Quasiparticle energy dispersion in doped two-dimensional quantum antiferromagnets

The quasiparticle dispersion in the one-hole $t-t^{\prime }-t^{\prime \prime }-J$ model is studied. Both finite-size diagonalization and the self-consistent Born-approximation calculations have been performed and compared. The quasiparticle band structures in the hole- and electron-doped high-$T_c$ cuprates are qualitatively different. In the hole-doped compounds, the band maxima are located at ($\pm \frac{\pi }{2}, \pm \frac{\pi }{2}$), while in the electron-doped compounds the band maxima are located at ($\pi , 0$) and its equivalent points. The angle-resolved photoemission data for the quasiparticle dispersion of ${\mathrm{Sr}}_2$Cu${\mathrm{O}}_2$ ${\mathrm{Cl}}_2$ can be quantitatively reproduced using the one-band $t-t^{\prime }-t^{\prime \prime }-J$ model with the three-site hopping term.