Effects of next-nearest-neighbor hopping $t^{\prime}$ on the electronic structure of cuprates

Photoemission spectra of underdoped and lightly-doped Bi$_{2-z}$Pb$_z$Sr$_2$Ca$_{1-x}${\it R}$_{x}$Cu$_2$O$_{8+y}$ ($R=$ Pr, Er) (BSCCO) have been measured and compared with those of La$_{2-x}$Sr$_x$CuO$_4$ (LSCO). The lower-Hubbard band of the insulating BSCCO, like Ca$_2$CuO$_2$Cl$_2$, shows a stronger dispersion than La$_2$CuO$_4$ from ${\bf k}\sim$($\pi/2,\pi/2$) to $\sim$($\pi,0$). The flat band at ${\bf k}\sim$($\pi,0$) is found generally deeper in BSCCO. These observations together with the Fermi-surface shapes and the chemical potential shifts indicate that the next-nearest-neighbor hopping $|t^{\prime}|$ of the single-band model is larger in BSCCO than in LSCO and that $|t^{\prime}|$ rather than the super-exchange $J$ influences the pseudogap energy scale.