Renormalization Of Phonon Frequencies Research Articles

Renormalization of phonon frequencies by conduction electrons in layer systems with application to YBa2Cu3O7

It is generally assumed that there are free electronic carriers associated with the CuO2 planes in high-temperature superconductors. Regarding these carriers as confined to these planes their influence on phonon frequencies is studied within the framework of a shell model of lattice dynamics taking into account the long-range part of the electron-phonon coupling. We find a complete suppression of the LO-TO splitting for modes polarized along the planes by metallic screening and a strong coupling of electronic plasmon and particle-hole excitations especially to some To-phonon branches polarized perpendicular to the conducting planes, particularly pronounced in systems with at least two CuO2 planes per unit cell. Numerical results are presented for YBa2Cu3O7.

Phonons in a strongly coupled electron-phonon system.

The theory of vibration excitations in a strongly coupled electron-phonon system is developed. The renormalization of phonon frequencies due to the strong electron-phonon interaction is obtained, taking into account the polaron narrowing of the electron band. Polaron-phonon interaction leads to a softening of the phonon frequencies and damping.

On nonlinear electron-lattice interaction and anharmonicity in HTSC

A model of electron-phonon coupling quadratic in the lattice displacements is applied to the Cu-0 and Bi-O based superconductors. Tc, the isotope effect and the renormalization of phonon frequencies are discussed.

Effects of strain on the optical and vibrational properties of ZnSe-ZnS xSe 1- x strained-layer superlattices

In this review article, we describe detailed optical properties of ZnSe-ZnS x Se 1- x strained-layer superlattices (SLS) grown on GaAs substrates by molecular beam epitaxy. Photoluminescence and excitation measurements were carried out to study effects of the strain and carrier confinement in this strained layer system. For the case where the total thickness of SLS is very small (∼1000Å) compared to its critical thickness, the structure grows pseudomorphic with the ZnSe buffer layer. In this case the ZnSe well layers are not strained and all the blue shift in the optical spectra is attributed to the carrier confinement effects only. At the other extreme, for the case of a SLS with very large total thickness (∼4 μm), we show that it can be treated as free standing with the ZnSe layers under in-plane biaxial compression and the ZnS x Se 1- x layers under biaxial tension. In the intermediate cases of total thicknesses, we show that SLSs are not fully relaxed to their equilibrium states by measuring the strains directly in the well layers. We also present photoluminescence data to show that SLSs grown on ZnSe buffer layers can exist in a continuous range from a perfectly coherent state to a totally free standing state as the total thickness of the SLS increases. In addition, we also observe the effect of strain produced by the SLS on the buffer layers. We also discuss in detail the depth dependence of the strains in a given SLS or a heteroepilayer by using Raman scattering measurements performed under laser excitation below and above the band gap. We find that the strain values near the top surface are driven by a stronger relaxation of the in-plane lattice constants towards equilibrium. Empirical values for the band offsets are obtained from the analysis of optical response as a function of the sample parameters. Theoretical calculations of the band offsets, based on the model-solid approach, were also performed and are found to agree with the experimental observations to within 0.05 eV. They indicate that all possible ZnSe-ZnS x Se 1- x interfaces will exhibit a very small conduction band offset. We also carried out resonant Raman-scattering experiments at low temperatures to study the optical modes of these SLS systems. The observed Raman modes can be classified into two groups: one corresponds to vibrations with amplitudes localized either in the ZnSe or in the ZnS x Se 1- x layers. These are confined modes. In the second group, the phonons with amplitudes in both layers are included, namely, interface vibrations and folded optical modes. The measured dependence of the confined and delocalized phonons on sample parameters (individual layer thicknesses, superlattice period, total superlattice thickness, and interfacial strain) and on resonant excitation is presented and discussed in detail. The trends that were established are compared with the theoretical predictions of lattice dynamic models for multilayer structures. Experimental data on the lattice dynamic properties of ZnS x Se 1- x alloys are included for comparison purposes and to distinguish unequivocally superlattice effects. These data were gathered with ternary layers grown and measured under similar conditions as the superlattices. Concomitant with vibrational characteristics, this work has also yielded an insight into other intrinsic properties of SLSs. The interplay between confinement and strain in the renormalization of phonon frequencies was elucidated from an experimental point of view and this information was applied to characterize the nature of superlattice transition from pseudomorphic to free standing.

Optical vibrational modes of ZnSe-ZnSxSe

Resonant-Raman-scattering experiments were carried out at low temperatures to study the optical lattice modes of ZnSe-${\mathrm{ZnS}}_{\mathrm{x}}$${\mathrm{Se}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$ strained-layer superlattices, which were grown by molecular-beam epitaxy on (100) surfaces of GaAs substrates. The observed Raman modes can be classified into two groups: One group corresponds to vibrations with amplitudes localized either in the ZnSe or in the ${\mathrm{ZnS}}_{\mathrm{x}}$${\mathrm{Se}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$ layers. These are the confined modes. In the second group, the phonons with amplitudes in both layers are included, namely, interface vibrations and folded optical modes. The measured dependence of the confined and delocalized phonons on sample parameters (individual layer thicknesses, superlattice period, total superlattice thickness, and interfacial strain) and on resonant excitation is presented and discussed in detail. The trends that were established are compared with the theoretical predictions of lattice-dynamic models for multilayer structures. Experimental data on the lattice-dynamic properties of ${\mathrm{ZnS}}_{\mathrm{x}}$${\mathrm{Se}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$ alloys are included for comparison purposes and to unequivocally distinguish superlattice effects. These data were gathered with ternary layers grown and measured under similar conditions as the superlattices. Concomitant with vibrational characteristics, this work has also yielded an insight into other intrinsic properties of strained-layer superlattices. The interplay between confinement and strain in the renormalization of phonon frequencies was elucidated from an experimental point of view and this information was applied to characterize the nature of the superlattice transition from pseudomorphic to free standing.

Measurement of Anharmonic Renormalization of Phonon Frequencies

Measurement of Anharmonic Renormalization of Phonon Frequencies