Recent measurements of higher levels n > 5 under magnetic fields up to 7 T compared the scaling of features in absorption spectra of Rydberg excitons in external fields to those of a hydrogen atom. The magnetoabsorption spectra of excitons in Cu 2O were extensively studied over the past decades 11, 14– 18. Further information can be obtained from the splitting of excitonic levels in applied electric or magnetic fields. Optical absorption spectra measured in zero fields give information about the excitonic Rydberg constant and the reduced mass of the electron-hole pair. In this paper we address these issues and resolve the discrepancy using high-resolution measurements of the low-energy magneto-optical absorption spectra of Cu 2O combined with numerical calculations of the spectra in the intermediate magnetic field regime. In addition, a detailed interpretation of the magneto-optical spectra is still lacking 14– 16. For example, there is a siginificant discrepancy between the effective masses of electrons and holes deduced from the optical measurements 11, 12 and the cyclotron resonance experiments 13. Despite the recent progress 3, 10, a number of fundamental problems, surprisingly, remain unsolved. These studies underscored the importance of a quantitative description of excitons in this material. GW and Bethe-Salpeter calculations, for which Cu 2O serves as an important benchmark system. ![]() The revival of interest in Cu 2O was motivated by the search for the Bose-Einstein condensation of the exciton gas 4– 8 and rapid developments of ab-initio methods 9, e.g. ![]() The corrections to the binding energy of the higher levels, produced by these mechanisms, are negligible. Due to the small size of the n = 1 exciton, its energy is strongly affected by exchange, central cell corrections and reduced screening of the Coulomb interaction 3. The only exception is the n = 1 exciton, which is dipole forbidden as the valence and conduction bands of this material have the same parity 2. These states give rise to hydrogen-like series of absorption lines in the optical absorption spectrum of Cu 2O at the photon energies described by the Rydberg formula, E n = E gap − Ry X/ n 2, where Ry X = 98 meV is the excitonic Rydberg constant and E gap = 2.17 eV is the optical gap. Focusing effects associated with these bifurcations cause some recurrences to be particularly strong.Cuprous oxide Cu 2O was the first material in which Wannier-Mott excitons 1 – the electron-hole pairs bound by the Coulomb interaction – were observed. These bifurcations can have generic structure, or sometimes the structures are modified by symmetries of the system. Other recurrences are created by period-tripling and higher-order bifurcations of existing orbits. The "main sequence" of orbits is produced from an orbit parallel to B through a sequence of pitchfork and period-doubling bifurcations. New "exotic" orbits suddenly appear "out of nowhere" through saddle-node bifurcations. Bifurcation theory provides organizing principles for understanding this proliferation and for interpreting the data. as the scaled energy is increased, observed recurrences proliferate, consistent with the change from orderly to chaotic motion of the electron. Closed-orbit theory gives formulas for these recurrence strengths. A Fourier transformation of this signal yields peaks which we interpret as "recurrence strengths" which depend upon the classical action of the closed orbit. ![]() The absorption rate was observed to exhibit sinusoidal fluctuations which we correlate with closed classical orbit of the electron. Taking advantage of a classical scaling law, the photon energy and the magnetic field strength were varied simultaneously in the experiment and the absorption rate vs. The measurements, performed by the Bielefeld, Germany experimental group, investigated the photoabsorption to levels near the ionization threshold in magnetic fields ranging from 2.7 to 6 Tesla. Measurements of the absorption spectrum of atomic H in strong magnetic fields have been analyzed.
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