Rydberg Series of Dark Excitons in Cu 2 O

We demonstrate the Rydberg series of dark excitons, known as paraexcitons, up to the principal quantum number $n=6$ for the yellow exciton series in ${\mathrm{Cu}}_{2}\mathrm{O}$, using second harmonic generation. Each of these states is optically inactive to all orders, but their observation becomes possible by application of a magnetic field which leads to mixing with the quadrupole-allowed bright excitons, called orthoexcitons, of the same $n$. The dark parastates are generally located below the bright orthostates, whose energies are increased by the electron-hole exchange interaction, except for $n=2$, where this order is reversed. This inversion occurs due to band mixing, namely, of the $2{S}_{y,o}$ orthoexciton of the yellow series with the $1{S}_{g,o}$ orthoexciton of the green exciton series.