Theory of excitons in the insulatingCu−O2plane

Abstract

We use a local model to study the formation and the structure of the low-energy charge-transfer excitations in the insulating ${\mathrm{C}\mathrm{u}\ensuremath{-}\mathrm{O}}_{2}$ plane. The elementary excitation is a bound exciton of spin singlet, consisting of a ${\mathrm{Cu}}^{+}$ and a neighboring spin singlet of Cu-O holes. The exciton can move through the lattice freely without disturbing the antiferromagnetic spin background, in contrast to the single hole motion. There are four eigenmodes of excitons with different symmetry. The $p$-wave-like exciton has a large dispersion width. The $s$-wave-like exciton mixes with the $p$ state at finite momentum, and its dipole transition intensity is strongly anisotropic. The model is in excellent agreement with the electron energy-loss spectra in the insulating ${\mathrm{Sr}}_{2}{\mathrm{CuO}}_{2}{\mathrm{Cl}}_{2}.$