Chemical potential shift in lightly-doped to overdoped   Bi$_2$Sr$_2$Ca$_{1-x}${\it R}$_{x}$Cu$_2$O$_{8+y}$ ({\it R} = Pr, Er)
  We have studied the chemical potential shift in the high-temperature superconductor Bi$_2$Sr$_2$Ca$_{1-x}${\it R}$_{x}$Cu$_2$O$_{8+y}$ ({\it R} = Pr, Er), where the hole concentration is varied from 0.025 to 0.17 per Cu, by precise measurements of core-level photoemission spectra. The result shows that the shift becomes slow in the underdoped region as in the case of La$_{2-x}$Sr$_{x}$CuO$_{4}$ (LSCO) but the effect is much weaker than in LSCO. The observed shift in the present system can be relatively well explained by numerical results on the doped two-dimensional Hubbard model, and suggests that the change of the electronic structure induced by hole doping is less influenced by stripe fluctuations than in LSCO. 
N. Harima, A. Fujimori, T. Sugaya and I. Terasaki