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Spectral Function of Superconducting Cuprates near Optimal Doping

In recent years, the bulk of studies of cuprate superconductors was focused on their unusual normal state properties. Less attention was paid to the behavior of cuprates in the superconducting state. It was generally believed that the superconducting behavior, even in underdoped cuprates, is rather conventional in the sense that most experiments can be explained in the framework of the BCS-type theory for a d-wave superconductor. Recently, however, this belief has been challenged by photoemission experiments on Bi2212 materials [1,2]. These experiments demonstrated that even in slightly overdoped cuprates and at T ? Tc, the spectral function Ask, vd near s0, pd is qualitatively different from the one expected for a conventional superconductor. Specifically, in a conventional case, Ask, vd possesses a single sharp peak at v › p D 2 1e 2 where Dk is the superconducting gap and ek is the fermionic dispersion. The photoemission data for Bi2212 do show a sharp quasiparticle peak near the Fermi surface, but they also reveal two extra features in Ask, vd: a dip at frequencies right above the peak and a broad maximum (hump) at somewhat larger frequencies. Moreover, as one moves away from the Fermi surface, the sharp peak looses its intensity but does not disperse, while the position of the hump varies with k and gradually recovers the normal state dispersion. Several phenomenological theories [1,3] identified the sharp peak observed in photoemission below Tc as a dispersionless collective mode of yet unknown origin. In the present Letter, we present an alternative explanation of the photoemission data. We argue that the unusual superconducting properties of cuprates can be explained by a strong interaction between electrons and overdamped spin fluctuations peaked at some momentum Q near sp, pd [4]. Similar arguments were earlier displayed by Grabowski et al. [5] who found peak-dip-hump features in their numerical study of the Hubbard model within the fluctuation exchange approximation. Our results qualitatively agree with theirs; however, we consider the problem analytically and present a physical explanation of the effect. Specifically, we show that the peak/dip/hump features in the spectral function emerge as a combination of two effects: (i) an almost complete destruction of the Fermi-liquid behavior in the normal state, which eliminates the quasiparticle peak and gives rise to a hump in the spectral function at higher frequencies, and (ii) a reduction of the spin damping at small frequencies in the superconducting state which, as a