Electron self-trapping in a discrete two-dimensional lattice (original) (raw)
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Spontaneously localized electron states in a discrete anisotropic two-dimensional lattice
Physica D: Nonlinear Phenomena, 2000
Spontaneously localized electron states are investigated numerically in a discrete anisotropic two-dimensional phonon lattice taking into account the electron-phonon interactions. Such a lattice is used as a model of the quasi-one-dimensional compounds, in the range of parameters characteristic of conjugated polymers, for which the interchain interactions are taken into account. It is shown that for certain ranges of parameters, there are soliton-like static solutions that correspond to fully delocalized electron states or to the very localized small polaron states. We show that the solutions of the first type are stable under small perturbations and we also analyze numerically their behaviour under relatively strong perturbations.
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.
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).
Soliton-like excitations and solectrons in two-dimensional nonlinear lattices
The European Physical Journal B, 2011
We discuss here the thermal excitation of soliton-like supersonic, intrinsic localized modes in two-dimensional monolayers of atoms imbedded into a heat bath. These excitations induce local electrical polarization fields at the nano-scale in the lattice which influence electron dynamics, thus leading to a new form of trapping. We study the soliton-mediated electron dynamics in such systems at moderately high temperatures and calculate the density of embedded electrons in a suitable adiabatic approximation.
Self-trapping of interacting electrons in crystalline nonlinear chains
The European Physical Journal B, 2012
Considering the nonlinearity arising from the interaction between electrons and lattice vibrations, an effective electronic model with a self-interaction cubic term is employed to study the interplay between electron-electron and electron-phonon interactions. Based on numerical solutions of the timedependent nonlinear Schroedinger equation for an initially localized two-electron singlet state, we show that the magnitude of the electron-phonon coupling χ necessary to promote the self-trapping of the electronic wave packet decreases as a function of the electron-electron interaction U. We show that such dependence is directly linked to the narrowing of the band of bounded two-electron states as U increases. We obtain the transition line in the χ × U parameter space separating the phases of self-trapped and delocalized electronic wave packets. The present results indicates that nonlinear contributions plays a relevant role in the electronic wave packet dynamics, particularly in the regime of strongly correlated electrons.
Spontaneous localization of electrons in lattices with nonlocal interactions
Physical Review B, 2003
We study spontaneously localized electron states in a D-dimensional lattice with a nonlocal electron-phonon interaction. We show that, in the adiabatic long-wave approximation, such electron states are described by a modified nonlinear Schrödinger equation with a nonlocal nonlinear interaction which, within certain ranges of the parameter values, admits localized soliton-type solutions. We also calculate nonadiabatic corrections and estimate conditions of the applicability of the adiabatic approximation in one-and two-dimensional cases. We show that the adiabatic approximation is valid at strong enough electron-phonon coupling.
The European Physical Journal B, 2019
We study the temporal and spatial nonlinear dynamical evolution of a coupled triangular lattice crystal bilayer system where in one layer one excess free electron is injected while an excess positive charge, a hole, is created in the other. The atoms of each of the backbone lattices interact with anharmonic (short range) Morse potentials whereas the charges interact via (long range) Coulomb potentials. Computer simulations are provided of the possibilities o↵ered by varying interlayer separation, strength of the Coulomb force between the charges and the diverse dynamical role played by excited solitons supersonically moving along crystallographic axes in one of the layers. Optimal conditions are identified for the occurrence of electron-hole pairs and for the more significant case of a boson-like electron-hole-soliton coupled compound, a new form of quasiparticle moving along the coupled bilayer system with no need of applying an external electric field.
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
Nonlinear soliton-like excitations in two-dimensional lattices and charge transport
The European Physical Journal Special Topics, 2013
We study soliton-like excitations and their time and space evolution in several two-dimensional anharmonic lattices with Morse interactions: square lattices including ones with externally fixed square lattice frame (cuprate model), and triangular lattices. We analyze the dispersion equations and lump solutions of the Kadomtsev-Petviashvili equation. Adding electrons to the lattice we find solectron bound states and offer computational evidence of how electrons can be controlled and transported by such acoustic waves and how electron-surfing occurs at the nanoscale. We also offer computational evidence of the possibility of long lasting, fast lattice soliton and corresponding supersonic, almost loss-free transfer or transport of electrons bound to such lattice solitons along crystallographic axes.
Spontaneous localization of electrons in two-dimensional lattices within the adiabatic approximation
Journal of Mathematical Physics, 2003
The conditions for spontaneous localization of electrons in an isotropic twodimensional electron-phonon lattice are investigated within the zero adiabatic approximation. It is shown that the localization occurs when the electron-phonon coupling takes values within certain finite interval of values g c,1 ϽgϽg c,2. At g Ͻg c,1 the energy minimum is attained for the delocalized states and at gϾg c,2 the strong localization on one lattice site takes place. In this paper we introduce an ansatz which, under a variational principle, allows us to describe all three regimes at the same time. The radius of the electron localization, as a function of electronphonon coupling constant, is evaluated analytically and shown to fit well the numerical data.