Deformation Potential Interaction Research Articles

Theory of cavity-polariton self-trapping and optical strain in polymer chains

Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824(Dated: February 6, 2008)We consider a semiconductor polymer chain coupled to a single electromagnetic mode in a cavity.The excitations of the chain have a mixed exciton-photon character and are described as polaritons.Polaritons are coupled to the lattice by the deformation potential interaction and can propagatein the chain. We find that the presence of optical excitation in the polymer induces strain on thelattice. We use a BCS variational wavefunction to calculate the chemical potential of the polaritonsas a function of their density. We analyze first the case of a short chain with only two unit cells inorder to check the validity of our variational approach. In the case of a long chain and for a strongcoupling with the lattice, the system undergoes a phase transition corresponding to the self-trappingof polaritons. The role of the exciton spontaneous emission and cavity damping are discussed in thecase of homogeneous optical lattice strain.I. INTRODUCTION

Electron–acoustic-phonon interaction and resonant Raman scattering in Ge quantum dots: Matrix and quantum confinement effects

Calculations of the electron-acoustic phonon interaction, and Raman scattering efficiency, in matrix embedded Ge quantum dots (QDs) are presented. The work is focused on the understanding of the inelastic light scattering process excited close to resonance with the confined ${E}_{1}$ transitions. Due to the large joint density of states at the ${E}_{1}$ point, many intermediate electronic states contribute to the overall scattering efficiency. This particular situation leads to quantum interference effects between different scattering paths and has, therefore, a strong impact on the Raman line shapes and intensities. Quantum confinement of the electron and hole states is treated within the envelope wave function approximation. The QD/matrix acoustic vibrations are deduced from elasticity theory. Deformation-potential interaction between the electrons (and holes) and acoustic vibrations is assumed. The resonant Raman spectra are calculated using third order perturbation quantum theory. A Raman-Brillouin electronic density is constructed as a linear combination of the electronic states involved in the inelastic light scattering. It allows one to plot, for each excitation energy, the spatial distribution of the electronic density that gives rise to the Raman (or Brillouin) signal. It is calculated for both diagonal and off-diagonal transitions between the confined electronic states. The dependence of the spectral line shapes and intensities on homogeneous broadening of the ${E}_{1}$ transitions, QD size, surface boundary conditions is discussed in details. The calculated spectra are then compared to those measured for different QD size distributions.

Phonon-induced electron relaxation in weakly confined single and coupled quantum dots

We investigate charge relaxation rates due to acoustic phonons in weakly confined quantum dot systems, including both deformation potential and piezoelectric field interactions. Single-electron excited states lifetimes are calculated for single and coupled quantum dot structures, both in homonuclear and heteronuclear devices. Piezoelectric field scattering is shown to be the dominant relaxation mechanism in many experimentally relevant situations. On the other hand, we show that appropriate structure design allows to minimize separately deformation potential and piezolectric field interactions, and may bring electron lifetimes in the range of microseconds.

Near-field spectra of quantum well excitons with non-Markovian phonon scattering

The excitonic absorption spectrum for a disordered quantum well in presence of exciton-acoustic phonon interaction is treated beyond the Markov approximation. Realistic disorder exciton states are taken from a microscopic simulation, and the deformation potential interaction is implemented. The exciton Green's function is solved with a self energy in second order Born quality. The calculated spectra differ from a superposition of Lorentzian lineshapes by enhanced inter-peak absorption. This is a manifestation of pure dephasing which should be possible to measure in near-field experiments.

Quantum chaos in nanoelectromechanical systems

We present a theoretical study of the electron-phonon coupling in suspended nanoelectromechanical systems (NEMS) and investigate the resulting quantum chaotic behavior. The phonons are associated with the vibrational modes of a suspended rectangular dielectric plate, with free or clamped boundary conditions, whereas the electrons are confined to a large quantum dot (QD) on the plate's surface. The deformation potential and piezoelectric interactions are considered. By performing standard energy-level statistics we demonstrate that the spectral fluctuations exhibit the same distributions as those of the Gaussian Orthogonal Ensemble (GOE) or the Gaussian Unitary Ensemble (GUE), therefore evidencing the emergence of quantum chaos. That is verified for a large range of material and geometry parameters. In particular, the GUE statistics occurs only in the case of a circular QD. It represents an anomalous phenomenon, previously reported for just a small number of systems, since the problem is time-reversal invariant. The obtained results are explained through a detailed analysis of the Hamiltonian matrix structure.

Anomalous quantum chaotic behaviour in suspended electromechanical nanostructures

It is predicted that for sufficiently strong electron-phonon coupling an anomalous quantum chaotic behavior develops in certain types of suspended electro-mechanical nanostructures, here comprised by a thin cylindrical quantum dot (billiard) on a suspended rectangular dielectric plate. The deformation potential and piezoelectric interactions are considered. As a result of the electron-phonon coupling between the two systems the spectral statistics of the electro-mechanic eigenenergies exhibit an anomalous behavior. If the center of the quantum dot is located at one of the symmetry axes of the rectangular plate, the energy level distributions correspond to the Gaussian Orthogonal Ensemble (GOE), otherwise they belong to the Gaussian Unitary Ensemble (GUE), even though the system is time-reversal invariant.

Hole spin relaxation: acoustical deformation potential scattering

Using the spin surface concept, the hole spin scattering matrix related to acoustical deformation potential interaction is considered. The obtained matrix is intimately associated with the momentum scattering time used in hole transport investigations. A detailed analysis of the spin matrix elements that connect different hole spin polarizations coupled by longitudinal and transverse acoustical phonons shows that the frequencies of spin flipping and conserving transitions caused by the interaction, in general, are of the same order as the momentum scattering frequency. The method of finding spin scattering time presented in this paper may be useful in the Monte Carlo simulation of spin-related properties where the spin–orbit interaction is important.

Hole spin relaxation: optical deformation potential scattering

The scattering of hole spin during hole intra- and intervalence band transitions due to optical deformation potential interaction in tetrahedral semiconductors is considered. Matrix elements for transitions mediated by longitudinal and transverse optical phonons are presented. It is shown that for this type of scattering, the spin relaxation time can be found from hole momentum scattering time.

Spin relaxation due to the phonon modulation of the spin–orbit interaction in quantum dots

We calculate the spin relaxation rates in InAs parabolic quantum dots due to the spin interaction with acoustical phonons. The electron–phonon deformation potential and piezoelectric interaction are described by means of the Pavlov–Firsov spin–phonon Hamiltonian. Our results demonstrate that for narrow gap materials the deformation potential interaction becomes dominant. This behavior is not observed in wide or intermediate gap semiconductors, where the piezoelectric coupling, in general, governs the relaxation processes. We also show that the spin relaxation rates are particularly sensitive to the value of the Landè g-factor, which depends strongly on the confinement.

Deformation potential limited spin relaxation in cubic semiconductors

The scattering of valence band hole spin by acoustical and optical phonons due to deformation potential interaction is considered. Six-band deformation potential matrix, which takes into account doubly degenerate heavy-mass, light-mass, and split-off energy bands, is used to evaluate the matrix elements for spin conserving and flipping transitions. The concept of the spin surface was addressed to define the initial and final states of the hole spin. It was found that, in agreement with experiment, the spin conserving and flipping transitions are of comparable magnitude in both intravalence and intervalence band scattering mediated by acoustical as well as optical phonons.

Continuum model for acoustic phonons in nanotubes: phonon bottleneck

AbstractElastic continuum model is used to model acoustic phonons in single wall nanotubes (SWNTs). Based on elastic continuum theory, acoustic vibrational modes are modeled for both zigzag and armchair nanotubes of finite length using a variational solution of Donnell's equation. The acoustic phonon modes in these calculations are determined for both even and odd modes of the acoustic displacement. The dispersion relations vary with the length of the tube, and the results indicate that phonon bottleneck effects occur in short SWNTs. The displacement field of the nanotube is used to calculate the deformation potential interaction Hamiltonian. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Thermopower of ap-typeSi/Si1−xGexheterostructure

We report thermopower measurements in zero and low magnetic fields for a p-type ${\mathrm{S}\mathrm{i}/\mathrm{S}\mathrm{i}}_{1\ensuremath{-}x}{\mathrm{Ge}}_{x}$ heterostructure. The diffusion components of both the longitudinal and transverse components are reasonably well described by the Mott approach, including the quantum oscillations at low magnetic fields. The magnetic-field dependence of thermopower shows that the diffusion contribution at zero field deviates from the linear temperature dependence that would be expected for a degenerate system, probably as a result of the nearby metal-insulator transition. Phonon drag also does not behave as expected. Instead of exhibiting an approximate ${T}^{6}$ dependence at low temperatures appropriate to screened, hole-phonon, deformation-potential scattering, an approximate ${T}^{4}$ dependence is observed. This is consistent with previous observations on the energy-loss rates in SiGe hole systems. The experimental data on drag are in good agreement with numerical calculations by assuming either hole-phonon scattering by an unscreened deformation-potential interaction or by assuming a screened piezoelectric plus screened deformation-potential coupling.

Nonparabolic multivalley balance-equation approach to high-field electron transport and impact ionization in ZnS: Comparison with full-band Monte Carlo simulations

Extended nonparabolic multivalley balance equations including impact ionization (II) process are presented and are applied to study electron transport and impact ionization in ZnS with a $\ensuremath{\Gamma},$ X, and L conduction-band structure at high electric field up to 2000 kV/cm. Hot-electron transport properties, such as electron drift velocity, electron energy, intervalley electron transfer, and electron-hole pair generation, are calculated by taking account of the scattering from polar optical, deformation potential, and intervalley interactions. Quantitative agreement is obtained among the results for drift velocity and II coefficient derived from the present calculations, from the recent full-band Monte Carlo simulations, and from experiments, thus confirming the validity of the present multivalley nonparabolic balance-equation approach.

Electron–phonon-induced spin relaxation in InAs quantum dots

We have calculated spin-relaxation rates in parabolic quantum dots due to the phonon modulation of the spin–orbit interaction in the presence of an external magnetic field. Both deformation potential and piezoelectric electron–phonon coupling mechanisms are included within the Pavlov–Firsov spin–phonon Hamiltonian. Our results have demonstrated that, in narrow gap materials, the electron–phonon deformation potential and piezoelectric coupling give comparable contributions to spin-relaxation processes. For large dots, the deformation potential interaction becomes dominant. This behavior is not observed in wide or intermediate gap semiconductors, where the piezoelectric coupling, in general, governs the spin-relaxation processes. We have also demonstrated that spin-relaxation rates are particularly sensitive to the Landé g-factor.

Quantized acoustic vibrations of single-wall carbon nanotube

Acoustic vibrational modes are derived for both zigzag and armchair nanotubes of finite length using the continuum theory and a variational solution of Donnell’s equation. Calculations of both even and odd modes of the displacement are performed. The dispersion relations are shown to vary with the length of the tube and the displacement field of the nanotube is used to calculate the deformation potential interaction Hamiltonian.

Multiphonon resonant Raman scattering in the semimagneticsemiconductor Cd1−xMnxTe:Fröhlich and deformation potential exciton–phonon interaction

A theory describing multiphonon resonant Raman scattering (MPRRS)processes in wide-gap diluted magnetic semiconductors is presented,with Cd1−xMnxTeas an example. The incident radiation frequency ωl istaken above the fundamental absorption region. The photoexcited electron andhole make real transitions through the LO phonon, when one considers Fröhlich (F)and deformation potential (DP) interactions. The strong exchange interaction,typical of these materials, leads to a large spin splitting of the exciton states inthe magnetic field. Neglecting Landau quantization, this Zeeman splittinggives rise to the formation of eight bands (two conduction and six valenceones) and ten different exciton states according to the polarization of theincident light. Explicit expressions for the MPRRS intensity of secondand third order, the indirect creation and annihilation probabilities, theexciton lifetime, and the probabilities of transition between different excitonstates and different types of exciton as a function of ωl andthe external magnetic field are presented. The selection rules for all hot excitontransitions via exciton–photon interaction and F and DP exciton–phononinteractions are investigated. The exciton energies, as a function ofB, the Mnconcentration x, andthe temperature T,are compared to a theoretical expression. Graphics for creation and annihilationprobabilities, lifetime, and Raman intensity of second and third order arediscussed.

Acoustic modes in free and embedded quantum dots

Acoustic phonon spectra were calculated for different quantum dots for the free-standing case and for the case in which the quantum dot is embedded in a selection of different matrix materials including semiconductors, plastic, and water. The case of water as a matrix embedding a quantum dot is of special interest in biology where quantum dots are being used as biological tags. The acoustic phonon modes can be normalized in the free-standing case and the Hamiltonians for the deformation potential interactions derived. The results demonstrate that the matrix can have a large effect on the acoustic phonon spectrum and therefore it should be included when calculating the acoustic modes of the quantum-dot heterostructures. Simple analytic results are used to specify completely the lowest-order spherical breathing mode for free-standing quantum dots.

Theory of pure dephasing and the resulting absorption line shape in semiconductor quantum dots

The pure dephasing of the optical polarization and the corresponding line shape of absorption spectra in small quantum dots due to the interaction of the exciton both with optical and acoustic phonons is calculated. By restricting ourselves to the exciton ground state we obtain a model which is known to be exactly solvable. We study the temperature dependence and the influence of a static electric field. The spectra exhibit strongly non-Lorentzian line shapes including a sharp zero-phonon line. Optical phonons lead to phonon sidebands which may acquire a finite width due to the dispersion of the phonon branch; the width increases with decreasing dot size. Acoustic phonons both due to deformation potential and piezoelectric coupling lead to a broad background in the spectra which is strongly temperature dependent. Typical features of the spectra are qualitatively well reproduced by a perturbative approach based on one-phonon processes. Multiphonon processes, however, give significant contributions in particular in the case of acoustic phonons. Lateral or vertical electric fields lead to an increasing efficiency of the polar interaction mechanisms while deformation potential interaction is much less influenced.

Exciton-acoustic-phonon linewidths in GaAs bulk and quantum wells

Experimental results have shown that the acoustic phonon contribution to the homogeneous exciton linewidth increases substantially in going from GaAs quantum wells to bulk GaAs. Perturbation theory for acoustic phonon scattering using the deformation potential interaction and parabolic exciton dispersion accounts for experiment in quantum wells, but it fails by nearly an order of magnitude for bulk GaAs. Here we develop a theory of exciton-acoustic-phonon homogeneous linewidths using the anisotropic exciton dispersion, and we find for bulk GaAs that the piezoelectric interaction dominates the scattering. These results show that perturbation theory including these effects accounts well for the low temperature exciton linewidth in bulk GaAs as well as that in GaAs quantum wells. This approach also accounts for the available experimental results for exciton linewidths in bulk ZnSe and in ZeSe quantum wells.

Ultrafast intersubband scattering of holes in p-type modulation-doped Si 1− xGe x/Si multiple quantum wells

We report on an experimental and theoretical study of intersubband relaxation of holes in p-type modulation-doped Si 1− x Ge x /Si multiple quantum wells. The ultrafast hole dynamics is studied in pump–probe experiments with 150 fs mid-infrared pulses. For 4.4 nm wide wells ( x=0.5) the lifetime of holes in the second heavy hole subband is only 250 fs due to rapid emission of optical phonons via the deformation potential interaction. Model calculations of hole–phonon scattering give an almost identical value and point to the crucial role of cascaded scattering via an intermediate subband with light-hole-split-off symmetry.