  Charge dynamics and its critical behavior are investigated near the
metal-insulator transition of layered-nickelate R2-xSrxNiO4 (R=Nd, Eu). The
polarized x-ray absorption spectroscopy experiment clearly shows the
multi-orbital nature which enables the x2-y2-orbital-based checkerboard-type
charge ordering or correlation to persist up to the critical doping region (x
sim 1). In the barely metallic region proximate to the charge-ordered
insulating phase, the nominal carrier density estimated from the Hall
coefficient markedly decreases in accord with development of the pseudogap
structure in the optical conductivity spectrum, while the effective mass is
least enhanced. The present findings combined with the results of recent
angle-resolved photoemission spectroscopy show that the pseudogap in the
metal-insulator critical state evolves due to the checkerboard-type charge
correlation to extinguish the coherent-motion carriers in a characteristic
momentum (k)-dependent manner with lowering temperature.
