<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>K</mml:mi></mml:math>-dependent exchange interaction of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>1</mml:mn><mml:mi>S</mml:mi></mml:mrow></mml:math>orthoexciton in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Cu</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:math>

Schweiner, Frank; Main, Jörg; Uihlein, Ch.

doi:10.1103/physrevb.94.115201

Cited by 13 publications

(25 citation statements)

References 38 publications

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“…Even though the applied magnetic field breaks timereversal invariance, at least one antiunitary symmetry, e.g., time reversal and a certain parity, remains and GOE statistics is observed [1,22,23].Excitons are fundamental quasi-particles in semiconductors, which consist of an electron in the conduction band and a positively charged hole in the valence band.Recently, T. Kazimierczuk et al [24] have shown in a remarkable high-resolution absorption experiment an almost perfect hydrogen-like absorption series for the yellow exciton in cuprous oxide (Cu 2 O) up to a principal quantum number of n = 25. This experiment has drawn new interest to the field of excitons experimentally and theoretically [25][26][27][28][29][30][31][32][33][34][35].Since excitons in semiconductors are often treated as the hydrogen analog of the solid state but also show substantial deviations from this behavior due to the surrounding solid, the question about their level spacing statistics in external fields arises. First experimental investigations of the level spacing statistics in an external magnetic field give indications on a breaking of antiunitary symmetries, which is, however, attributed to the interaction of excitons and phonons [31].Very recently, we have shown that it is indispensable to account for the complete valence band structure of Cu 2 O in a quantitative theory of excitons [28] to explain the striking experimental findings of a fine structure splitting and the observability of F excitons [25].…”

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Magnetoexcitons Break Antiunitary Symmetries

Schweiner

Main

2017

Phys. Rev. Lett.

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We show analytically and numerically that the application of an external magnetic field to highly excited Rydberg excitons breaks all antiunitary symmetries in the system. Only by considering the complete valence band structure of a direct band gap cubic semiconductor, the Hamiltonian of excitons leads to the statistics of a Gaussian unitary ensemble (GUE) without the need for interactions with other quasi-particles like phonons. Hence, we give theoretical evidence for a spatially homogeneous system breaking all antiunitary symmetries.PACS numbers: 05.30.Ch, 78.40.Fy, For more than 100 years one distinguishes in classical mechanics between two fundamentally different types of motion: regular and chaotic motion. Their appearance strongly depends on the presence of underlying symmetries, which are connected with constants of motion and reduce the degrees of freedom in a given system. If symmetries are broken, the classical dynamics often becomes nonintegrable and chaotic. However, since the description of chaos by trajectories and Lyapunov exponents is not possible in quantum mechanics, it has been unknown for a long time how classical chaos manifests itself in quantum mechanical spectra [1,2].The Bohigas-Giannoni-Schmit conjecture [3] suggests that quantum systems with few degrees of freedom and with a chaotic classical limit can be described by random matrix theory [4,5] and thus show typical level spacings. At the transition to quantum chaos, the level spacing statistics will change from Poissonian statistics to the statistics of a Gaussian orthogonal ensemble (GOE) or a Gaussian unitary ensemble (GUE) as symmetry reduction leads to a correlation of levels and hence to a strong suppression of crossings [1].To which of the two universality classes a given system belongs is determined by remaining antiunitary symmetries in the system. While GOE statistics can be observed in many different systems like, e.g., in atomic [6,7] and molecular spectra [8], for nuclei in external magnetic fields [9][10][11][12] There is no example for a system showing GUE statistics in atomic physics. This is especially true for one of the prime examples when studying quantum chaos: the highly excited hydrogen atom in strong external fields. Even though the applied magnetic field breaks timereversal invariance, at least one antiunitary symmetry, e.g., time reversal and a certain parity, remains and GOE statistics is observed [1,22,23].Excitons are fundamental quasi-particles in semiconductors, which consist of an electron in the conduction band and a positively charged hole in the valence band.Recently, T. Kazimierczuk et al [24] have shown in a remarkable high-resolution absorption experiment an almost perfect hydrogen-like absorption series for the yellow exciton in cuprous oxide (Cu 2 O) up to a principal quantum number of n = 25. This experiment has drawn new interest to the field of excitons experimentally and theoretically [25][26][27][28][29][30][31][32][33][34][35].Since excitons in semiconductors are often treated as the hydro...

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Magnetoexcitons Break Antiunitary Symmetries

Schweiner

Main

2017

Phys. Rev. Lett.

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“…As we already stated in Ref. [14], a simple restriction to the Γ + 7 band neglecting the Γ + 8 band and considering the nonparabolicity of the Γ + 7 band via p 4 terms as has been done in Ref. [27] does not treat the problem correctly.…”

Section: A Band Structure Of Cu2omentioning

confidence: 99%

“…Recently, the yellow series could be followed up to a spectacular high principal quantum number of n = 25 [2]. This outstanding experiment has launched the new field of research of giant Rydberg excitons and led to a variety of new theoretical and experimental investigations on the topic of excitons in Cu 2 O [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

The even exciton series in Cu$_2$O

Schweiner,

Main,

Wunner

et al. 2017

Preprint

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Recent investigations of excitonic absorption spectra in cuprous oxide (Cu2O) have shown that it is indispensable to account for the complex valence band structure in the theory of excitons. In Cu2O parity is a good quantum number and thus the exciton spectrum falls into two parts: The dipole-active exciton states of negative parity and odd angular momentum, which can be observed in one-photon absorption (Γ − 4 symmetry) and the exciton states of positive parity and even angular momentum, which can be observed in two-photon absorption (Γ + 5 symmetry). The unexpected observation of D excitons in two-photon absorption has given first evidence that the dispersion properties of the Γ + 5 orbital valence band is giving rise to a coupling of the yellow and green exciton series. However, a first theoretical treatment by Ch. Uihlein et al. [Phys. Rev. B 23, 2731] was based on a simplified spherical model. The observation of F excitons in one-photon absorption is a further proof of a coupling between yellow and green exciton states. Detailed investigations on the fine structure splitting of the F exciton by F. Schweiner et al. [Phys. Rev. B 93, 195203 (2016)] have proved the importance of a more realistic theoretical treatment including terms with cubic symmetry. In this paper we show that the even and odd parity exciton system can be consistently described within the same theoretical approach. However, the Hamiltonian of the even parity system needs, in comparison to the odd exciton case, modifications to account for the very small radius of the yellow and green 1S exciton. In the presented treatment we take special care of the central-cell corrections, which comprise a reduced screening of the Coulomb potential at distances comparable to the polaron radius, the exchange interaction being responsible for the exciton splitting into ortho and para states, and the inclusion of terms in the fourth power of p in the kinetic energy being consistent with O h symmetry. Since the yellow 1S exciton state is coupled to all other states of positive parity, we show how the central-cell corrections affect the whole even exciton series. The close resonance of the 1S green exciton with states of the yellow exciton series has a strong impact on the energies and oscillator strengths of all implied states. The consistency between theory and experiment with respect to energies and oscillator strengths for the even and odd exciton system in Cu2O is a convincing proof for the validity of the applied theory.

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“…For states of symmetry Γ + 5 it has been shown in Ref. [25] that the nonanalytic exchange interaction can be written as…”

Section: B 5 × 5 Matrix Modelmentioning

confidence: 99%

Exciton-polaritons in cuprous oxide: Theory and comparison with experiment

et al. 2017

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The observation of giant Rydberg excitons in cuprous oxide (Cu2O) up to a principal quantum number of n = 25 by T. Kazimierczuk et al. [Nature 514, 343, (2014)] inevitably raises the question whether these quasi-particles must be described within a multi-polariton framework since excitons and photons are always coupled in the solid. In this paper we present the theory of excitonpolaritons in Cu2O. To this end we extend the Hamiltonian which includes the complete valence band structure, the exchange interaction, and the central-cell corrections effects, and which has been recently deduced by F. Schweiner et al. [Phys. Rev. B 95, 195201, (2017)], for finite values of the exciton momentum K. We derive formulas to calculate not only dipole but also quadrupole oscillator strengths when using the complete basis of F. Schweiner et al., which has recently been proven as a powerful tool to calculate exciton spectra. Very complex polariton spectra for the three orientations of K along the axes [001], [110], and [111] of high symmetry are obtained and a strong mixing of exciton states is reported. The main focus is on the 1S ortho exciton-polariton, for which pronounced polariton effects have been measured in experiments. We set up a 5 × 5 matrix model, which accounts for both the polariton effect and the K-dependent splitting, and which allows treating the anisotropic polariton dispersion for any direction of K. We especially discuss the dispersions for K being oriented in the planes perpendicular to [110] and [111], for which experimental transmission spectra have been measured. Furthermore, we compare our results with experimental values of the K-dependent splitting, the group velocity, and the oscillator strengths of this exciton-polariton. The results are in good agreement. This proves the validity of the 5 × 5 matrix model as a useful theoretical model for further investigations on the 1S ortho exciton-polariton.

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K-dependent exchange interaction of the1Sorthoexciton inCu2O

Cited by 13 publications

References 38 publications

Magnetoexcitons Break Antiunitary Symmetries

Magnetoexcitons Break Antiunitary Symmetries

The even exciton series in Cu$_2$O

Exciton-polaritons in cuprous oxide: Theory and comparison with experiment

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