Self-trapping of interacting electrons in crystalline nonlinear chains (original) (raw)

Self-trapping in quasi-one-dimensional electron- and exciton-phonon systems

Physical Review B, 1993

We study self-trapping of electrons (excitons) in one-dimensional systems with three realistic types of coupling with phonons, applying a variational procedure valid for the whole range of system parameters. Various types of self-trapped states are identified and mapped in the parameter space. Our results are compared to the results of previous studies. The particular case of biological systems is studied and it is shown that the Davydov-soliton concept can be used for the description of electron transport in biological systems, but not for the energy transfer in terms of amide-I vibrations (CO stretching vibration mode).

Electron self-trapping in a discrete two-dimensional lattice

Physica D: Nonlinear Phenomena, 2001

We study analytically and numerically the electron-phonon interaction in an isotropic two-dimensional lattice. We show that the properties of the system depend crucially on the electron-phonon coupling constant and that the system admits stationary soliton-like solutions when the coupling constant takes numerical values within some finite interval. We predict the lower critical value of the coupling constant and study some properties of the corresponding solutions. We estimate the period of oscillation of the slightly excited field configurations. We also prove that above the upper critical value of the coupling constant the regime of strong localisation (small polaron) takes place.

Universal features of self-trapping in nonlinear tight-binding lattices

Physical Review B, 2000

We show that nonlinear tight-binding lattices of different geometries and dimensionalities, display an universal selftrapping behavior. First, we consider the single nonlinear impurity problem in various tight-binding lattices, and use the Green's function formalism for an exact calculation of the minimum nonlinearity strength to form a stationary bound state. For all lattices, we find that this critical nonlinearity parameter (scaled by the energy of the bound state), in terms of the nonlinearity exponent, falls inside a narrow band, which converges to e 1/2 at large exponent values. Then, we use the Discrete Nonlinear Schrödinger (DNLS) equation to examine the selftrapping dynamics of a single excitation, initially localized on the single nonlinear site, and compute the critical nonlinearity parameter for abrupt dynamical selftrapping. For a given nonlinearity exponent, this critical nonlinearity, properly scaled, is found to be nearly the same for all lattices. Same results are obtained when generalizing to completely nonlinear lattices, suggesting an underlying selftrapping universality behavior for all nonlinear (even disordered) tight-binding lattices described by DNLS.

Self-trapping problem of electrons or excitons in one dimension

Physical Review B, 1998

We present a detailed numerical study of the one-dimensional Holstein model with a view to understanding the self-trapping process of electrons or excitons in crystals with short-range particle-lattice interactions. Applying a very efficient variational Lanczos method, we are able to analyze the groundstate properties of the system in the weak-and strong-coupling, adiabatic and non-adiabatic regimes on lattices large enough to eliminate finite-size effects. In particular, we obtain the complete phase diagram and comment on the existence of a critical length for self-trapping in spatially restricted onedimensional systems. In order to characterize large and small polaron states we calculate self-consistently the lattice distortions and the particle-phonon correlation functions. In the strong-coupling case, two distinct types of small polaron states are shown to be possible according to the relative importance of static displacement field and dynamic polaron effects. Special emphasis is on the intermediate coupling regime, which we also study by means of direct diagonalization preserving the full dynamics and quantum nature of phonons. The crossover from large to small polarons shows up in a strong decrease of the kinetic energy accompanied by a substantial change in the optical absorption spectra. We show that our numerical results in all important limiting cases reveal an excellent agreement with both analytical perturbation theory predictions and very recent density matrix renormalization group data.

SELFTRAPPING DYNAMICS IN TWO-DIMENSIONAL NONLINEAR LATTICES

Modern Physics Letters B, 1999

We compute numerically the selftrapping dynamics for an electron or excitation initially located on a single site of a two-dimensional nonlinear lattice of arbitrary nonlinear exponent. The time evolution is given by the Discrete Nonlinear Schrödinger (DNLS) equation and we focus on the long-time average probability at the initial site and the mean square displacement in terms of both the exponent and strength of the nonlinearity. For the square and triangular nonlinear lattices, we find selftrapping for nonlinearity parameters greater than an exponent-dependent critical value, whose magnitude increases (decreases) with the nonlinear exponent when this is larger (smaller) than one, approximately. PACS Number(s): 72.10.-d, 72.90.+y

Dynamics of one electron in a nonlinear disordered chain

2012

Abstract In this paper we report new numerical results on the disordered Schrödinger equation with nonlinear hopping. By using a classical harmonic Hamiltonian and the Su–Schrieffer–Heeger approximation we write an effective Schrödinger equation. This model with off-diagonal nonlinearity allows us to study the interaction of one electron and acoustical phonons.

Nonlinear Quantum Dynamics of Strong Vibration: Relaxation Jumps and Phonon Bursts*

Zeitschrift für Physikalische Chemie, 1996

We examine quantum decay of localized vibrations in anharmonic crystal lattice. The theory which describes two-phonon anharmonic relaxation can be applied both to local modes associated with substitutional impurity and to intrinsic local modes (ILM) in perfect lattices. It is found that for sufficiently high initial excitations relaxation of vibrations is non-exponential, it demonstrates explosion-like behavior at specific stages of evolution. The course of the relaxation is determined by the initial value of energy, temperature, direction of vibrations. As an example we present the results of calculations of the relaxation of an odd local (impurity) mode in a simple cubic lattice and discuss the influence of quantum fluctuations on the stability of the ILM in one-dimensional monatomic chain.

Electron Transport Mediated by Nonlinear Excitations in Atomic Layers

Contributions to Plasma Physics, 2013

We study the quantum dynamics in tight‐binding approximation (TBA) of an electron interacting with a classical nonlinear lattice of atoms. By computer simulations we show the existence of fast and nearly loss‐free motions of electrons along crystallographic axes of a two‐dimensional dynamic triangular lattice. Moving bound states between electrons and lattice solitons are formed. These so‐called solectrons allow to transfer charge which initially is localized at certain site to a different place along the same crystallographic axis, with negligible spreading of probability density. The relation to experimental findings about controlling electrons by surface acoustic waves (SAW) in piezoelectric materials is pointed out. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Dynamics of self-trapping in the discrete nonlinear Schrödinger equation

Physica D: Nonlinear Phenomena, 1993

We study dynamical aspects of the discrete nonlinear Schr6dinger equation (DNLS) for chains of different sizes with periodic and open boundary conditions. We focus on the occurrence of a self-trapping transition in the different geometries. The initial condition used is that which places the particle (or power) on one lattice site (or nonlinear waveguide) and the quantity studied is the time-averaged probability for the particle to remain in that site. We show that the self-trapping transition in long chains occurs for parameter values not very different from that for very small clusters.