Phonon Satellites Research Articles

Phonon induced pseudospin rotation in graphene

Pseudospin, a degree of freedom in a two-level quantum system of two sublattices, is a basic quantum number that poses a fundamental symmetry prone to the electronic nature of graphene. We propose an extended Hamiltonian that involves the SU(2) rotation of the pseudospin for electron-phonon scattering, which has a significant advantage over the conventional second-quantized polar coupling. A phonon satellite accompanied by an electron linearly pumped to the upper Dirac cone corresponds to a rotated pseudospin within a scheme of the time-resolved photoemission spectroscopy (TRPES), which is found to carry nonzero angular momenta and induce nonvanishing Berry curvatures through the dichroic mode of TRPES. A phonon bringing the pseudospin rotation is identified to be an elliptically polarized one, which compensates for the angular momenta delivered to the pseudospin. This is an indication of the chiral phonon excitation without the circularly polarized pulse pumping. Our findings suggest that the controlled generation of phonon builds up a new roadmap for engineering the Berry curvature and topology in Dirac semiconductors.

Many-body photoemission theory for organic molecular crystals

A many-body photoemission theory based on Keldysh nonequilibrium Green's functions is developed and applied to photoemission from extended states of organic molecules and their crystals, in particular excited by ultraviolet and soft X-ray radiation. In this energy region, electron-phonon interaction and radiation filed screening play some important roles. To incorporate the latter effects, we should use quantum electrodynamics (QED) approach. To discuss the electron-phonon interaction, we apply the Hedin equation including the screened Coulomb interaction mediated by the electron-phonon interaction. This theoretical framework gives us a unified picture of the UPS spectra from organic solids. Furthermore some illustrative numerical calculations are shown to discuss the relative importance of the multiple scatterings, Debye-Waller factors, the peak width of the quasi-particles, and the angular dependence of the phonon satellites. We demonstrate some specific features of ultraviolet photoemission spectroscopy (UPS) spectra from particularly anisotropic organic solids.

Decoupling Carrier Concentration and Electron-Phonon Coupling in Oxide Heterostructures Observed with Resonant Inelastic X-Ray Scattering.

We report the observation of multiple phonon satellite features in ultrathin superlattices of the form nSrIrO_{3}/mSrTiO_{3} using resonant inelastic x-ray scattering (RIXS). As the values of n and m vary, the energy loss spectra show a systematic evolution in the relative intensity of the phonon satellites. Using a closed-form solution for the RIXS cross section, we extract the variation in the electron-phonon coupling strength as a function of n and m. Combined with the negligible carrier doping into the SrTiO_{3} layers, these results indicate that the tuning of the electron-phonon coupling can be effectively decoupled from doping. This work both showcases a feasible method to extract the electron-phonon coupling in superlattices and unveils a potential route for tuning this coupling, which is often associated with superconductivity in SrTiO_{3}-based systems.

Generalized method of Feynman-Pines diagram technique in the theory of energy spectrum of two-level quasiparticle renormalized due to multi-phonon processes at cryogenic temperature

Theory of the spectrum of localized two-level quasi-particle renormalized due to interaction with polarization phonons at cryogenic temperature is developed using the generalized method of Feynman-Pines diagram technique. Using the procedure of partial summing of infinite ranges of the main diagrams, mass operator is obtained as a compact branched chain fraction, which effectively takes into account multi-phonon processes. It is shown that multi-phonon processes and interlevel interaction of quasiparticle and phonons cardinally change the renormalized spectrum of the system depending on the difference of energies of two states, which either resonates with phonon energy or does not. The spectrum of non-resonant system contains renormalized energies of the main states and two similar infinite series of groups of phonon satellite levels. The spectrum of a resonant system contains a renormalized ground state and infinite series of satellite groups.

Electron-plasmon and electron-phonon satellites in the angle-resolved photoelectron spectra of n -doped anatase TiO2

We develop a first-principles approach based on many-body perturbation theory to investigate the effects of the interaction between electrons and carrier plasmons on the electronic properties of highly-doped semiconductors and oxides. Through the evaluation of the electron self-energy, we account simultaneously for electron-plasmon and electron-phonon coupling in theoretical calculations of angle-resolved photoemission spectra, electron linewidths, and relaxation times. We apply this methodology to electron-doped anatase TiO2 as an illustrative example. The simulated spectra indicate that electron-plasmon coupling in TiO2 underpins the formation of satellites at energies comparable to those of polaronic spectral features. At variance with phonons, however, the energy of plasmons and their spectral fingerprints depends strongly on the carrier concentration, revealing a complex interplay between plasmon and phonon satellites. The electron-plasmon interaction accounts for approximately 40% of the total electron-boson interaction strength and it is key to improve the agreement with measured quasiparticle spectra.

Quasiparticles and phonon satellites in spectral functions of semiconductors and insulators: Cumulants applied to the full first-principles theory and the Fröhlich polaron

The electron-phonon interaction causes thermal and zero-point motion shifts of electron quasiparticle (QP) energies $\epsilon_k(T)$. Other consequences of interactions, visible in angle-resolved photoemission spectroscopy (ARPES) experiments, are broadening of QP peaks and appearance of sidebands, contained in the electron spectral function $A(k,\omega)=-{\Im m}G_R(k,\omega) /\pi$, where $G_R$ is the retarded Green's function. Electronic structure codes (e.g. using density-functional theory) are now available that compute the shifts and start to address broadening and sidebands. Here we consider MgO and LiF, and determine their nonadiabatic Migdal self energy. The spectral function obtained from the Dyson equation makes errors in the weight and energy of the QP peak and the position and weight of the phonon-induced sidebands. Only one phonon satellite appears, with an unphysically large energy difference (larger than the highest phonon energy) with respect to the QP peak. By contrast, the spectral function from a cumulant treatment of the same self energy is physically better, giving a quite accurate QP energy and several satellites approximately spaced by the LO phonon energy. In particular, the positions of the QP peak and first satellite agree closely with those found for the Fr\"ohlich Hamiltonian by Mishchenko $\textit{et al.}$ (2000) using diagrammatic Monte Carlo. We provide a detailed comparison between the first-principles MgO and LiF results and those of the Fr\"ohlich Hamiltonian. Such an analysis applies widely to materials with infra-red active phonons. We also compare the retarded and time-ordered cumulant treatments: they are equivalent for the Fr\"ohlich Hamiltonian, and only slightly differ in first-principles electron-phonon results for wide-band gap materials.

Strong anharmonicity in the phonon spectra of PbTe and SnTe from first principles

At room temperature, PbTe and SnTe are efficient thermoelectrics with a cubic structure. At low temperature, SnTe undergoes a ferroelectric transition with a critical temperature strongly dependent on the hole concentration, while PbTe is an incipient ferroelectric. By using the stochastic self-consistent harmonic approximation, we investigate the anharmonic phonon spectra and the occurrence of a ferroelectric transition in both systems. We find that vibrational spectra strongly depend on the approximation used for the exchange-correlation kernel in density-functional theory. If gradient corrections and the theoretical volume are employed, then the calculation of the phonon frequencies as obtained from the diagonalization of the free-energy Hessian leads to phonon spectra in good agreement with experimental data for both systems. In PbTe we evaluate the linear thermal expansion coefficient $\ensuremath{\gamma}=2.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}\phantom{\rule{4.pt}{0ex}}{\text{K}}^{\ensuremath{-}1}$, finding it to be in good agreement with experimental value of $\ensuremath{\gamma}=2.04\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}\phantom{\rule{4.pt}{0ex}}{\text{K}}^{\ensuremath{-}1}$. Furthermore, we study the phonon spectrum and we do reproduce the transverse optical mode phonon satellite detected in inelastic neutron scattering and the crossing between the transverse optical and the longitudinal acoustic modes along the $\mathrm{\ensuremath{\Gamma}}\mathrm{X}$ direction. The phonon satellite becomes broader at high temperatures but its energy is essentially temperature independent, in agreement with experiments. We decompose the self-consistent harmonic free energy in second-, third-, and fourth-order anharmonic terms. We find that the third- and fourth-order terms are small. However, treating the third-order term perturbatively on top of the second-order self-consistent harmonic free energy overestimates the energy of the satellite associated with the transverse optical mode. On the contrary, a perturbative treatment on top of the harmonic Hamiltonian breaks down and leads to imaginary phonon frequencies already at 300 K. In the case of SnTe, we describe the occurrence of a ferroelectric transition from the high-temperature $Fm\overline{3}m$ structure to the low-temperature $R3m$ one. The transition temperature is, however, underestimated with respect to the experimental one. No satellites are present in the SnTe phonon spectra despite a not negligible anharmonic broadening of the zone-center TO mode.

Pressure dependency of electron-phonon renormalization in diamond

Employing ab initio many-body perturbation theory, the carrier-phonon and carrier-carrier vertex functions are evaluated in diamond crystal under different hydrostatic pressure up to 140GPa and the phonon induced quasiparticle renormalization is measured at diverse linear and non-linear pressure regimes. Our results illustrate that the degree of carrier coupling to phonon satellite differs substantially from linear to non-linear regimes, due to changing the nature of the carrier dynamics. Particularly, reduction of the phonon induced renormalization with increasing pressure on the system is an indication of a transition from strong to a weak polaronic nature, which is in good accordance with experimental and theoretical studies. It demonstrates the significant role of the pressure in tuning the electron phonon coupling in a system. Furthermore, going to the higher pressure yields relevant discrepancy in electron energies from second-order phonon-induced to the first-order phonon perturbation. Our study recommends the hydrostatic pressure adjusts the significant contribution of electron-phonon self-energy in the electronic-related features of carbon-based materials as a new probe.

Polaronic correlation offsets in tetrahedral semiconductors

Employing the first principle calculation combined with many-body perturbation theory, the carrier–phonon vertex function is evaluated in tetrahedral semiconductor silicon and diamond crystal. Moreover, the phonon induced quasiparticle spectral renormalization factors, phonon line-widths and carrier velocity renormalizations are evaluated at different temperatures. Our results illustrate a pronounced difference between the degree of carrier coupling to phonon satellite in silicon and diamond by analysis of the rates of thermalization. Particularly, for diamond, the large amount of renormalization is an indication of strong polaronic nature, which is in good agreement with experimental and theoretical studies, which prove the significant role of electron phonon coupling. Further, going to the higher temperatures makes considerable deviation from first-order phonon-induced to the second-order phonon perturbation of electron energies. Our study suggests for the significant contribution of electron–phonon self-energy in the electronic-related features of carbon-based rather than silicon-based materials.

Absorption Spectra of Defect-Free Semiconductor Quantum Dots

The presence of accompanying resonances to the longitudinal optical phonon satellites in the optical spectra of semiconductor quantum dots is confirmed theoretically by a non-adiabatic approach of the optical absorption. The theory is applied to simulate features of the optical spectra of spherical quantum dots.

Microscopic equation-of-motion approach to the multiphonon assisted quantum emission of a semiconductor quantum dot

We present a microscopical model for the multiphonon assisted quantum emission from an externally excited semiconductor quantum dot. In the high driving field limit, our model predicts several strong coupling features, in particular, a phonon-assisted Mollow-triplet splitting and anticrossings between the Mollow sidebands and the phonon satellite peaks. The observed anticrossing scales with the effective LO-phonon coupling and can be used as a measure for the phonon coupling strength. Further, we investigate the non-Markovian temporal emission dynamics of the main and multiphonon assisted triplet structures.

Phonon-assisted shot noise through a quantum dot weakly coupled to Luttinger liquid

In the present paper, by applying the Lang–Firsov canonical transformation and the nonequilibrium Green function technique, we investigate joint effects of the electron–phonon interaction and intralead electron interaction on the differential shot noise and Fano factor through a vibrating quantum dot weakly coupled to Luttinger liquid leads. The influences of electron–phonon coupling and intralead electron interaction on differential shot noise and Fano factor are studied in detail. Variation of the main resonant peak and phonon satellite peaks with the electron–phonon interaction and electron–electron interaction of the leads is analyzed numerically. Besides, we also reproduced the result for the differential conductance derived by Skorobagat’ko and Krive using the master equation.

Bi^2+-doped strontium borates for white-light-emitting diodes

We report on Bi(2+)-doped SrB(4)O(7) and SrB(6)O(10) as orange and red phosphors for white-light-emitting diodes. In both compounds, absorption due to (2)P(1/2)-->(2)S(1/2) in Bi(2+) could be observed and quantified. The emission redshift from SrB(4)O(7) to SrB(6)O(10) and their different phonon satellite spectra are attributed to the enhancement of phonon-electron interaction. Investigation of the reduction mechanism of Bi(3+) to Bi(2+) suggests that in oxidizing atmosphere, Bi(2+) can be stabilized on Sr(2+) sites only in such lattices that are dominated by tetrahedrally coordinated boron.

Influence of electron‐phonon coupling on transport through a quantum dot in the Kondo regime

AbstractTransport through a quantum dot attached to nonmagnetic electrodes subject to spin bias and charge bias is studied theoretically within the non‐equilibrium Green function formalism and effects of local vibrational modes are analysed. A presence of phonons strongly influences the spin and charge conductance characteristics leading to an appearance of phonon satellites apart from Kondo peaks.Superposition of the main Kondo resonances and their phonon satellites in the conductance curves corresponding to two individual spin channels can lead to a variety of peak patterns in dependence on the charge voltage applied to the system (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Phonon-Assisted Kondo Resonance in Spin-Dependent Transport through a Quantum Dot

Effects of local vibrational modes on electron transport through a quantum dot attached to ferromagnetic electrodes are studied in the Kondo regime by the non-equilibrium Green function formalism based on the equation of motion method. Differential conductance is calculated for parallel and antiparallel configurations of the leads’ magnetic moments, and well defined Kondo resonance peaks and their phonon satellites are found. The influence of a compensating magnetic field on the peak positions is also discussed.

Impurity-induced Huang–Rhys factor in beryllium δ-doped GaAs/AlAs multiple quantum wells: fractional-dimensional space approach

This paper reports the observation of phonon sidebands in the photoluminescence spectra of Be acceptor-doped GaAs/AlAs multiple quantum wells. The intensity and energetic positions of the sideband lines are investigated experimentally for several quantum wells having various doping concentrations and photoluminescence excitation intensities. Theoretical analysis of a sideband-related lineshape, considering their energy position and impurity-induced spectra, has shown that phonon satellites can be attributed to free-electron–Be acceptor transitions involving longitudinal optical phonons of the GaAs—the host material of the studied quantum wells. The Huang–Rhys factor which determines the distribution of luminescence intensities between the phonon replicas and the main no-phonon peak was examined both experimentally and theoretically by varying the quantum well width. Thus, it has been found that this factor increases monotonically from 0.052 to 0.11 as the width of the quantum well decreases from 20 nm to 5 nm. The dependence of the Huang–Rhys factor on the width of the quantum well for a free-to-acceptor recombination was calculated applying the fractional-dimensional space approach. The proposed model adequately describes the experimentally determined dependence of the Huang–Rhys factor.

Phonon satellites and time-resolved studies of carrier recombination dynamics in InGaN quantum wells

Abstract We have studied the photoluminescence and time-resolved photoluminescence of a set of InGaN quantum wells with well thickness from 1 to 7.5 nm. An analysis of the phonon satellites at 5 K shows Huang–Rhys factors from 0.32 to 0.44. The increase of this factor is caused by the electron–hole separation induced by the piezoelectric field. The time-resolved photoluminescence at room temperature shows that the decay time of the 1 and 2 nm wells does not depend on the wavelength. The maximum decay time is around 600 ps for the 2, 3 and 4 nm wells. However, for the 3 and 4 nm wells a decrease of the photoluminescence decay time is observed at the highest wavelengths. This suggest the onset of a non-radiative process in these samples. The optimum well width for efficient emission for these single quantum wells was found to be 2 nm.

Photoluminescence and phonon satellites of single InGaN∕GaN quantum wells with varying GaN cap thickness

Variations in thickness of the GaN caps above single InGaN quantum wells have been studied using photoluminescence spectroscopy. Data are presented from two series of samples designed to promote energy transfer to luminescent species on the surface. Improvements in the optical properties as the GaN cap thickness increases from 2.5to15nm are accompanied by clear changes in the intensity of the LO-phonon satellites. Analysis of the strength of successive phonon satellites and the associated Huang-Rhys factors indicates that the amount of localization of the excitons is increased for the thinner cap samples. Surface depletion fields are also considered.

Hot Carrier Dynamics and Carrier-Phonon Interaction in GaN

probe energies are synchronized, recovering the full time resolution of our laser pulse. Our Monte-Carlo simulation agrees well with the unchirped NDS spectrum, which shows the development of the carrier distribution at early times, where phonon satellites are seen, together with a strong non-thermal electron distribution in the region of the LO-phonon energy arising from the remarkably strong electron-LO phonon interaction. By employing a new technique which involves the integration of the normalized NDS multiplied by the corresponding energy, a measure of the mean energy of the carriers in non-thermal states is obtained. By comparing the timedependent energy loss with the theoretical energy loss rate, we estimate the eective temperature of the phonon modes as well as the population of phonons.

Time-resolved spectroscopy of non-thermal carrier dynamics in GaN

Abstract The dynamics of carriers in GaN epilayers is investigated using femtosecond pump-probe spectroscopy. After the residual chirp on the continuum probe is removed, the normalized difference spectra (NDS) for different probe energies are synchronized, recovering the full time resolution of our laser pulse. Our Monte-Carlo simulation agrees well with the unchirped NDS spectrum, which shows the development of the carrier distribution at early times, where phonon satellites are seen, together with a strong non-thermal electron distribution in the region of the LO-phonon energy arising from the remarkably strong electron–LO phonon interaction. Employing a new technique which involves the integration of the normalized NDS multiplied by the corresponding energy, a measure of the mean energy of the carriers in non-thermal states is obtained. By comparing the time-dependent energy loss with the theoretical energy loss rate, we estimate the effective temperature of the phonon modes as well as the population of phonons.