Electronic Raman scattering intensity in layered high-T_c superconductors: threshold energy, symmetry and anisotropy of energy gap

Abstract

At very low temperatures, low-frequency electronic Raman scattering in a superconductor arises from pair-breaking excitations across the energy gap. In principle, this allows the possible determination of the nature of the energy gap, including its symmetry. To examine this carefully, a simplified general expression was derived for the electronic Raman scattering intensity, suitable for high-T_c layered superconductors with widely open Fermi surfaces in the k_z direction, perpendicular to the k_x, k_y reciprocal layer plane. The unscreened part of the single-particle scattering from both charge-density fluctuations (CDF) and spin-density fluctuations (SDF) was taken into account. The shape of the resulting electronic Raman spectrum depends crucially on the directions of the incident and scattered light polarizations, e_i and e_s, the wavevector transfer q=q_i-q_s, the nature of constant normal-state single-particle energy surfaces near the Fermi energy and the form of the energy gap function Δ(k). A careful analysis of the results for different symmetries of the gap function Δ and interaction vertex functions |Y ^CDF| and |Y ^SDF|, averaged over k_z, for the tetragonal D_4hpoint group, showed that currently available experimental data for different high-T_c cuprates do not allow one to determine the symmetry of the gap function uniquely. Although d_x²_-y² symmetry for the gap function in these materials may be a strong possibility, a highly anisotropic s-wave type gap function cannot be ruled out completely.