Excitons in insulating cuprates

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 $p_{\pi }$ 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 $t-J$ model, the excitonic states of the insulator include hybrid $d_{\mathrm{xy}}-p_{\pi }$ 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.