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

Photoemission spectra of underdoped and lightly-doped ${\mathrm{Bi}}_{2-z}{\mathrm{Pb}}_z{\mathrm{Sr}}_2{\mathrm{Ca}}_{1-x}{R}_x{\mathrm{Cu}}_2{\mathrm{O}}_{8+y}$ ($R=\mathrm{Pr}$, $\mathrm{Er}$) (BSCCO) have been measured and compared with those of ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ (LSCO). The lower-Hubbard band of the insulating BSCCO, like ${\mathrm{Ca}}_2{\mathrm{CuO}}_2{\mathrm{Cl}}_2$, shows a stronger dispersion than ${\mathrm{La}}_2{\mathrm{CuO}}_4$ from $\mathbf{k}\sim \left(\pi ∕2,\pi ∕2\right)$ to $\sim \left(\pi ,0\right)$. The flat band at $\mathbf{k}\sim \left(\pi ,0\right)$ 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 $\mid t^{\prime }\mid$ of the single-band model is larger in BSCCO than in LSCO and that $\mid t^{\prime }\mid$ rather than the super-exchange $J$ influences the pseudogap energy scale.

Figure 1

ARPES spectra of insulating ${\mathrm{Bi}}_{1.2}{\mathrm{Pb}}_{0.8}{\mathrm{Sr}}_2{\mathrm{ErCu}}_2{\mathrm{O}}_8$ along the (0,0)-$\left(\pi ,\pi \right)$ direction. (a) EDC’s, (b) intensity plot in the $E\text{−}k$ plane. The white circles indicate the energy of the maximum curvature in the EDC’s.

Figure 2

ARPES spectra of ${\mathrm{Bi}}_{1.2}{\mathrm{Pb}}_{0.8}{\mathrm{Sr}}_2{\mathrm{ErCu}}_2{\mathrm{O}}_8$ along the “underlying Fermi surface” in the second BZ. (a) EDC’s. (b) Intensity plot in the $E\text{−}k$ plane. Vertical bars in (a) and the white circles in (b) indicate the points of maximum curvature in the EDC’s. (c) Peak positions referenced to the binding energy of the peak at $\left(\pi ∕2,\pi ∕2\right)$ plotted against $\mid \cos k_{x}a-\cos k_{y}a\mid ∕2$. Also plotted are data for ${\mathrm{La}}_2{\mathrm{CuO}}_4$ (LCO) and ${\mathrm{Ca}}_2{\mathrm{CuO}}_2{\mathrm{Cl}}_2$ (CCOC) (Ref. 23).

Figure 3

AIPES spectra (solid curve) and ARPES spectra at $\left(\pi ,0\right)$ (dashed curve) for various doping levels in BSCCO (a) and LSCO (b). Solid vertical bars indicate the point of maximum curvature and the dashed vertical bars mark the position of the flat band $E\left(\pi ,0\right)$ (BB and AB at higher and lower binding energies, respectively, for BSCCO). ARPES data for BSCCO with $\delta ⩾0.1$ was taken from Refs. 27, 28, 29.

Figure 4

Doping dependence of the flat band position $E\left(\pi ,0\right)$ in BSCCO and LSCO determined by the second derivatives of AIPES spectra (squares) and ARPES spectra (triangles). The average energy position of BB and AB, $\overline{\mid E\left(\pi ,0\right)\mid }$, for BSCCO (diamond) and $T_c$ (circle) are also shown.