Hot electron relaxation in one-dimensional models: exact polaron dynamics versus relaxation in the presence of a Fermi sea

We present the exact solution for the time evolution of the electron and phonon momentum distribution for a one-dimensional polaron model with alinear electronic energy dispersion. The electron momentum distribution is shown to obey aMarkovian quantum kinetic equation. Numerical results for the polaron model are compared to the corresponding exact results, when the negative momentum states are filled in the initial state. The presence of this Fermi sea modifies the dynamics except in the short time regime. The different, long time dynamics might show up in comparison of hot electron relaxation of undoped and doped semiconductors.     

Magnetic transition and polaron crossover in a two-site single polaron model including double exchange interaction

A two-site double exchange model with a single polaron is studied using a perturbation expansion based on the modified Lang-Firsov transformation. The antiferromagnetic to ferromagnetic transition and the crossover from small to large polaron are investigated for different values of the antiferromagnetic interaction (J) between the core spins and the hopping (t) of the itinerant electron. Effect of the external magnetic field on the small to large polaron crossover and on the polaronic kinetic energy are studied. When the magnetic transition and the small to large polaron crossover coincide for some suitable range of J/t, the magnetic field has very pronounced effect on the dynamics of polarons. Received 1 June 2000     

Repulsive Polarons in One-Dimensional Fermi Gases

Using the variational method, we study the properties of a spin-down impurity immersed in a onedimensional(1 D) spin-up Fermi sea. With repulsive interactions between them, the impurity is dressed up by surrounding particles in Fermi sea and forms a polaron. We clearly calculate the binding energy, effective mass, momentum distribution, Tan contact, and pair correlation. Even in strong repulsive regimes, the results can agree with the exact Bethe Ansatz results. The repulsive polaron energy E+ is below Fermi energy EF and no negative effective masses are found in whole interaction regimes, unequal masses polarons are also calculated. We show a clear momentum distribution and calculate the Tan contact from three different aspects. Furthermore, we explore the particle-hole excitation and find that the hole terms in Fermi sea have a great influence on the polaron energy and contact in repulsive regime. These results show that the variational method can still be used effectively in 1 D repulsive polaron system.     

Some approaches to polaron theory

Here, in our approximation of polaron theory, we examine the importance of introducing theT product, which turn out to be a very convenient theoretical approach for the calculation of thermodynamical averages.We focus attention on the investigation of the so-called linear polaron Hamiltonian and present in detail the calculation of the correlation function, spectral function, and Green function for such a linear system.It is shown that the linear polaron Hamiltonian provides an exactly solvable model of our system, and the result obtained with this approach holds true for an arbitrary coupling constant which describes the strength of interaction between the electron and the lattice vibrations. Then, with the help of a variational technique, we show the possibility of reducing the real polaron Hamiltonian to a socalled trial or approximate linear model Hamiltonian.We also consider the exact calculation of free energy with a special technique that reduces calculations with the help of the T product, which, in our opinion, works much better and is easier than other analogous considerations, for example, the path-integral or Feynman-integral method.^(1,2) Here we furthermore recall our own work,⁽⁴⁾ where it was shown that the results of Refs. 7 and 8 concerning the impedance calculation in the polaron model may be obtained directly without the use of the path-integral method.The study of the polaron system's thermodynamics is carried out by us in the framework of the functional method. A calculation of the free energy and the momentum distribution function is proposed.Note also that the polaron systems with strong coupling⁽⁹⁾ proved to be useful in different quantum field models in connection with the construction of dynamical models of composite particles. A rigorous solution of the special strong-coupling polaron problem, describing the interaction of a nonrelativistic particle with a quantum field, was given by Bogolubov.⁽³⁾ The works of Tavkhelidze, Fedyanin, Khrustalev, and others^(10–13) are dedicated to the further development and generalization of the Bogolubov method.Notice, too, that the electron-photon interaction effects play an important part in many problems of modern solid state theory (see, e.g., Refs. 7 and 14–19).The present paper summarizes a set of lectures delivered as a special course in the physics department of Moscow State University.     

An analytic study of the E ⊗ e Jahn-Teller polaron

An analytic study is presented of the E⊗e Jahn-Teller (JT) polaron, consisting of a mobile e_g electron linearly coupled to the local e_g normal vibrations of a periodic array of octahedral complexes. Due to the linear coupling, the parity operator and the angular momentum operator commute with the JT part and cause a twofold degeneracy of each JT eigenvalue. This degeneracy is lifted by the anisotropic hopping term. The Hamiltonian is then mapped onto a new Hilbert space, which is isomorphic to an eigenspace of belonging to a fixed angular momentum eigenvalue j > 0. In this representation, the Hamiltonian depends explicitly on j and decomposes into a Holstein term and a residual JT interaction. While the ground state of the JT polaron is shown to belong to the sector j = 1/2, the Holstein polaron is obtained for the “unphysical” value j = 0. The new Hamiltonian is then subjected to a variational treatment, yielding the dispersion relations and effective masses for both kinds of polarons. The calculated polaron masses are in remarkably good agreement with recent quantum Monte Carlo data. The possible relevance of our results to the magnetoresistive manganite perovskites is briefly discussed. Received 6 July 2001     

Exciton relaxation in self-assembled semiconductor quantum dots

The present study focuses on the effect of excited states on the exciton–polaron spectrum for self-assembled InAs/GaAs semiconductor quantum dots. The analytical model takes into account the Coulomb interactions between the electron and the hole as well as, each carrier, the coupling with the longitudinal optical phonon field. Furthermore, the key role played by the exciton continuum in the dot spectrum is also introduced. Such an approach is well fitted to analyze recent experimental findings about single-dot spectroscopy and allows peaks assignment, line width estimation, relaxation time evaluation, etc., necessary steps toward an understanding of the internal dynamics of quantum dots.     

On Algebraic Integrability of the Deformed Elliptic Calogero-Moser Problem

Abstract

We discuss stationary solutions of the discrete nonlinear Schrödinger equation (DNSE) with a potential of the ? ⁴ type which is generically applicable to several quantum spin, electron and classical lattice systems. We show that there may arise chaotic spatial structures in the form of incommensurate or irregular quantum states. As a first (typical) example we consider a single electron which is strongly coupled with phonons on a 1D chain of atoms — the (Rashba)–Holstein polaron model. In the adiabatic approximation this system is conventionally described by the DNSE. Another relevant example is that of superconducting states in layered superconductors described by the same DNSE. Amongst many other applications the typical example for a classical lattice is a system of coupled nonlinear oscillators. We present the exact energy spectrum of this model in the strong coupling limit and the corresponding wave function. Using this as a starting point we go on to calculate the wave function for moderate coupling and find that the energy eigenvalue of these structures of the wave function is in exquisite agreement with the exact strong coupling result. This procedure allows us to obtain (numerically) exact solutions of the DNSE directly. When applied to our typical example we find that the wave function of an electron on a deformable lattice (and other quantum or classical discrete systems) may exhibit incommensurate and irregular structures. These states are analogous to the periodic, quasiperiodic and chaotic structures found in classical chaotic dynamics.     

半导体量子阱中电子自旋弛豫和动量弛豫

根据电子自旋轨道耦合对自旋极化弛豫影响的DP机理进一步导出了半导体中电子自旋弛豫与动量弛豫及载流子浓度的关系，并采用飞秒抽运探测技术在室温下测量AlGaAs/GaAs 多量子阱中载流子浓度在 1×10¹⁷—1×10¹⁸cm^-3范围内，电子自旋弛豫时间由58ps增加至82 ps的变化情况，与理论计算值符合，说明了随着载流子浓度的增加，载流子间的频繁散射加速了电子动量驰豫，减弱了电子自旋轨道耦合作用，从而延长了电子自旋寿命. 关键词： 电子自旋轨道耦合 电子自旋弛豫和动量弛豫 飞秒光谱技术     

Compton profiles of electron momentum distribution inβ-Ga

We report for the first time the Compton profiles of electron momentum distribution inβ-gallium calculated along the crystallographic directions (100), (110) and (111). The conduction electron states for this purpose are determined in the energy band calculations using model potential. The core states, on the other hand, are represented each by a single tight-binding function. The results show that the Compton profiles are nearly isotropic with very little directional dependence, which is suggestive of a free-electron-like distribution of the conduction electrons in this system. The latter conclusion is in close confirmity with similar conclusions drawn in augmented plane wave (APW) calculation of energy bands and the derived Knight-shift results inβ-Ga.     

Spectral properties of the 2D Holstein polaron

The two-dimensional Holstein model is studied by means of direct Lanczos diagonalization preserving the full dynamics and quantum nature of phonons. We present numerical exact results for the single-particle spectral function, the polaronic quasiparticle weight, and the optical conductivity. The polaron band dispersion is derived both from exact diagonalization of small lattices and analytic calculation of the polaron self-energy.     

First-principles study of electron dynamics with explicit treatment of momentum dispersion on Si nanowires along different directions

ABSTRACT

In this research, ground-state electronic structure and optical properties along with photoinduced electron dynamics of Si nanowires oriented in various directions are reviewed. These nanowires are significant functional units of future nano-electronic devices. All observables are computed for a distribution of wave vectors at ambient temperature. Optical properties are computed under the approximation of momentum conservation. The total absorption is composed of partial contributions from fixed values of momentum. The on-the-fly non-adiabatic couplings obtained along the ab initio molecular dynamics nuclear trajectories are used as parameters for Redfield density matrix equation of motion. The main outcomes of this study are transition energies, light absorption spectra, electron and hole relaxation rates, and electron transport properties. The results of these calculations would contribute to the understanding of the mechanism of electron transfer process on the Si nanowires for optoelectronic applications.     

Polar optical phonon limited energy and momentum relaxation of hot electrons in a GaAs-quantum well (QW)

The average energy loss rate, the energy- as well as the momentum relaxation time of hot electrons confined in a GaAs-square quantum well are calculated as a function of the external controllable parametersn _s (electron density),T (lattice temperature) andT _e (electron temperature) for the interaction of the charge carriers with bulk- and surface polar optical phonons. Analytical expressions are derived in the limit of vanishing quantum well width at non-degeneracy and degeneracy of the electron system. Both energy-and momentum relaxation time are found to be complicated functions of the ratiosT _D /T _e andT _D /T withT _D being the Debye-temperature of the polar optical phonon involved in the scattering. In a thick (very thin) QW the energy loss rate to bulk PO-phonons is found to be larger (smaller) than the corresponding loss rate to surface modes. The energy- (momentum-) relaxation times are found to be constant (increasing) functions ofn _s at non-degeneracy (degeneracy) of the electron system. Dedicated to Professor Karlheinz Seeger on the occasion of his 60th birthday     

Electron acceleration via collisions with ions in plasma under the action of a relativistically strong laser field

Electron-ion collisions in plasma in a strong electromagnetic field are considered in the ultrarelativistic limit (in which the vector potential A is such that a = eA/mc ² ? 1). Expressions relating the electron drift coordinates and momentum to those in the laboratory frame are obtained using exact canonical transformations with allowance for adiabatic effects. The appearance of ultrafast particles with a maximum energy proportional to the third power of the laser pulse vector potential is predicted. Expressions for the energy (and number) distribution function of such high-energy (hot) electrons appearing as a result of electron-ion collisions are obtained. These distribution functions obey a power law, which agrees with the results recently obtained by Mangles et al. [1] in experiments with a petawatt laser.     

Dynamics of interchain delocalized polarons in polymers

Polaron dynamics in a system of highly ordered conjugated polymer chains is investigated based on the tight binding model. With the interchain coupling enhancing,it takes longer time for the electron added to the system to induce a localized polaron state. Beyond a certain strength of the interchain coupling,the electron evolves into a two-dimensional delocalized polaron state. Dynamical simulations suggest that the well-ordered organic molecule systems with two-dimensional polarons exhibit higher mobilitie...     

Sharp transition for single polarons in the one-dimensional Su-Schrieffer-Heeger model

We study a single polaron in the Su-Schrieffer-Heeger (SSH) model using four different techniques (three numerical and one analytical). Polarons show a smooth crossover from weak to strong coupling, as a function of the electron-phonon coupling strength λ, in all models where this coupling depends only on phonon momentum q. In the SSH model the coupling also depends on the electron momentum k; we find it has a sharp transition, at a critical coupling strength λ(c), between states with zero and nonzero momentum of the ground state. All other properties of the polaron are also singular at λ=λ(c). This result is representative of all polarons with coupling depending on k and q, and will have important experimental consequences (e.g., in angle-resolved photoemission spectroscopy and conductivity experiments).     

Small polaron mass with a long range density-displacement type interaction

In this work renormalization of the effective mass of an electron due to a small polaron formation is studied within the framework of the extended Holstein model. It is assumed that an electron moves along the one-dimensional chain of ions and interacts with ions vibrations of a neighboring chain via a long-range density-displacement type force. By means of the exact calculations a renormalized mass of a nonadiabatic small polaron is obtained at strong coupling limit. The obtained results compared with the mass of small polaron of ordinary Holstein model. The effect of ions vibrations polarization on the small polaron mass is addressed.     

An exact solution for a rotating body with negligible mass

If it becomes possible to test general relativity by laboratory experiments on rotation, the ratios of mass to angular momentum per unit mass are likely to be extremely small. Solutions for a rotating body with low m/a are therefore of interest. Here I discuss Papapetrous exact solution, which has zero mass and arbitrary angular momentum.     

Dynamics of ionization mechanisms in relativistic collisions involving heavy and highly-charged ions

The dynamics of mechanisms associated with the ionization of inner-shell electrons in relativistic collisions involving heavy and highly-charged ions is investigated within a nonperturbative approach formulated explicitly in the time domain. The theoretical treatment is based on the exact numerical solution of the time dependent Dirac equation for two Coulomb centers on a lattice in momentum space. We present results for ionization in encounters between 100 MeV/u Au⁷⁹⁺ projectile ions impinging on a hydrogen-like uranium target. By directly visualizing the collision dynamics we identify a new ionization mechanism in which electrons are emitted from the internuclear region preferentially in the transverse direction with respect to the projectile trajectory. A striking characteristic of this ionization mechanism is that the velocity of the electron is higher than the projectile velocity. Received 26 June 2001 and Received in final form 27 November 2001     

Investigation of the antineutrino angular distribution in experiments on the β decay of polarized neutrons

Since the emission of γ grays unavoidably accompanies β decay, the final state after the β decay of a neutron includes a photon along with a proton, an electron, and an antineutrino, i.e., four particles, rather than three. Therefore, when only the electron and proton momenta are detected and the γ-ray momentum is not detected in an experiment, the antineutrino momentum cannot be uniquely reconstructed, and only its mean value over a γ-ray momentum distribution determined from corresponding calculations can be considered. The γ grays are significant for finding the asymmetry parameter B of the antineutrino angular distribution from experiments on the β decay of polarized neutrons, where the electron momentum p directed along the x axis and the projection of the proton momentum P _x onto the x axis are detected, and the neutron polarization vector ξ is parallel or antiparallel to x. Since the γ rays are not detected in such experiments, the antineutrino kinematics are not uniquely specified by the observables p and P _x and can be reconstructed only on the average, so that the antineutrino momentum distribution averaged over a γ-ray momentum distribution is considered. Thus, the exact value of B cannot be obtained from these experiments, but the true value of B can be estimated on the average by considering the mean (most likely) value 〈B〉 and the dispersion (rms deviation) ΔB. The unavoidable uncertainty in the estimate of B amounts to several percent and is thus significant for present-day experiments, which are intended to obtain the value of B to a very high accuracy of ∼ (0.1–1)%. If electromagnetic interactions are taken into account, measurements of the electron and proton momentum distributions can also be used to obtain g _A, i.e., the axial β-decay amplitude, to high accuracy. Zh. éksp. Teor. Fiz. 116, 1505–1522 (November 1999)