Momentum average approximation for models with electron-phonon coupling dependent on the phonon momentum

We generalize the momentum average (MA) approximation to study the properties of models with momentum-dependent electron-phonon coupling. As in the case of the application of the original MA to the Holstein model, the results are analytical, numerically trivial to evaluate, exact for both zero bandwidth and for zero electron-phonon coupling, and are accurate everywhere in parameter space. Comparison with available numerical data confirms this accuracy. We then show that further improvements can be obtained based on variational considerations, using the one-dimensional breathing-mode Hamiltonian as a specific example. For example, by using this variational MA, we obtain ground state energies within at most 0.3% error of the numerical data.Comment: 15 pages, 10 figure

Sub-nanosecond delay of light in (Cd,Zn)Te crystal

We study excitonic polariton relaxation and propagation in bulk CdZnTe using time- resolved photoluminescence and time-of-flight techniques. Propagation of picosecond optical pulses through 0.745 mm thick crystal results in time delays up to 350 ps, depending on the photon energy. Optical pulses with 150 fs duration become strongly stretched. The spectral dependence of group velocity is consistent with the dispersion of the lower excitonic polariton branch. The lifetimes of excitonic polariton in the upper and lower branches are 1.5 and 3 ns, respectively.Comment: 5 pages, 4 figure

A Variational Approach to Nonlocal Exciton-Phonon Coupling

In this paper we apply variational energy band theory to a form of the Holstein Hamiltonian in which the influence of lattice vibrations (optical phonons) on both local site energies (local coupling) and transfers of electronic excitations between neighboring sites (nonlocal coupling) is taken into account. A flexible spanning set of orthonormal eigenfunctions of the joint exciton-phonon crystal momentum is used to arrive at a variational estimate (bound) of the ground state energy for every value of the joint crystal momentum, yielding a variational estimate of the lowest polaron energy band across the entire Brillouin zone, as well as the complete set of polaron Bloch functions associated with this band. The variation is implemented numerically, avoiding restrictive assumptions that have limited the scope of previous assaults on the same and similar problems. Polaron energy bands and the structure of the associated Bloch states are studied at general points in the three-dimensional parameter space of the model Hamiltonian (electronic tunneling, local coupling, nonlocal coupling), though our principal emphasis lay in under-studied area of nonlocal coupling and its interplay with electronic tunneling; a phase diagram summarizing the latter is presented. The common notion of a "self-trapping transition" is addressed and generalized.Comment: 33 pages, 11 figure

On fractional Choquard equations

We investigate a class of nonlinear Schrodinger equations with a generalized Choquard nonlinearity and fractional diffusion. We obtain regularity, existence, nonexistence, symmetry as well as decays properties.Comment: revised version, 22 page

Fractal and chaotic solutions of the discrete nonlinear Schr\"odinger equation in classical and quantum systems

We discuss stationary solutions of the discrete nonlinear Schr\"odinger equation (DNSE) with a potential of the $\phi^{4}$ 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

Analysis on reflection spectra in strained ZnO thin films

Thin films of laser molecular-beam epitaxy grown ZnO films were studied with respect to their optical properties. 4-K reflectivity was used to analyze various samples grown at different biaxial in-plane strain. The spectra show two structures at 3.37 eV corresponding to the A-free exciton transition and at 3.38 eV corresponding to the B-free exciton transition. Theoretical reflectivity spectra were calculated using the spatial dispersion model. Thus, the transverse energies, the longitudinal transversal splitting (ELT,), the oscillator strengths, and the damping parameters were determined for both the A- and B-free excitons of ZnO. As a rough trend, the strain dependence of the energy E_LT for the A-excitons is characterized by a negatively-peaking behavior with a minimum around the zero strain, while ELT for the B-excitons is an increasing function of the strain field values.Comment: 4 pages, 2 figures, 1 table, conference: ICMAT2005 (Singapore), to appear in an issue of J. Cryst. Growt

Solid-state physics : a historic experiment redesigned

PostprintPeer reviewe

Electron-phonon interaction via Pekar mechanism in nanostructures

We consider an electron-acoustic phonon coupling mechanism associated with the dependence of crystal dielectric permittivity on the strain (the so-called Pekar mechanism) in nanostructures characterized by strong confining electric fields. The efficiency of Pekar coupling is a function of both the absolute value and the spatial distribution of the electric field. It is demonstrated that this mechanism exhibits a phonon wavevector dependence similar to that of piezoelectricity and must be taken into account for electron transport calculations in an extended field distribution. In particular, we analyze the role of Pekar coupling in energy relaxation in silicon inversion layers. Comparison with the recent experimental results is provided to illustrate its potential significance

Coherent Propagation of Polaritons in Semiconductor Heterostructures: Nonlinear Pulse Transmission in Theory and Experiment

The influence of coherent optical nonlinearities on polariton propagation effects is studied within a theory-experiment comparison. A novel approach that combines a microscopic treatment of the boundary problem in a sample of finite thickness with excitonic and biexcitonic nonlinearities is introduced. Light-polarization dependent spectral changes are analyzed for single-pulse transmission and pump-probe excitation