  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.
