Spin Excitation in d-wave Superconductors: A Fermi Liquid Picture

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A detailed study of the Inelastic Neutron Scattering (INS) spectra of the high-Tc cuprates based on the Fermi liquid (FL) picture is given. We focus on the issue of the transformation between the commensurate and incommensurate (IC) excitation driven by frequency or temperature. For La₂₋ₓSrₓCuO₄ (LSCO), the condition of small Δ(0)/vF a (where a is the lattice constant, and henceforth will be set to 1) can simultaneously reproduces the always existing IC peaks in the superconducting (SC) and normal state, and the always fixed location at temperature or frequency change. For YBa₂Cu₃O₆₊ₓ (YBCO), a moderate Δ(0)/vF a and proximity of the van Hove singularity (vHS) at M=(0,π) to the Fermi level can reproduce the frequency- and temperature-driven shifting IC peaks in the SC state, and the vanishing of the IC peak in the normal state. The commensurate peak is found to be more appropriately described as a random phase approximation (RPA) effect. We address the conditional peak shifting behavior to a refined consideration on the nesting effect which is previously overlook. As a result, both the data on LSCO and the recent data on YBCO (on YBa₂Cu₃O₆.₇ by Arai et al. and YBa₂Cu₃O₆.₈₅ by Bourges et al.) can be reasonably reconciled within a FL picture. We also point out that the one-dimensional-like data by Mook et al. on a detwinned and more underdoped sample YBa₂Cu₃O₆.₆ could be due to a gap anisotropy effect discussed by Rendell and Carbotte, and we proceed to suggest a way of clarifying it.