Long-wave Optical Phonons Research Articles

Quantum transport through a quantum dot side-coupled to a Majorana bound state pair in the presence of electron-phonon interaction

We theoretically study quantum transport through a quantum dot coupled to Majorana bound states confined at the ends of a topological superconducting nanowire. The topological superconductor forms a loop and is threaded by a tunable magnetic flux, which allows one to control the electron transport in the system. In particular, we investigate phonon-assisted transport properties in the device when the central quantum dot interacts with a single long-wave optical phonon mode. We find that when the two Majorana bound states are unhybridized, the zero-temperature linear conductance has a $2\pi$ periodicity as a function of magnetic flux phase, independent of the electron-phonon interaction, the quantum dot energy, or the finite values of dot-Majorana couplings. For a finite overlap between the Majorana bound states, the linear conductance periodicity generally changes to $4\pi$ either due to a finite electron-phonon coupling strength, or a dot energy level that is tuned away from the Fermi level. Additionally, the differential conductance periodicity changes from $2\pi$ to $4\pi$ when the Majorana bound states hybridize and the electron-phonon coupling is finite. Our results provide insight into transport signatures expected in topological quantum computational platforms that integrate quantum dots as a means for Majorana qubit readout. The energy exchange with an environmental bath, here a single phonon mode, significantly alters the current signatures expected from Majorana modes.

Anisotropy of optical phonons in biaxially stressed zinc-blende- and diamond-type semiconductors and alloys

The splitting of long-wave optical phonons that arises in biaxially stressed zinc-blende- and diamond-type crystals due to violation of cubic symmetry in such crystals was studied both theoretically and experimentally (using micro-Raman technique). The anglular dispersion of optical phonons near the center of the Brillouin zone was calculated for split modes in biaxially stressed (001)-oriented films. The results obtained were used to analyze the effects due to strain and alloying on optical-phonon frequencies in stressed Ge, InGaAs and InAlAs films grown on GaAs (001) substrates. The developed approach permits a more precise determination of both the composition and the biaxial strain in AIIIBV alloy films based on an analysis of Raman spectra taken from such films.

Dispersion relations of interface and quasi-confined phonon modes in ZnO/BeZnO quantum wells

The long-wave optical phonon frequencies of BexZn1−xO alloys are determined within the modified random-element isodisplacement model. The results indicate a two-mode behavior for A1 and E1 branches of the optical phonons. The dispersions of the interface and quasi-confined modes in the polar ZnO/BexZn1−xO quantum wells are calculated within the dielectric continuum model up to x=0.2. In the absence of strain, the quantum wells yield as many as three distinct frequency ranges for the IF modes. However, the quasi-confined modes have two separate frequency ranges with boundaries determined by the ZnO-like and ZnO phonons. With the inclusion of strain, the boundaries of the frequency ranges for each mode are modified but without any change in the overall picture.

The effects of optical phonon on the binding energy of bound polaron in a wurtzite ZnO/MgxZn1−xO quantum well

An improved Lee-Low-Pines intermediate coupling method is used to study the energies and binding energies of bound polarons in a wurtzite ZnO/MgxZn1−xO quantum well. The contributions from different branches of long-wave optical phonons, i.e., confined optical phonons, interface optical phonons, and half-space optical phonons are considered. In addition to electron-phonon interaction, the impurity-phonon interaction, and the anisotropy of material parameters, such as phonon frequency, electron effective mass, and dielectric constant, are also included in our computation. Ground-state energies, binding energies and detailed phonon contributions from various phonons as functions of well width, impurity position and composition are presented. Our result suggests that total phonon contribution to ground state and binding energies in the studied wurtzite ZnO/Mg0.3Zn0.7O quantum wells varies between 28–23 meV and 62–45 meV, respectively, which are much larger than the corresponding values (about 3.2–1.8 meV and 1.6–0.3 meV) in GaAs/Al0.3Ga0.7As quantum wells. For a narrower quantum well, the phonon contribution mainly comes from interface and half-space phonons, for a wider quantum well, most of phonon contribution originates from confined phonons. The contribution from all the phonon modes to binding energies increases slowly either when impurity moves far away from the well center in the z direction or with the increase in magnesium composition (x). It is found that different phonons have different influences on the binding energies of bound polarons. Furthermore, the phonon contributions to binding energies as functions of well width, impurity position, and composition are very different from one another. In general, the electron-optical phonon interaction and the impurity center-optical phonon interaction play an important role in electronic states of ZnO-based quantum wells and cannot be neglected.

Effects of optical phonon and built-in electric field on the binding energy of bound polarons in a wurtzite In0.19Ga0.81N/GaN quantum well

The energies and binding energies of the bound polarons in a wurtzite In0.19Ga0.81N/GaN quantum well are investigated by means of a modified Lee-Low-Pines variational method. Contributions of ground state binding energies and different branches of a longwave optical phonon mode to the energies and binding energies of the bound polarons as a function of the well width and impurity center position are given. Effects of the anisotropy of phonon frequency and built-in electric field in the system on the energies and binding energies, and the electron and impurity center-optical phonon interaction, are included in the calculations. Results show that the contributions of optical phonons and built-in electric field to the ground state energy and binding energy of the bound polarons in a wurtzite In0.19Ga0.81N/GaN quantum well are very large, and result in the reduction of energy and binding energy. The binding energy decreases monotonically with increasing well width, and the speed of decrease is fast in the narrower well while the speed of decrease is slow in the wider well. Contributions of different branches of phonons to the energies and binding energies as a function of well width are different. In the narrower well, contributions of the confined phonon (withoud built-in electric field) are smaller than those of the interface and half-space phonons, while in the wider well, contributions of the confined phonons are larger than those of the interface and half-space phonons. Contributions of the confined phonon (with built-in electric field) become larger, whereas those of the interface and half-space phonons become smaller, and the total contribution of phonons also have obvious change. Contributions of these optical phonons to the ground state energies and binding energies of the bound polarons in In0.19Ga0.81N/GaN quantum wells are larger than the corresponding values (about 3.11.6 meV and 1.50.3 meV) of those in GaAs/Al0.19Ga0.81As quantum wells. The binding energies in In0.19Ga0.81N/GaN quantum wells decrease monotonically with increasing location Z0 of the impurity center for a constant well width d =8 nm, and the decrease of speed becomes faster. As the position of the impurity center is increasing, the contributions of the the interface and half-space phonons decrease slowly, and those of the confined phonons increase slowly as well.

Single-mode phonon transmission in symmetry-broken carbon nanotubes: Role of phonon symmetries

We investigate the single-mode phonon transmission in symmetry-broken carbon nanotubes with the Stone-Wales defect using a mode-matching method. To gain an insight into the features of the transmission, the symmetry properties of phonons are analyzed within the line group symmetry theory for single-walled carbon nanotubes. Our results show that the transmission for acoustic phonons with low group velocity is heavily suppressed, and the long-wave optical phonons near the Γ point are strongly scattered by defects. We clarify that this reduction in transmission for phonons with small group velocity is a universal behavior resulting from the broken translational invariance. Furthermore, fine structures of dips in the transmission are observed for some phonon modes, depending on the unmatched symmetry operations between the specific phonon mode and the defect. Our findings reveal that heat generation in experiments for the defective nanotubes may be contributed largely from the phonons with low group velocity because of their low transmissions. We propose the mode-dependent transmission for the single-mode phonon be utilized to identify the different phonon modes through the features for the fine structures of the transmission in experiments.

Shift and damping of optical phonons caused by interaction with electrons

Frequency shift and damping of long-wave optical phonons caused by interaction with electrons are calculated. The equations of the dynamic theory of elasticity are considered together with the Maxwell equations and the kinetic equation for determining the deformation field, the electric field, and the distribution function of electrons. Changes in the spectrum of electrons are described using a local potential. Coulomb screening of the longitudinal electric field is taken into account.

Linear photovoltaic effect in gyrotropic crystals

The ballistic and shift linear photovoltaic effects caused by asymmetry of the probability of optical transitions between subbands M1′ and M2′ in tellurium (involving long-wave optical phonons) and by carrier shift in real space at quantum transitions, respectively, are considered. The temperature and frequency dependences of the current of both ballistic and shift linear photovoltaic effects for the photon and phonon mechanisms are analyzed.

Radiative corrections to the long-wavelength optical-mode spectrum of the electron-phonon model: Absence of mode-splitting effects and hardening of the mode

Renormalization of the phonon spectrum of the Einstein form due to a weak coupling with electrons is calculated. No splitting of the phonon mode is found. A $q$-dependent hardening of the long-wave optical phonons contrasts with the softening of acoustic phonons in a weakly coupled electron-phonon system and with the softening of all phonons in the strong-coupling polaronic regime.

Anisotropic pairing caused by unscreened long-range interactions

Anisotropy of the order parameter in high-T c superconductors is explained by unscreened interaction of charge carriers with long-wave optical phonons. Screening is absent due to the low frequency of long-wave plasmons in layered structures.

Anisotropic pairing caused by unscreened long-range interactions.

Anisotropy of the order parameter in high-Tc superconductors is explained by unscreened interaction of charge carriers with long-wave optical phonons. Screening is absent due to the low frequency of long-wave plasmons in layered structures.

Magnetoplasmon-phonon coupling in semiconductor quantum wells

The collective excitations of a double heterostructure in the presence of a magnetic field are examined in detail. The polarization function of the quasi-two-dimensional electron gas in the presence of a perpendicular quantizing magnetic field is calculated within various long-wave approximations and in the random-phase approximation. Using these polarization functions the dispersion curves of the coupled intra- and inter-subband magnetoplasmon-phonons are calculated and plotted in graphical form. The calculation of the dispersion relation is done for GaAs-Ga1-xAlxAs double heterostructures and include both quantum size effects and the correct spectrum of the long-wave optical phonons. In this paper the higher resonances of the quasi-two-dimensional magnetoplasma, the Bernstein modes, are also investigated. It is shown that the intra- and inter-subband magnetoplasmon-phonons are free of Landau damping for finite perpendicular quantizing magnetic fields.

Electron-phonon interaction, dynamical screening and collective excitations in heterostructures: I. Electron-phonon interaction

Considering a GaAs-Ga 1− x Al x As heterostructure we investigate the single-particle Hamiltonian of the electron-(long-wave optical) phonon interaction. In detail the dispersion relations of long-wave optical phonons, i.e. of longitudinal optical (LO) phonons and of interface phonons of the polar semiconductor heterostructures are analyzed. The coupling function of the electron-phonon interaction is calculated using a continuum theory. The coupling functions describing the modified Fröhlich interaction of a single electron with the continuous field of polarization of the LO and interface phonons are discussed and presented in graphical form.

Long‐Wave Optical Phonons in InSbSe3 Layer Single Crystals

physica status solidi (b)Volume 153, Issue 1 p. K89-K92 Short Note Long-Wave Optical Phonons in InSbSe3 Layer Single Crystals N. M. Gasanly, N. M. Gasanly Department of Physics, Azerbaidzhan State University, Baku Search for more papers by this authorB. A. Natig, B. A. Natig Department of Physics, Azerbaidzhan State University, Baku Search for more papers by this authorA. E. Bakhyshov, A. E. Bakhyshov Department of Physics, Azerbaidzhan State University, Baku Search for more papers by this authorK. G. Shirinov, K. G. Shirinov Department of Physics, Azerbaidzhan State University, Baku Search for more papers by this author N. M. Gasanly, N. M. Gasanly Department of Physics, Azerbaidzhan State University, Baku Search for more papers by this authorB. A. Natig, B. A. Natig Department of Physics, Azerbaidzhan State University, Baku Search for more papers by this authorA. E. Bakhyshov, A. E. Bakhyshov Department of Physics, Azerbaidzhan State University, Baku Search for more papers by this authorK. G. Shirinov, K. G. Shirinov Department of Physics, Azerbaidzhan State University, Baku Search for more papers by this author First published: 1 May 1989 https://doi.org/10.1002/pssb.2221530160Citations: 2 P. Lumumba Str. 23, SU-370602 Baku, USSR. AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Citing Literature Volume153, Issue11 May 1989Pages K89-K92 RelatedInformation

Landau damped collective excitations of the quasi-two-dimensional polaron gas in double heterostructures

The spectrum of the collective and single-particle excitations of the quasi-two-dimensional polaron gas of a modulation doped GaAs-Ga 1- x Al x As double heterostructure is analyzed using the random-phase approximation for the electron gas. Caused by the plasmon-phonon coupling the long-wave optical phonons of the double heterostructure, the confined LO phonons and the interface phonons, become Landau damped in the regions of the single-particle intra- and intersubband continuum. Numerical results are presented for the dispersion curves and the energy-loss function. We have found additional non-phonon-like modes existing within the single-particle intra- and intersubband continuum.

Free carrier scattering from quasi-2D optical phonons in semiconductor quantum wells and superlattices

The scattering rates of free carriers in GaAsGa 1−xAl xAs double heterostructures and superlattices are analyzed for both polar/Fröhlich and optical deformation potential coupling including the correct spectrum of the long-wave optical phonons of these layered systems.

Phase transformation in the oxides

This paper reviews phase transformations in the oxides, and briefly examines the similarities and dissimilarities with the phase transitions in metals. A few topics selected for the discussion, include, displacive phase transitions, order-disorder transitions, and clustering and precipitation. The displacive transition involves the oxygen polyhedra, and is usually found in ferroelectric and antiferroelectric oxides, such as, BaTiO3, SrTiO3, PbZrO3, and other oxides of perovskite structure. In lattice dynamics studies, this transition has been associated with an instability of a long-wave optical phonon. The condensation of the ferroelectric soft mode causes the static distortion of the lattice at the phase transition. The order-disorder transformation in the oxides may occur in different forms. It may be the hydrogen ordering in KDP, the catio distributions in spinel MgFe2O4,the Li-Fe ordering of the octahedral sites in LiFe5O8, or the formations of layer structures in the double perovskites, such as Ba2CoWO6, Ba2CoReO6, and others. Clustering and precipitations are commonly observed phenomena in oxide systems. They result in phase separations in both the crystalline, and the glassy systems. Heat treatments to control the crystallization processes in glasses result in glass ceramics, which have been proven to be superior to both the original glass, and to the precipitated crystalline phase.

The Modulation of Light by Non‐Equilibrium Optical Phonons in n‐Ge

AbstractThe modulation of light near the edge of the direct transitions in Ge in strong pulsed electric fields was investigated. High‐resistance n‐Ge (ϱ = 40 Ωcm) and low‐resistance p‐Ge (ϱ = 1.0 Ωcm) exhibit the Franz‐Keldysh effect only. The low‐resistance samples of n‐Ge (ϱ = 1.0 and 0.3 Ωcm) exhibit Franz‐Keldysh effect together with a variation of the absorption coefficient ΔαDE which is proportional to the free carrier concentration and has a threshold approximately at the photon energy deficit equal to the energy of the longwave optical phonon (0.037 eV). The additional absorption ΔαDE is caused by the indirect band‐to‐band transitions with participation of non‐equilibrium optical phonons, emitted by hot electrons. From a comparison of the experimental and calculated results for ΔαDE the lifetime is estimated to be 5 × 10−11 s at T0 = 90 °K for the long‐wave optical phonons. This value is in satisfactory agreement with Klemens' theory and also with the results of Raman scattering in Ge.

Optical lattice vibrations in finite ionic crystals: I

A theory for the properties of long-wave optical vibration modes in finite ionic crystals of arbitrary shape is given. Neglecting retardation effects, it is found that in finite specimens there exist transverse and longitudinal bulk modes as well as surface modes, which are neither transverse nor longitudinal and which have intermediate frequencies. Explicit solutions are given for diatomic crystal samples with one, two and three dimensions finite. The modifications which arise from more complex unit cells and polarizable ions are given. A detailed calculation of the properties of long-wave optical phonons in finite specimens of strontium titanate is presented.

Optical lattice vibrations in finite ionic crystals: II

A theory for the polariton modes (long-wave optical phonons coupled to photons) in finite ionic crystals of arbitrary shape is given. The theory is exemplified by detailed calculations for the case of a spherical specimen. Stationary polariton states of three types are obtained, which, for small enough crystals, are characterized by (i) large amplitudes inside the solid (bulk modes), (ii) large amplitudes near the surface of the solid (surface modes) and (iii) small amplitudes inside the solid (vacuum modes). The absorption spectrum of spherical diatomic samples is calculated and it is found that the polariton modes cause absorption in regions which are forbidden for infinite crystals. The generalization of the theory to the case of complex cubic crystals is given and applied to interpret the absorption spectrum of small SrTiO3 spheres.