Longitudinal-transverse Splitting Research Articles

Exciton longitudinal-transverse splitting in GaAs/AlGaAs superlattices and multiple quantum wells

The exciton longitudinal-transverse splitting, ω LT , has been investigated both theoretically and experimentally in periodic GaAs/AlGaAs heterostructures. It has been shown that the 2D-3D transition manifests itself in the ω LT dependence on the SL period, (L z + L b), more dramatically than in the exciton binding energy dependence on the period.

Longitudinal-transverse splitting in Wannier excitons and polariton states

In the theory of Wannier excitons, the long-range nonanalytical part of the exchange interaction is usually expressed in terms of the dipole matrix element between Wannier functions. We show that it can be expressed in terms of the dipole matrix element between zone-centre Bloch functions, without any assumption on the localization of Wannier functions. We obtain an expression for the longitudinal-transverse splitting in terms of the dipole matrix element between the crystal ground state and the excition state. This is required in order to prove that the transverse upper polariton is degenerate with the longitudinal exciton in the limitk ex→0. A new expression for the short-range part of the exchange interaction is also obtained, which is more suitable for microscopic calculations and which is evaluated for the case of CuCl. The resulting exchange parameter isΔ ex = 12.6 meV, which compares well with the experimental value.

Three-photon spectroscopy of excitons and polaritons in alkali halides.

Three-photon spectra of nine alkali halides are presented. The nonlinear-optical method of three-photon spectroscopy allows one to measure resonances on the upper polariton branch and the longitudinal exciton at different values of the total k vector. The analysis of the polariton dispersion yields reliable values of the longitudinal-transverse splitting. In Cs halides new exciton lines of ${\ensuremath{\Gamma}}_{5}^{\mathrm{\ensuremath{-}}}$ symmetry are resolved which are forbidden for one-photon optical transitions. In high magnetic fields transitions to paraexcitons of ${\ensuremath{\Gamma}}_{5}^{\mathrm{\ensuremath{-}}}$ and ${\ensuremath{\Gamma}}_{3}^{\mathrm{\ensuremath{-}}}$ symmetry are allowed. The g values for the uppermost valence band and the lowest conduction band are derived from the Zeeman splitting of the paraexcitons and the transverse polariton. In addition, the exchange energy for KI and RbI is gained from the three-photon spectra in high magnetic fields.

Exchange effects on excitons in quantum wells.

Exchange splitting of quasi-two-dimensional excitons confined in quantum wells is studied theoretically by performing a simplified calculation with a scaling argument. Both the exchange energy and the longitudinal-transverse splitting are found to be enhanced drastically when the confinement of the exciton increases. Taking into account the difference of the enchange interaction between the heavy-hole and the light-hole exciton, the intrinsic splittings of the exciton ground states are calculated for GaAs-${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Al}}_{\mathrm{x}}$As quantum wells within the envelope-function approximation.

Three-photon spectroscopy of excitons and polaritons in alkali halides

Three-photon spectra of the lowest exciton in KI are presented. The longitudinal-transverse splitting and the energy of the longitudinal exciton are determined by use of K-space spectroscopy. The detailed analysis of magnetooptic experiments yields reliable data for the exchange energy and g values.

Three-photon spectroscopy of exciton polaritons in alkali halides.

Three-photon spectroscopy is introduced as a useful tool for the investigation of electronic transitions in solids. This technique is used to study resonances on the upper polariton branch, and even on the longitudinal exciton. This is the first such application for a system with inversion symmetry. The polariton structure of the lowest exciton in KI is analyzed with use of different wave-vector configurations. The fit of the experimental data yields a longitudinal-transverse splitting of 110 meV. For the more complicated exciton structure of CsI, a correspondingly complicated polariton structure is expected. For CsI, results are presented only for one wave-vector configuration.

Excitons and polaritons in InP.

We report an investigation of the reflectivity spectra of InP at normal incidence, at pumped-helium temperature, and under [100] uniaxial stress. Three transverse exciton frequencies associated to the 1s ground state and the 2s and 3s excited states have been found. We deduce an exciton binding energy ${E}_{\mathrm{ex}=5.1\ifmmode\pm\else\textpm\fi{}0.1}$ meV. From a detailed investigation of the 1s ground state in terms of the three-branch polariton dispersion curves we achieve a very satisfactory agreement between theory and experiment. Resolving the fine structure of the exciton ground state, we find (i) the exchange energy \ensuremath{\Delta}=0.04\ifmmode\pm\else\textpm\fi{}0.02 meV and (ii) the longitudinal-transverse splitting ${E}_{\mathrm{LT}=0.17\ifmmode\pm\else\textpm\fi{}0.02}$ meV. The surface dead layer which corresponds with the best experimental fit is twice the exciton Bohr radius, as expected for an intrinsic surface-exciton-free layer.

Effects of strong anharmonicity in the spectra of optical phonons and polaritons

This review discusses the results of theoretical and experimental studies of biphonons (phonons bound to one another) and other effects of strong anharmonicity for the spectral region of overtones and compound tones of high-frequency optical vibrations of the crystal lattice. Longitudinal-transverse splitting of a biphonon and features of the structure of its spectrum in anisotropic crystals and Fermi resonance with bulk and surface polaritons are discussed, as well as the effect of this resonance on the dispersion of polaritons. Considerable attention is paid to analyzing the experimental data (infrared and Raman spectra) in which biphonons and cardinal rearrangement of the dispersion of a polariton in the region of a Fermi resonance have been found. The influence of a Fano antiresonance and singular points of the density of states are discussed in connection with Raman spectra of polaritons.

Interference effect and dispersion in thin RbI crystals

Reflection spectra of thin RbI crystals have been measured in the vicinity of the exciton resonance at 11 K, showing the structures due to the Fabry-Perot interference. From the analysis of dispersion curve, the background dielectric constant, the transverse exciton energy and the longitudinal-transverse splitting are determined to be 3.20, 5.735 eV and 175 meV, respectively. These experimental values are discussed in connection with the polariton picture in RbI.

Exchange energy and oscillator strengths of excitons in cadmium sulfide.

The Hamiltonians of A and B excitons are derived, taking into account the linear k term of conduction and valence band, the longitudinal transverse splitting, and the exchange energy. We show that the data on A-excitonic polaritons provide the parameters of B-excitonic polaritons. We deduce (i) the exchange energy, scrE=0.23\ifmmode\pm\else\textpm\fi{}0.07 meV, from available data on A-excitonic polaritons, and (ii) the parameter ${q}_{7}$ (determining the B-hole wave function in Gutsche-Jahne notation), ${q}_{7}^{2}$=0.39, from available data on B-excitonic polaritons.

Excitonic Surface Polaritons in Luminescence from ZnTe Crystals

AbstractThe form and structure of reflection and exciton–polariton luminescence spectra of ZnTe crystals are studied in the region of the ground (n = 1) exciton state. The longitudinal–transverse splitting magnitude ΔELT is determined from the shape of the reflection spectra. A detected doublet structure of an emission band from the lower polariton branch is associated with the k‐linear term. The evolution of bulk and surface polariton luminescence spectra versus temperature and wave length of the exciting light is investigated.

Collective excitations in the Van Vleck enhanced nuclear antiferromagnet HoVO4. II. Dispersion curves

For pt.I see ibid., vol.15, p.1663 (1982). The Green function formalism of Haley and Erdos and of Bak is used to compute the excitation curves epsilon (q) versus q for the Van Vleck enhanced nuclear antiferromagnet HoVO4 in the ordered state. Calculations are presented and discussed for both the linear and puckered antiferromagnetic spin structures. In particular, it is shown that HoVO4 is characterised by a vanishing energy gap, below the Neel temperature(4.8 mK), in accord with the Goldstone theorem for a continuously broken symmetry. Other features such as (i) magnon/single-ion excited-state interactions and (ii) the longitudinal-transverse splitting at q=0 associated with the dipole-dipole interactions are identified and discussed. Particular attention is paid to the symmetry properties of the enhanced dipole-dipole interaction Fij and its Fourier transform f(q) for the HoVO4 lattice. These symmetries are used not only to reduce the calculations to a minimum but also to identify crossing and anti-crossing behaviour between the various excitation branches. Finally some comments are made concerning the possibility of NMR and neutron scattering experiments in the nuclear ordered phase.

High-resolution resonant Brillouin scattering and the effect of stress on GaAs

Five-pass Fabry-Perot interferometry is used to obtain the linewidths of exciton polaritons resonant Brillouin scattered in GaAs. Both interbranch and intrabranch peaks are measured. An interpretation of the results in terms of excitons with an energy-independent damping is shown to be inadequate for GaAs. The effect of uniaxial stress is investigated and discussed. Stress-induced splitting (greater than the longitudinal-transverse splitting of the exciton) of the degenerate valence band at the $\ensuremath{\Gamma}$ point accounts for the observed decrease in the masses of the decoupled excitons. The values of these masses are in agreement with band-structure parameters. The value $\ensuremath{\delta}=0.0\ifmmode\pm\else\textpm\fi{}0.02$ meV for the exciton exchange parameter has been determined from these data.

Longitudinal-transverse splitting of dipole modes in hyper-Raman scattering spectra of liquid CCl 4

The first observation of the longitudinal-transverse splitting of dipole vibrations in liquid CCl 4 is reported. Using the hyper-Raman scattering technique, we have obtained the spectra of transverse (313, 760 and 782 cm -1) and longitudinal (≁770 and 800 cm -1) modes in CCl 4. Polarization analysis is shown to be used to distinguish longitudinal and transverse modes of dipole vibrations in hyper-Raman spectra.

Polariton time of flight measurement in a thin crystal of CdSe

We measured the polariton time of flight in a thin CdSe crystal. From the analysis of the delay time of light as a function of frequency, we find the value of the longitudinal-transverse splitting energy, ΔE LT = 1 meV and the effective mass, m = 0.45 M o. We compare the information given by our measurement with that given by the analysis of interferences in the reflectivity spectrum.

Wave-Number Dependent Oscillator Strength and Longitudinal-Transverse Splitting of Exciton in CuCl

Wave-number dependence of exciton longitudinal-transverse splitting was considered in a previous paper, where a microscopic calculation of the electron-hole exchange interaction was shown to account for experiment on CuCl. In this paper, macroscopic approach, based on considerations on the dielectric function, is taken to the same problem. For exciton with finite wave number, it is necessary to distinguish between longitudinal and transverse oscillator strength; the former is proportional to the longitudinal-transverse splitting of exciton. Equivalence of the two approaches is proved.

The Oscillator Strength and Life Time Broadening of Exciton Polaritons in GaAs

The optical reflectance and transmission spectra of GaAs at low temperatures has been interpreted in order to derive the basic parameters of exciton polaritons. Taking into account a well defined repulsive surface potential acting on the excitons and using a frequency independent life time broadening Γ it is possible to explain the observed spectra in great detail. The results are ℏΓ = 0.010 meV and the longitudinal transverse splitting ℏωLT = 0.17 ± 0.02 meV.

Local-field effects and the ir optical properties of ternary semiconductor alloys

We present a calculation of the infrared dielectric function of a three-dimensional ternary semiconductor alloy $A{B}_{1\ensuremath{-}x}{C}_{x}$. The diagonal disorder (masses) is treated in the coherent potential approximation; the off-diagonal disorder (force constants) as well as all the electronic properties (background dielectric constant, electronic screening) is handled by the virtual-crystal approximation. We use a nearest-neighbor single-force-constant potential which is shown to be sufficient to account for the optical properties. With the data of ${\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Al}}_{x}\mathrm{As}$, the calculated density of states shows one acoustic band and two optical bands, one near the gap mode of Ga in AlAs, and the other near the localized mode of Al in GaAs. Particular attention has been given to the local-field effects caused by the ionic and electronic polarization and by the screening due to the electronic delocalization. The line broadening induced by the disorder forces one to make a precise definition of the longitudinal and transverse frequencies. In addition to the well-known two-mode behavior of ${\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Al}}_{x}\mathrm{As}$, the model predicts a third very weak mode (about a hundred times weaker), which is a disorder-activated zone-edge mode. The model also predicts a rapid variation of the longitudinal-transverse splitting of the two main modes when one approaches the pure-crystal limit. The numerical results agree well with the experimental data and are also compared with those of the linear diatomic chain.

Electronic interband transitions: Plasmons, Frenkel- and Wannier-excitons

From the equation of motion for electron-hole pairs, an eigenvalue equation for electronic interband transitions of a two-band model is derived. In addition to the continuum of free electron-hole pairs, its spectrum shows discrete excitonic and plasmonic lines. Applying complementary approximations to the integral kernel of the eigenvalue equation, one obtains alternatively the hydrogenic spectrum of the Wannier excitons or a transverse Frenkel exciton and a longitudinal plasmon. As regards the solution of the full eigenvalue equation, the possibility of coexistence between excitons and plasmons is established, and longitudinal-transverse splitting of the Wannier excitons is found.

Coupling between photons and exciton polaritons across surfaces of direct-gap semiconductors

The coupling between external photons and bulk exciton polaritons is investigated theoretically in the case of an appropriate repulsive surface potential for the exciton motion. The analysis of the limitations of the Hopfield-Thomas model indicates that it gives too large values of the lifetime broadening or the longitudinal-transverse splitting. The calculated effective dead-layer thicknesses to be expected in fitting the Hopfield-Thomas model to experiments agree well with experimental results also in the case of very small oscillator strengths giving thick dead layers.