Properties of nano-scale soliton-like excitations in two-dimensional lattice layers (original) (raw)
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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.
Localized nonlinear, soliton-like waves in two-dimensional anharmonic lattices
Wave Motion, 2011
We discuss here nano-scale size localized wave excitations, which are intrinsic localized traveling modes in two-dimensional anharmonic crystal lattice systems. In particular, using different initial conditions of coordinates and momenta we search for the longest lasting excitations in triangular lattices. As most stable and longest lasting unaltered appear quasi-one-dimensional Toda-like solitons running in rectilinear chains along the main crystallographic axes of such lattices. Furthermore, by following the trace of high energetic excitations like in "bubble chamber" methodology (or in scanning tunneling microscopy) we show how such localized nonlinear waves appearing spontaneously in heated systems can be detected and followed in space-time.
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.
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.
Open Physics, 2010
Systematic results of collisions between discrete spatiotemporal dissipative Ginzburg-Landau solitons in two-dimensional photonic lattices are reported. The generic outcomes are identified for (i) the collision of two identical solitons located in the corner, at the edge, and in the center of the photonic lattice, and for (ii) the collision of two non-identical corner and edge solitons located at different distances from the boundaries of the photonic lattice. Depending on the values of the kick (collision momentum) and of the nonlinear (cubic) gain, the collision scenarios include soliton merging, creation of an extra soliton, soliton bouncing, soliton spreading, and quasi-elastic (symmetric) interactions.
Two-dimensional solitons in saturable media with a quasi-one-dimensional lattice potential
Physical Review E, 2006
We study families of solitons in a two-dimensional (2D) model of the light transmission through a photorefractive medium equipped with a (quasi-)one-dimensional photonic lattice. The soliton families are bounded from below by finite minimum values of the peak and total power. Narrow solitons have a single maximum, while broader ones feature side lobes. Stability of the solitons is checked by direct simulations. The solitons can be set in motion across the lattice (actually, made tilted in the spatial domain), provided that the respective boost parameter does not exceed a critical value. Collisions between moving solitons are studied too. Collisions destroy the solitons, unless their velocities are sufficiently small. In the latter case, the colliding solitons merge into a single stable pulse.
Compounds of paired electrons and lattice solitons moving with supersonic velocity
Physical Review E, 2008
We study the time evolution of two correlated electrons of opposite spin in an anharmonic lattice chain. The electrons are described quantum mechanically by the Hubbard model while the lattice is treated classically. The lattice units are coupled via Morse-Toda potentials. Interaction between the lattice and the electrons arises due to the dependence of the electron transfer-matrix element on the distance between neighboring lattice units. Localized configurations comprising a paired electron and a pair of lattice deformation solitons are constructed such that an associated energy functional is minimized. We investigate long-lived, stable pairing features. It is demonstrated that traveling pairs of lattice solitons serve as carriers for the paired electrons realizing coherent transport of the two correlated electrons. We also observe dynamical narrowing of the states, that is, starting from an initial double-peak profile of the electron probability distribution, a single-peak profile is adopted going along with enhancement of localization of the paired electrons. Interestingly, a parameter regime is identified for which supersonic transport of paired electrons is achieved.
Two-dimensional solitons and clusters in dissipative lattices
Journal of the Optical Society of America B, 2014
We study the dynamics of two-dimensional spatial solitons in the structured optical medium modeled by the complex Ginzburg-Landau equation with cubic-quintic nonlinearity and a spatially periodic modulation of the local gain-loss coefficient [a dissipative lattice (DL)]. The analysis, following the variation of the DL's amplitude and period, reveals several dynamical scenarios: stable or unstable propagation of a single dissipative soliton (the unstable propagation entails generation of an irregular multisoliton cluster), transformation of the input soliton into stable or unstable regular clusters patterned as the underlying DL, and decay of the input. Most results are obtained by means of systematic simulations, but the boundary of the single-soliton stability domain is explained analytically.
Two-Dimensional Anharmonic Crystal Lattices: Solitons, Solectrons, and Electric Conduction
Springer Proceedings in Physics, 2014
Reported here are salient features of soliton-mediated electron transport in anharmonic crystal lattices. After recalling how an electron-soliton bound state (solectron) can be formed we comment on consequences like electron surfing on a sound wave and ballistic transport, possible percolation in 2d lattices, and a novel form of electron pairing with strongly correlated electrons both in real space and momentum space. 2. Soliton assisted electron transfer in 1d lattices.