Excitons in insulating cuprates

Abstract

We study the electronic excitations near the charge-transfer gap in insulating Cu${\mathrm{O}}_{2}$ planes, starting from a six-band model which includes ${p}_{\ensuremath{\pi}}$ and ${d}_{\mathrm{xy}}$ orbitals and Cu-O nearest-neighbor repulsion ${U}_{\mathrm{pd}}$. While the low-lying electronic excitations in the doped system are well described by a modified $t\ensuremath{-}J$ model, the excitonic states of the insulator include hybrid ${d}_{\mathrm{xy}}\ensuremath{-}{p}_{\ensuremath{\pi}}$ states of ${A}_{2g}$ symmetry. We also obtain excitons of symmetries ${B}_{1g}$ and ${E}_{u}$, and eventually ${A}_{1g}$, which can be explained within a one-band model. The results agree with observed optical absorption and Raman excitations.