with these excitations in several high-${\mathit{T}}_{\mathit{c}}$ superconductors (${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$, ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$, ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{CuO}}_{6}$, ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{CaCu}}_{2}$${\mathrm{O}}_{8}$, ${\mathrm{Tl}}_{2}$${\mathrm{Ba}}_{2}$${\mathrm{CaCu}}_{2}$${\mathrm{O}}_{8}$, and ${\mathrm{Tl}}_{2}$${\mathrm{Ba}}_{2}$${\mathrm{Ca}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{10}$) including the cases of a single dipole and those of a linear and a planar system of dipoles in a uniform field as illustrative examples. The absence of inversion symmetry at the oxygen sites and the high polarizability of the atoms such as oxygens are found to be necessary for the existence of these quantized collective dipole excitations.Our calculations show good consistency between the existence of superconductivity and the presence of such collective dipole oscillations in the conducting planes of the high-${\mathit{T}}_{\mathit{c}}$ superconductor crystals, as expected by our earlier explanation of the variation in ${\mathit{T}}_{\mathit{c}}$ versus \ensuremath{\delta} in ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ by the same mechanism. The associated frequencies characteristic of these excitations in the conducting planes in all high-${\mathit{T}}_{\mathit{c}}$ superconductors are found to be of the order of ${10}^{14}$ Hz as predicted previously. Furthermore, the variation of these characteristic excitation frequencies in ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ as a function of the oxygen-stoichiometry parameter \ensuremath{\delta} has been found to agree with our previous deductions. The density of states of these collective dipole excitations show broader bandwidth, unlike the case of excitons. The present mechanism is likely to be a good candidate to explain many observed features of the high-${\mathit{T}}_{\mathit{c}}$ superconductors, particularly the optical properties. For the ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ system, our calculated density of states predicts two optical absorption peaks, one at 0.36 eV and another at 2.5 eV, which compare very well with the observed peaks close to 0.37 and 2.5 eV, respectively.Similarly for the ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Ba}}_{\mathit{x}}$${\mathrm{CuO}}_{4}$ system, our predicted peaks are at 0.17 and 1 eV, which are also in agreement with the observed peaks around 0.18 and 1.3 eV, respectively. The existence of similar peaks due to these collective dipole excitations in the other superconductors has been predicted. The optical absorption peaks at frequencies around 1\ifmmode\times\else\texttimes\fi{}${10}^{14}$ Hz with broad bandwidth are expected to be observed in all high-${\mathit{T}}_{\mathit{c}}$ oxide superconductors. The possibility of explaining other important properties via this collective dipole mechanism, such as the pressure effect and the isotope effect observed in the high-${\mathit{T}}_{\mathit{c}}$ superconductors, has been discussed.