Carrier resonance in Cu2O

Goltzené, A.; Schwab, C.; Wolf, Hans Christoph

doi:10.1016/0038-1098(76)90394-x

Cited by 27 publications

(15 citation statements)

References 7 publications

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“…As pointed out already by Yu and Shen, 19,20 there is a discrepancy between the effective exciton mass M 0 derived from the band masses of the conduction band m e and the 21 Assuming the crystals in the resonant Raman experiments were oriented along the k = ͓001͔, their results have to be interpreted as follows: Looking at Fig. 1(b) we find that only the E 1,3 level is optically allowed, which means that the investigated orthoexciton is shifted by −⌬ 3 from E 0 .…”

Section: Influence On the Effective Exciton Massmentioning

confidence: 96%

Wave-vector-dependent exchange interaction and its relevance for the effective exciton mass inCu2O

et al. 2004

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The wave-vector dependence of electron-hole exchange interaction is investigated. For the yellow 1S exciton in Cu 2 O the exchange is derived up to the order k 2 . The theoretical predictions are verified experimentally by high-resolution absorption experiments. In agreement with theory the fine structure shows a characteristic dependence on the direction of the wave vector. The exchange splitting of the orthoexciton triplet are distinguished from strain-induced perturbations. The exchange gives rise to an isotropic and an anisotropic correction of the effective exciton mass. This can explain the discrepancies in the measurements of the exciton mass in Cu 2 O.

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Section: Influence On the Effective Exciton Massmentioning

confidence: 96%

Wave-vector-dependent exchange interaction and its relevance for the effective exciton mass inCu2O

et al. 2004

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“…The components of the effective electron and hole masses for Cu 2 O along different symmetry directions are reported in Table IV together with the available experimental data obtained by cyclotron resonance to allow comparison. [34][35][36] In the absence of spin-orbit splitting, the states at the top of the valence band are triply degenerate ͑Fig. 7͒.…”

Section: E Effective Electron and Hole Massesmentioning

confidence: 99%

Electronic structure and properties ofCu2O

et al. 1997

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The structural and electronic properties of Cu 2 O have been investigated using the periodic Hartree-Fock method and a posteriori density-functional corrections. The lattice parameter, bulk modulus, and elastic constants have been calculated. The electronic structure of and bonding in Cu 2 O are analyzed and compared with x-ray photoelectron spectroscopy spectra, showing a good agreement for the valence-band states. To check the quality of the calculated electron density, static structure factors and Compton profiles have been calculated, showing a good agreement with the available experimental data. The effective electron and hole masses have been evaluated for Cu 2 O at the center of the Brillouin zone. The calculated interaction energy between the two interpenetrated frameworks in the cuprite structure is estimated to be around Ϫ6.0 kcal/mol per Cu 2 O formula. The bonding between the two independent frameworks has been analyzed using a bimolecular model and the results indicate an important role of d 10 -d 10 type interactions between copper atoms. ͓S0163-1829͑97͒01735-9͔

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“…Naturally, previous measurement of M have not taken these contributions into account. As we have seen, the exchange shifts are on the order of few µeV and hence comparable to the kinetic energy of the exciton at the exciton-photon resonance |k| = k 0 = 2.62·10 [5]. Having in mind the wave vector dependent exchange the exciton mass has to be interpreted as follows: We assume the crystal in the resonant Raman experiments were oriented along k = [001].…”

mentioning

confidence: 99%

“…The solid symbols mark experimental values. The energy shifts ∆E include the exchange contributions J Q ex , J 3 , and J 5 One might argue that the exchange contributions of order k 2 are relatively small. They are about three orders of magnitude smaller than the conventional k-independent exchange between ortho-and paraexcitons.…”

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Anisotropic effective exciton mass in Cu ₂ O

Dasbach

Fröhlich

Stolz

et al. 2005

phys. stat. sol. (c)

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The degeneracy of the yellow 1S orthoexcitons in Cu2O is lifted by wave vector dependent electron-hole exchange. This interaction scales quadratically with k and strongly depends on the direction of the wave vector. Therefore it is interpreted as an anisotropic correction of the effective exciton mass. This can explain the discrepancies in the measurements of the exciton mass in Cu2O reported so far.Spins are coupled via exchange interaction. For exciton physics the exchange between the coupled electron-hole pairs is of increased interest. Despite being studied intensively the understanding of electronhole exchange even in bulk materials is far from being complete. The electron-hole exchange interaction depends on the full band structure and hence on the wave vector k of the exciton center-of-mass motion. However, normally it is approximated as a spin-spin interaction, which is independent of the wave vector. This represents a severe simplification of the exchange interaction.Recently the wave-vector-dependence of the electron-hole exchange has been derived and experimentally verified for the yellow 1s orthoexciton in Cu 2 O.[1] In this article we will summarize the essential results and discuss the impact of wave-vector-dependent exchange for the interpretation of the effective exciton mass.In Cu 2 O excitonic transitions with holes in the Γ + 7 band and electrons in the Γ + 6 band give the socalled yellow exciton series. One finds four 1S excitons that are split by k-independent exchange into the threefold Γ + 5 states termed orthoexcitons and a single Γ + 2 level referred to as paraexciton. In the following we will solely concentrate on the orthoexcitons. In lowest order, the orthoexcitons couple to light via quadrupole interaction. Exchange interaction of order k 0 leaves the orthoexcitons degenerate. When calculating exchange of higher order in k one finds that the k-linear terms vanish. The calculation of the terms of order k 2 is described in great detail in Ref. [1,2]. Summarizing one finds the long range exchange term

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Carrier resonance in Cu2O

Cited by 27 publications

References 7 publications

Wave-vector-dependent exchange interaction and its relevance for the effective exciton mass inCu2O

Wave-vector-dependent exchange interaction and its relevance for the effective exciton mass inCu2O

Electronic structure and properties ofCu2O

Anisotropic effective exciton mass in Cu ₂ O

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Carrier resonance in Cu2O

Cited by 27 publications

References 7 publications

Wave-vector-dependent exchange interaction and its relevance for the effective exciton mass inCu2O

Wave-vector-dependent exchange interaction and its relevance for the effective exciton mass inCu2O

Electronic structure and properties ofCu2O

Anisotropic effective exciton mass in Cu 2 O

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Anisotropic effective exciton mass in Cu ₂ O