Fine structure of Rydberg excitons in cuprous oxide

In 1952, E.F. Gross and N.A. Karryev discovered excitons of big radius also called the Wannier–Mott excitons. Their energy spectrum, response to external electric and magnetic fields, and also elastic deformations of a crystal were extensively studied in the 1960s–1970s. The second wave of interest to excitons in Cu$_2$O crystals appeared comparatively recent, in 2014, after the “giant” highly excited exciton states had been observed in this material. A theoretical description of highly excited exciton states needs, as a rule, new approaches, because, for such states, a deviation from the exactly solved hydrogen-like model becomes substantial and a numerical solution of the Schrödinger equation with allowance made for the features of the crystal energy band structure becomes extremely resource consuming. This report is a brief review of recent theoretical and experimental studies of the fine structure of the exciton energy spectrum in copper protoxide.