Hopping Transport and Stochastic Dynamics of Electrons in Plasma Layers

Abstract

We investigate the stochastic dynamics and the hopping transfer of electrons embedded into two-dimensional atomic layers. First we formulate the quantum statistics of general atom -electron systems based on the tightbinding approximation and express -following linear response transport theory -the quantum-mechanical time correlation functions and the conductivity by means of equilibrium time correlation functions. Within the relaxation time approach an expression for the effective collision frequency is derived in Born approximation, which takes into account quantum effects and dynamic effects of the atom motion through the dynamic structure factor of the lattice and the quantum dynamics of the electrons. In the last part we derive Pauli equations for the stochastic electron dynamics including nonlinear excitations of the atomic subsystem. We carry out Monte Carlo simulations and show that mean square displacements of electrons and transport properties are in a moderate to high temperature regime strongly influenced by by soliton-type excitations and demonstrate the existence of percolation effects.

Control of electron and electron–hole pair dynamics on nonlinear lattice bilayers by strong solitons

“…3 For sufficiently deep wells, bound states, where the electron wave function is localized ("solectrons"), may be formed. 3,4 Let us consider a two-dimensional (2D) crystal lattice layer with units interacting via anharmonic Morse potentials. Furthermore, let us consider that we can inject an excess electron whose evolution is governed by the Schrödinger equation [here in the tight binding approximation (TBA)].…”

“…In the previous work, we have studied the coupled dynamics of injected electrons and nonlinear 2D atomic lattice excitations (acoustic solitons), leading to the effect of "electron surfing." 3,4 In particular, we included effects of degeneracy 5 and transport 6 and focused on possible applications of controlling electron transport. 7,8 Our computer simulations have been compared successfully with experimental data on polydiacetylene crystals.…”

Nonlinear excitations and bound states of electrons, holes and solitons in bilayers of triangular lattices

“…Let us now focus on the electrical interactions between the two coupled lattices. At large separation distances, the two layers are practically uncoupled thus behaving as independent networks [14][15][16]18,19,21]. When the two layers come closer together, the Coulomb forces between electrons and holes come into play and at small distances e-h pairing can occur.…”

“…The charge density will try to follow up these changes thus leading to "solectron" formation [14][15][16].…”

“…In recent works we discussed already the coupling of electron dynamics to nonlinear excitations in atomic 2d-lattices. In particular we studied the interaction of acoustic lattice soliton excitations [8] in 2d-lattices with injected electrons, and found a form of electron surfing [14][15][16] including effects of degeneracy [17] and transport [18,19]. In particular we discussed also possible applications of controlling electron transport by nonlinear effects [20,21].…”