Bound states of electrons with soliton-like excitations in thermal systems - adiabatic approximations

Abstract

We study the bound states of electrons with solitonic excitations in one and two-dimensional atomic systems. We include Morse interactions between the atoms in a temperature range from low to physiological temperatures. The atoms are treated by classical Langevin equations. In a first approach, the places of compressions are visualized by drawing the overlap of the densities of the core electrons. Then we study the effect of nonlinear vibrations on the added, free electrons moving on the background of the atoms. We study the coupled classical and quantum-mechanical dynamics of the electrons on the lattice in tight-binding approximation (TBA). Further we consider the formation of solectrons, i. e., dynamic electron-soliton bound states in adiabatic approximations based on the energy spectrum and the canonical distribution.

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“…(5.1). Similar results were found for a solectron, that is, a soliton binding a single electron in a lattice with Morse potential, within the tight binding approximation13, 17, 19–34. Noteworthy is that, on the one hand, for given fixed energy of a solectron structure, its velocity becomes subsonic for strong enough electron–lattice coupling and, on the other hand, in the subsonic regime the velocity decreases with the increase of the electron–lattice coupling constant.…”

“…If this ratio is sufficiently small, the Coulomb repulsion is weak and will not destroy the bound state. It seems pertinent to recall that in earlier computations for discrete Morse lattices21–34, the single‐electron‐soliton bound state (solectron) energies in heated lattices at moderately high temperatures, T = 0.2 D –0.8 D [for simplicity here D = 9/(8γ 2 ) is the depth of the Morse potential well (4.2)], are in the range 4–6 D . Assuming Morse parameters in the range D = 0.1 – 0.4 eV and lattice spacing around 4–5 Å, such solectron energies could reach the range of 0.5–1 eV and their lattice extension around 10–20 Å.…”

“…In such studies, the lattice was taken with harmonic interactions. Although going beyond this, in earlier work, it has been established that lattice solitons can bind one or two electrons, the known results are scarce, mostly numerical simulations, and unsystematic11–34. In view of the above, here, we explicitly and systematically analyze how the lattice “anharmonicity” added to the electron–phonon interaction facilitates electron pairing in a 1D crystal lattice and also helps overcoming Coulomb repulsion with electron spins satisfying Pauli's exclusion principle.…”

Bound States of Electrons in Harmonic and Anharmonic Crystal Lattices

“…Therefore, we expect, that numerically found solutions are close to the solutions found above for the particular velocity (12.113). To a large extent this conclusion is supported by the numerical simulations of the dynamics of two electrons in the anharmonic Morse lattice [14,15,25,28,46,47],where the trapping of two electrons by the supersonic lattice soliton has been observed (see also [14,15].…”

“…In this section we compare the above obtained analytical results with the results obtained numerically in [25,46] for a discrete lattice with Morse interaction with two added excess electrons, described by the Hubbard Hamiltonian. The Morse potential…”