The recent observation of dipole-allowed P -excitons up to principal quantum numbers of n = 25 in cuprous oxide has given insight into exciton states with unprecedented spectral resolution. While so far the exciton description as a hydrogen-like complex has been sufficient for cubic crystals, we demonstrate here distinct deviations: The breaking of rotational symmetry leads to mixing of high angular momentum F -and H-excitons with the P -excitons so that they can be observed in absorption. The F -excitons show a three-fold splitting that depends systematically on n, in agreement with theoretical considerations. From detailed comparison of experiment and theory we determine the cubic anisotropy parameter of the Cu2O valence band. PACS numbers:Introduction. Excitonic effects are decisive for the optical properties of semiconductors and insulators [1]. Not only leads the Coulomb interaction between an electron and a hole to a series of bound states, the excitons, with energies below the band gap, but also above the gap the Coulomb effects lead to a massive redistribution of oscillator strength towards the low-energy states compared to a free particle description. Due to this importance it has been a major goal to develop a detailed understanding of excitons on a quantitative level [1]. The description of the bound exciton states by the hydrogenic model has turned out to be extremely successful in this respect, in particular, for bulk semiconductors of cubic symmetry.For excitons with wavefunction extensions much larger than the crystal unit cell (the Mott-Wannier excitons) the hydrogen formula for their binding energy, R/n 2 with the Rydberg energy R in a state of principal quantum number n, can be simply adapted to the solid state case by (i) changing the reduced mass of electron and proton m to that of electron and hole m * , and (ii) screening the carrier interaction by the dielectric constant ε:The influence of the many-body crystal environment is thus comprised in material properties that for cubic semiconductors are, as a rule, isotropic such as the scalar dielectric constant ε, leading to a formula for excitonic energies that is identical to the one in a system with rotational symmetry. The material environment typically causes a reduction of the atomic Rydberg energy by 2 − 3 orders of magnitude into the meV range.For the hydrogen problem the spatial symmetry is determined by the continuous rotation group SO(3), where the square of the orbital momentum L 2 = l(l + 1)

Two of the most striking experimental findings when investigating exciton spectra in cuprous oxide using high-resolution spectroscopy are the observability and the fine structure splitting of F excitons reported by J. Thewes et al. [Phys. Rev. Lett. 115, 027402 (2015)]. These findings show that it is indispensable to account for the complex valence band structure and the cubic symmetry of the solid in the theory of excitons. This is all the more important for magnetoexcitons, where the external magnetic field reduces the symmetry of the system even further. We present the theory of excitons in Cu2O in an external magnetic field and especially discuss the dependence of the spectra on the direction of the external magnetic field, which cannot be understood from a simple hydrogen-like model. Using high-resolution spectroscopy, we also present the corresponding experimental spectra for cuprous oxide in Faraday configuration. The theoretical results and experimental spectra are in excellent agreement as regards not only the energies but also the relative oscillator strengths. Furthermore, this comparison allows for the determination of the fourth Luttinger parameter κ of this semiconductor.

Recent high-resolution absorption spectroscopy on excited excitons in cuprous oxide [Nature 514, 343 (2014)] has revealed significant deviations of their spectrum from that of the ideal hydrogenlike series. Here we show that the complex band dispersion of the crystal, determining the kinetic energies of electrons and holes, strongly affects the exciton binding energies. Specifically, we show that the nonparabolicity of the band dispersion is the main cause of the deviation from the hydrogen series. Experimental data collected from high-resolution absorption spectroscopy in electric fields validate the assignment of the deviation to the nonparabolicity of the band dispersion.

Rydberg atoms have attracted considerable interest due to their huge interaction among each other and with external fields. They demonstrate characteristic scaling laws in dependence on the principal quantum number $n$ for features such as the magnetic field for level crossing. While bearing striking similarities to Rydberg atoms, fundamentally new insights may be obtained for Rydberg excitons, as the crystal environment gives easy optical access to many states within an exciton multiplet. Here we study experimentally and theoretically the scaling of several characteristic parameters of Rydberg excitons with $n$. From absorption spectra in magnetic field we find for the first crossing of levels with adjacent principal quantum numbers a $B_r \propto n^{-4}$ dependence of the resonance field strength, $B_r$, due to the dominant paramagnetic term unlike in the atomic case where the diamagnetic contribution is decisive. By contrast, in electric field we find scaling laws just like for Rydberg atoms. The resonance electric field strength scales as $E_r \propto n^{-5}$. We observe anticrossings of the states belonging to multiplets with different principal quantum numbers. The energy splittings at the avoided crossings scale as $n^{-4}$ which we relate to the crystal specific deviation of the exciton Hamiltonian from the hydrogen model. We observe the exciton polarizability in the electric field to scale as $n^7$. In magnetic field the crossover field strength from a hydrogen-like exciton to a magnetoexciton dominated by electron and hole Landau level quantization scales as $n^{-3}$. The ionization voltages demonstrate a $n^{-4}$ scaling as for atoms. The width of the absorption lines remains constant before dissociation for high enough $n$, while for small $n \lesssim 12$ an exponential increase with the field is found. These results are in excellent agreement with theoretical calculations.Comment: 16 pages, 13 figure

We study the Rydberg exciton absorption of Cu_{2}O in the presence of free carriers injected by above-band-gap illumination. Already at plasma densities ρ_{EH} below one hundredth electron-hole pair per μm^{3}, exciton lines are bleached, starting from the highest observed principal quantum number, while their energies remain constant. Simultaneously, the band gap decreases by correlation effects with the plasma. An exciton line loses oscillator strength when the band gap approaches its energy, vanishing completely at the crossing point. Adapting a plasma-physics description, we describe the observations by an effective Bohr radius that increases with rising plasma density, reflecting the Coulomb interaction screening by the plasma.