Possible zero sound in layered perovskites with ferromagnetic ss-dd exchange interaction

We analyze the conditions for observation of zero sound in layered perovskites with transition metal ion on chalcogenide oxidizer. We conclude that propagation of zero sound is possible only for anti-ferromagnetic sign of the $s$-$d$ interaction. If the $s$-$d$ exchange integral $J_{sd}$ has antiferromagnetic sign, as it is perhaps in the case for layered cuprates, zero sound is a thermally activated dissipation mode,which generates only "hot spots" in the Angle Resolved Photoemission Spectroscopy (ARPES) data along the Fermi contour. We predict that zero sound will be observable for transition metal perovskites with 4$s$ and 3$d$ levels close to the $p$-level of the chalcogenide. The simultaneous lack of superconductivity, the appearance of hot spots in ARPES data, and the proximity of the three named levels, represents the significant hint for the choice of material to be investigated.Comment: 7 pages, 4 figures, 30 reference

Hot spots along the Fermi contour of high-TcT_c cuprates analyzed by ss-dd exchange interaction

We perform a thorough theoretical study of the electron properties of a generic CuO$_2$ plane in the framework of Shubin-Kondo-Zener $s$-$d$ exchange interaction that simultaneously describes the correlation between $T_c$ and the Cu4$s$ energy. To this end, we apply the Pokrovsky theory [J. Exp. Theor. Phys. 13, 447-450 (1961)] for anisotropic gap BCS superconductors. It takes into account the thermodynamic fluctuations of the electric field in the dielectric direction perpendicular to the conducting layers. We microscopically derive a multiplicatively separable kernel able to describe the scattering rate in the momentum space, as well as the superconducting gap anisotropy within the BCS theory. These findings may be traced back to the fact that both the Fermi liquid and the BCS reductions lead to one and the same reduced Hamiltonian involving a separable interaction, such that a strong electron scattering corresponds to a strong superconducting gap and vice versa. Moreover, the superconducting gap and the scattering rate vanish simultaneously along the diagonals of the Brillouin zone. We would like to stress that our theoretical study reproduces the phenomenological analysis of other authors aiming at describing Angle Resolved Photoemission Spectroscopy measurements. Within standard approximations one and the same $s$-$d$ exchange Hamiltonian describes gap anisotropy of the superconducting phase and the anisotropy of scattering rate of charge carriers in the normal phase.Comment: 10 pages, 3 figures, 56 reference