Phonon-induced Relaxation Research Articles

Quantitative modeling of spin relaxation in quantum dots

We use numerically exact diagonalization to calculate the spin-orbit and phonon-induced triplet-singlet relaxation rate in a two-electron quantum dot exposed to a tilted magnetic field. Our scheme includes a three-dimensional description of the quantum dot, the Rashba and the linear and cubic Dresselhaus spin-orbit coupling, the ellipticity of the quantum dot, and the full angular description of the magnetic field. We are able to find reasonable agreement with the experimental results of Meunier et al. [Phys. Rev. Lett. 98, 126601 (2007)] in terms of the singlet-triplet energy splitting and the spin relaxation rate, respectively. We analyze in detail the effects of the spin-orbit factors, magnetic-field angles, and the dimensionality, and discuss the origins of the remaining deviations from the experimental data.

Spin-phonon coupling in single Mn-doped CdTe quantum dot

The spin dynamics of a single Mn atom in a laser driven CdTe quantum dot is addressed theoretically. Recent experimental results\cite{Le-Gall_PRL_2009,Goryca_PRL_2009,Le-Gall_PRB_2010}show that it is possible to induce Mn spin polarization by means of circularly polarized optical pumping. Pumping is made possible by the faster Mn spin relaxation in the presence of the exciton. Here we discuss different Mn spin relaxation mechanisms. First, Mn-phonon coupling, which is enhanced in the presence of the exciton. Second, phonon-induced hole spin relaxation combined with carrier-Mn spin flip coupling and photon emission results in Mn spin relaxation. We model the Mn spin dynamics under the influence of a pumping laser that injects excitons into the dot, taking into account exciton-Mn exchange and phonon induced spin relaxation of both Mn and holes. Our simulations account for the optically induced Mn spin pumping.

Theoretical Study of Electron–Phonon Relaxation in PbSe and CdSe Quantum Dots: Evidence for Phonon Memory

Wehavecombinedanalyticaltheorywithabinitio nonadiabatic molecular dynamics to study the phonon-induced relaxation of photoexcited charge carriers in PbSe and CdSe semiconductorquantumdots(QDs).Densityfunctionaltheory calculations show dense distributions of electronic levels near the energy gap, attributed to the reconstruction and lack of absolute symmetry of the QD surface. Most of these states are optically dark, but they do couple to phonons and facilitate charge carrier relaxation. The time-domain simulations show a complex, nonexponential relaxation, in agreement with the observed non-Lorenzian spectral line shapes. The relaxation accelerates athigherphotoexcitationenergiesduetobothahigherdensityofcarrierstatesandalargernonadiabaticelectronphononcoupling. Overtime,carrier relaxation changes fromGaussian toexponential. TheGaussian componentislargerinsmallerdots;this maybea manifestation of the phonon bottleneck effect. Since Markovian rate models give exponential decay, we suggest that the more complex form of the carrier relaxation, observed in our simulations, can be attributed to phonon memory. The analytic theory developed within the framework of quantized Hamilton dynamics rationalizes this observation. It shows that a detailed description of the phonon modes is more important than a model for the electronic states.

Microscopic study of the efficiency of Coulomb- and phonon-induced relaxation channels in graphene

We present a microscopic approach on ultrafast relaxation dynamics of optically excited carriers in graphene. In agreement with experimental differential transmission spectra, we find the dynamics to be characterized by two timescales: the ultrafast femtosecond thermalization and the carrier cooling on a picosecond timescale. The framework of the density matrix theory allows to separately analyze the strength of different relaxation channels, such as carrier–carrier and carrier–phonon scattering, resolved in time, momentum, and angle. Our calculations reveal that the initial thermalization is governed by the Coulomb interaction, however the carrier–phonon scattering also considerably contributes to the process of forming a hot Fermi distribution. The energy dissipation and the cooling of carriers is determined by phonon-induced intra- and interband scattering.

Phonon-induced relaxation in theCr7Nimagnetic molecule probed by NMR

We study the phonon-induced relaxation dynamics in the heterometallic ${\text{Cr}}_{7}\text{Ni}$ ring. By assuming that spin-phonon coupling occurs through the modulation of local crystal fields, we investigate the decay of time correlations of molecular observables, such as fluctuations of the cluster magnetization. Single-crystal $^{1}\text{H}$ nuclear magnetic resonance measurements have been performed for two orthogonal orientations of the applied magnetic field. The nuclear spin-lattice relaxation rate $1/{T}_{1}$ probes fluctuations of specific molecular observables, thus allowing to determine the magnetoelastic coupling strength and to calculate the magnetization relaxation time as well as phonon-induced level lifetimes. The knowledge of these time scales is crucial to control the spin dynamics of the magnetic cluster in view of the potential technological applications.

Theory of the Spin Relaxation of Conduction Electrons in Silicon

A realistic pseudopotential model is introduced to investigate the phonon-induced spin relaxation of conduction electrons in bulk silicon. We find a surprisingly subtle interference of the Elliott and Yafet processes affecting the spin relaxation over a wide temperature range, suppressing the significance of the intravalley spin-flip scattering, previously considered dominant, above roughly 120 K. The calculated spin relaxation times T1 agree with the spin resonance and spin injection data, following a T(-3) temperature dependence. The valley anisotropy of T1 and the spin relaxation rates for hot electrons are predicted.

The influence of polaron–phonon interaction on absorption spectra in molecular crystals

We investigate theoretically the possible manifestation of the small-polaron effect in the IR absorption spectrum of the one-dimensional molecular crystals. Phonon-induced relaxation of small-polarons is taken into account explicitly on the microscopic level. It was found that it may have substantial influence on optical properties of molecular crystals. Consequently, the accounting of the polaron relaxation effects on the microscopic level is necessary for proper understanding of the optical spectra of molecular crystals. Their hitherto interpretation in terms of polaron model, based on the phenomenological treatment of the polaron damping, has been critically assessed on the basis of our results.

Magnetization and spin dynamics of a Cr-based magnetic cluster: [formula omitted

We study the magnetization and the spin dynamics of the Cr 7 Ni ring-shaped magnetic cluster. Measurements of the magnetization at high pulsed fields and low temperature are compared to calculations and show that the spin Hamiltonian approach provides a good description of the Cr 7 Ni magnetic molecule. In addition, the phonon-induced relaxation dynamics of molecular observables has been investigated. By assuming the spin–phonon coupling to take place through the modulation of the local crystal fields, it is possible to evaluate the decay of fluctuations of two generic molecular observables. The nuclear spin–lattice relaxation rate 1 / T 1 directly probes such fluctuations, and allows to determine the magnetoelastic coupling strength.

Symmetric band structures and asymmetric ultrafast electron and hole relaxations in silicon and germanium quantum dots: time-domain ab initio simulation

State-of-the-art time domain density functional theory and non-adiabatic (NA) molecular dynamic simulations are used to study phonon-induced relaxation of photoexcited electrons and holes in Ge and Si quantum dots (QDs). The relaxation competes with productive processes and causes energy and voltage losses in QD solar cells. The ab initio calculations show that quantum confinement makes the electron and hole density of states (DOS) more symmetric in Si and Ge QDs compared to bulk. Surprisingly, in spite of the symmetric DOS, the electron and hole relaxations are quite asymmetric: the electrons decay faster than the holes. The asymmetry arises due to stronger NA coupling in the conduction band (CB) than in the valence band (VB). The stronger NA coupling of the electrons compared to the holes is rationalized by the larger contribution of the high-frequency Ge-H and Si-H surface passivating bonds to the CB relative to the VB. Linear relationships between the electron and hole relaxation rates and the CB and VB DOS are found in agreement with Fermi's golden rule. The faster relaxation of the electrons compared to the holes in the Ge and Si QDs is unexpected and is in contrast with the corresponding dynamics in the majority of binary QDs, such as CdSe. It suggests that Auger processes will transfer energy from holes to electrons rather than in the opposite direction as in CdSe, and that a larger fraction of the photoexcitation energy will be transferred to phonons coupled with electrons rather than holes. The difference in the phonon-induced electron and hole decay rates is larger in Ge than Si, indicating that the Auger processes should be particularly important in Ge QDs. The simulations provide direct evidence that the high-frequency ligand modes on the QD surface play a pivotal role in the electron-phonon relaxation dynamics of semiconductor QDs.

Electric-field-controlled electron relaxation in lateral double quantum dots embedded in a suspended slab

This study investigates phonon-induced electron relaxation in a lateral double quantum dot that is embedded in a suspended slab. Exact calculations are made in electric fields. The dependence of the relaxation rate on the parameters of the dots and the slabs is analyzed. Numerical results indicate that the relaxation rate depends strongly on the phonon character of the slab. Unlike in the bulk environment, phonon-subband quantization clearly influences the behavior. In particular, the relaxation rate can be greatly suppressed or enhanced by tuning the electric fields. This fact may be useful in manipulating the relaxation rate in lateral double quantum dots.

Calculation of Anharmonic Coupling Constants between Phonon Modes in GaAs

Anharmonic coupling between phonon modes of a crystal determine many of its properties, thermal conductivity being a standard example. Although anharmonicity-related effects observed in bulk crystals (decay of the zone-center longitudinal optical (LO) phonon or acoustic wave attenuation) rely only on a small subset of anharmonic couplings, the full set of such constants is needed for a complete description of phonon-induced dephasing and relaxation of electrons and excitons in quantum dots [1–4]. The reason for this is that breaking of the translational symmetry and appearance of a quantized spectrum completely changes the energy-momentum conservation conditions and opens decoherence (relaxation and dephasing) paths which are not allowed in a bulk crystal. So far, only the anharmonic couplings between acoustic branches have been completely described [5], while the only known coupling involving optical phonons is that between the LO phonon and two longitudinal acoustic (LA) phonons, which seems to be responsible for the decay of the zone-center LO phonon in a bulk crystal [6] and is therefore accessible experimentally [7]. In this paper, we derive third-order anharmonic coupling constants between various phonon modes in a zinc-blende crystal. We use a model combining the

Control of electron spin and orbital resonances in quantum dots through spin-orbit interactions

The influence of a resonant oscillating electromagnetic field on a single electron in coupled lateral quantum dots in the presence of phonon-induced relaxation and decoherence is investigated. Using symmetry arguments, it is shown that the spin and orbital resonances can be efficiently controlled by spin-orbit interactions. The control is possible due to the strong sensitivity of the Rabi frequency to the dot configuration (the orientation of the dot and the applied static magnetic field); the sensitivity is a result of the anisotropy of the spin-orbit interactions. The so-called easy passage configuration is shown to be particularly suitable for a magnetic manipulation of spin qubits, ensuring long spin relaxation times and protecting the spin qubits from electric field disturbances accompanying on-chip manipulations.

Comparative analysis of electron-phonon relaxation in a semiconducting carbon nanotube and a PbSe quantum dot

Abstract The key features of the phonon-induced relaxation of electronic excitations in the (7,0) zig-zag carbon nanotube (CNT) and the Pb16Se16 quantum dot (QD) are contrasted using a time-domain ab initio density functional theory (DFT) simulation. Upon excitation from the valence to the conduction band (CB), the electrons and holes nonradiatively decay to the band-edge in both materials. The paper compares the electronic structure, optical spectra, important phonon modes, and decay channels in the CNT and QD. The relaxation is faster in the CNT than in the QD. In the PbSe QD, the electronic energy decays by coupling to low-frequency acoustic modes. The decay is nonexponential, in agreement with non-Lorentzian line-shapes observed in optical experiments. In contrast to the QD, the excitation decay in the CNT occurs primarily via high-frequency optical modes. Even though the holes have a higher density of states (DOS), they relax more slowly than the electrons, due to better coupling to low-frequency vibrations. Further, the expected phonon bottleneck is not observed in the QD, as rationalized by a high density of optically dark states. The same argument applies to the CNT. The computed results agree well with experimentally measured ultrafast relaxation time-scales and provide a unique atomistic picture of the electron-phonon relaxation processes.

Theory of optical excitation and relaxation phenomena at semiconductor surfaces: linking density functional and density matrix theory

A theory for the description of optical excitation and the subsequent phonon-induced relaxation dynamics of nonequilibrium electrons at semiconductor surfaces is presented. In the first part, the fundamental dynamical equations for electronic occupations and polarisations are derived using density matrix formalism (DMT) for a surface-bulk system including the interaction of electrons with the optical field and electron–phonon interactions. The matrix elements entering these equations are either determined empirically or by density functional theory (DFT) calculations. In the subsequent parts of the paper, the dynamics at two specific semiconductor surfaces are discussed in detail. The electron relaxation dynamics underlying a time-resolved two photon photoemission experiment at an InP surface is investigated in the limit of a parabolic four band model. Moreover, the electron relaxation dynamics at a Si(100) surface is analysed. Here, the coupling parameters and the band structure are obtained from an DFT calculations.

Phonon-induced electron relaxation in quantum rings

We study electron--acoustic-phonon scattering and electron relaxation in quantum rings in the absence and in the presence of external magnetic fields. The electron-phonon interaction is accounted for both the deformation potential and piezoelectric coupling. At zero magnetic field and small ring radius, the deformation potential phonon scattering is orders of magnitude larger than the piezoelectric one. However, the piezoelectric coupling is found to become important when the ring radius and magnetic field increase. It can be the dominant scattering mechanism at large ring radii and/or large magnetic fields. In comparison with the quantum dot case, the acoustic phonon scattering is stronger in quantum rings.

Ab Initio Time-Domain Study of Phonon-Assisted Relaxation of Charge Carriers in a PbSe Quantum Dot

The phonon-induced relaxation dynamics of charge carriers in a PbSe quantum dot is studied for the first time by ab initio density functional theory in the time-domain. The picosecond time scale of the relaxation and the absence of the phonon bottleneck are rationalized by relatively high electron and hole state densities. While many of these states show only weak optical activity, most of them participate in the electron-vibrational relaxation. Our simulations demonstrate that the slight asymmetry in the electron and hole band structure is sufficient to allow symmetry-forbidden S-P, P-S, etc. transitions, which are seen in the experimental absorption spectra. The relaxation is nonexponential, in agreement with the strongly non-Lorentzian spectral line shapes observed in experiments. The energy exchanged during individual transitions is typically greater than the characteristic phonon energy, indicating that the transitions are multiphonon. Both electrons and holes interact better with low-frequency acoustic phonons, rather than higher frequency optical modes. Holes decay only slightly faster than electrons, rendering the hole-assisted Auger relaxation pathways inefficient. This relatively symmetric vibrational relaxation of electrons and holes proceeds on a picosecond time scale, much slower than the ultrafast highly efficient carrier multiplication that was reported recently in relation to improved solar power conversion.

Relaxation of the magnetization in a molecule containing [formula omitted] ions : [formula omitted

We investigate the phonon-induced relaxation dynamics in the V 12 cluster, which contains ions with spin 1 2 . By assuming the spin–phonon coupling to take place through modulation of anisotropic exchange, we calculate the decay of the autocorrelation of the molecular magnetization, and the associated nuclear-spin relaxation rate 1 / T 1 . Excellent quantitative agreement with existing experimental 1 / T 1 data is obtained.

Nuclear spin-lattice relaxation inn-type insulating and metallic GaAs single crystals

The coupling of electron and nuclear spins in $n\text{\ensuremath{-}}\mathrm{Ga}\mathrm{As}$ changes significantly as the donor concentration $n$ increases through the insulator-metal critical concentration ${n}_{\mathrm{C}}\ensuremath{\sim}1.2\ifmmode\times\else\texttimes\fi{}{10}^{16}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$. The present measurements of the $^{71}\mathrm{Ga}$ relaxation rates $W$ made as a function of magnetic field $(1--13\phantom{\rule{0.3em}{0ex}}\mathrm{T})$ and temperature $(1.5--300\phantom{\rule{0.3em}{0ex}}\mathrm{K})$ for semi-insulating GaAs and for three doped $n\text{\ensuremath{-}}\mathrm{Ga}\mathrm{As}$ samples with donor concentrations $n=5.9\ifmmode\times\else\texttimes\fi{}{10}^{15}$, $7\ifmmode\times\else\texttimes\fi{}{10}^{16}$, and $2\ifmmode\times\else\texttimes\fi{}{10}^{18}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$, show marked changes in the relaxation behavior with $n$. Korringa-like relaxation is found in both metallic samples for $T<30\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, while for $T>30\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ phonon-induced nuclear quadrupolar relaxation is dominant. The relaxation rate measurements permit determination of the electron probability density at $^{71}\mathrm{Ga}$ sites. A small Knight shift of $\ensuremath{-}3.3\phantom{\rule{0.3em}{0ex}}\mathrm{ppm}$ was measured on the most metallic $(2\ifmmode\times\else\texttimes\fi{}{10}^{18}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3})$ sample using magic-angle spinning at room temperature. For the $n=5.9\ifmmode\times\else\texttimes\fi{}{10}^{15}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$ sample, a nuclear relaxation model involving the Fermi contact hyperfine interaction, rapid spin diffusion, and exchange coupled local moments is proposed. While the relaxation rate behavior with temperature for the weakly metallic sample, $n=7\ifmmode\times\else\texttimes\fi{}{10}^{16}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$, is similar to that found for the just-insulating sample, the magnetic field dependence is quite different. For the $5.9\ifmmode\times\else\texttimes\fi{}{10}^{15}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$ sample, increasing the magnetic field leads to a decrease in the relaxation rate, while for the $7\ifmmode\times\else\texttimes\fi{}{10}^{16}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$ sample this results in an increase in the relaxation rate ascribed to an increase in the density of states at the Fermi level as the Landau level degeneracy is increased.

Phonon-induced relaxation of a two-state system in solids

We study phonon-induced relaxation of quantum states of a particle (e.g., electron or proton) in a rigid double-well potential in a solid. The relaxation rate due to Raman two-phonon processes has been computed. We show that in the two-state limit symmetry arguments allow one to express these rates in terms of independently measurable parameters. In general, the two-phonon processes dominate relaxation at higher temperature. Due to parity effects in a biased two-state system, their rate can be controlled by the bias.

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.