Vanishing pseudogap around $(\pi,0)$ in an electron-doped high-$\mathrm{T_{c}}$ superconductor: a simple picture

Abstract

Recent ARPES measurement on electron-doped cuprate $\mathrm{Pr}_{1.3-x}\mathrm{La}_{0.7}\mathrm{Ce}_{x}\mathrm{CuO}_{4}$ finds that the pseudogap along the boundary of the antiferromagnetic Brillouin zone(AFBZ) exhibits dramatic momentum dependence. In particular, the pseudogap vanishes in a finite region around the anti-nodal point, in which a single broadened peak emerges at the un-renormalized quasiparticle energy. Such an observation is argued to be inconsistent with the antiferromagnetic(AFM) band-folding picture, which predicts a constant pseudogap along the AFBZ boundary. On the other hand, it is claimed that the experimental results are consistent with the prediction of the cluster dynamical mean field theory(CDMFT) simulation on the Hubbard model, in which the pseudogap is interpreted as a s-wave splitting between the Hubbard bands and the in-gap states. Here we show that the observed momentum dependence of the pseudogap is indeed consistent with AFM band-folding picture, provided that we assume the existence of a strongly momentum dependent quasiparticle scattering rate. More specifically, we show that the quasiparticle scattering rate acts to reduce the spectral gap induced by AFM band-folding effect. The new quasiparticle poles corresponding to the AF-split bands can even be totally eliminated when the scattering rate exceeds the bare band folding gap, leaving the system with a single pole at the un-renormalized quasiparticle energy. We predict that the pseudogap should close in a square root fashion as we move toward $(\pi,0)$ along the AFBZ boundary. Our results illustrates again that the quasiparticle scattering rate can play a much more profound role than simply broadening the quasiparticle peak in the quasiparticle dynamics of strongly correlated electron systems.