Effect of the higher d-wave gap harmonics and possible s -wave component on spin dynamics in electron-doped high-TcTc superconductors

In this paper, we examine the effect on spin dynamics of three kinds of possible superconducting (SC) gap in electron-doped high-TcTc systems, that is, the dx2-y2dx2-y2-wave, the mixed dx2-y2+higherdx2-y2+higherd  -wave harmonics (cos(6ϕ))(cos(6ϕ)), and the dx2-y2+isdx2-y2+is-wave. Starting from the slave-boson mean-field approach to the t-t′-Jt-t′-J model, a higher d-wave gap term and an is  -wave component are included in a phenomenological form, respectively. With the random-phase approximation (RPA), we present a detailed analysis of the momentum, frequency and doping dependence of the spin susceptibility. It is found that at low frequencies, the spin response is commensurate in the SC state and there is a crossover frequency ωcωc above which the spin response begins to be incommensurate, and the crossover frequency ωcωc increases with doping. So the dispersion of the excitation is different from the hole-doped cuprates, in which a hourglass-like dispersion is observed. We also find that a spin resonance appears in the underdoped and optimally doped regime. These similar characters for the three kinds of superconducting gap suggest the underlying importance of Fermi surface (FS) topology. On the other hand, the incommensurate spin fluctuation at high frequencies is found to exhibit a ring structure around (π,π)(π,π) for the mixed cos(2ϕ)+cos(6ϕ)cos(2ϕ)+cos(6ϕ)-wave, while others show maxima along the (π,π+δπ)(π,π+δπ) and its symmetric directions. Below ωcωc, the spin response remains to be commensurate all along to the lowest frequency for the dx2-y2+isdx2-y2+is-wave, while the others cross to a small incommensurate structure with further decreasing the frequency. These may be taken to probe the possible subdominant SC components.