Shadow features and shadow bands in the paramagnetic state of cuprate superconductors

The conditions for the precursors of antiferromagnetic bands in cuprate superconductors are studied using a weak-to-intermediate coupling approach. It is shown that there are, in fact, three different precursor effects due to the proximity to antiferromagnetic instability: (i) the shadow band which is associated with a pole in the Green's function, (ii) the dispersive shadow feature due to the thermal enhancement of the scattering rate, and (iii) the nondispersive shadow feature due to quantum spin fluctuation that exists only in a k-→ scan of the spectral function A(${\mathrm{\omega }}_{\mathrm{fixed}}$,k-→). I found that dispersive shadow peaks in A(ω,k-→) can exist at finite temperature T in the renormalized classical regime, when T≫:${\mathrm{\omega }}_{\mathrm{sf}}$, ${\xi }_{\mathrm{AFM}}$>${\xi }_{\mathrm{th}}$=${\mathrm{v}}_{\mathrm{F}}$/T (${\mathrm{\omega }}_{\mathrm{sf}}$ is the characteristic energy of spin fluctuations, ${\xi }_{\mathrm{th}}$ is the thermal wavelength of electron). In contrast at zero temperature, only a nondispersive shadow feature in A(${\mathrm{\omega }}_{\mathrm{fixed}}$,k-→) has been found. I found, however, that the latter effect is always very small. The theory predicts no shadow effects in the optimally doped materials. The conditions for which shadow peaks can be observed in photoemission are discussed.