Electron pairing in one‐dimensional anharmonic crystal lattices

Velarde, Manuel G.; Brizhik, L. S.; Chetverikov, A. P.; Cruzeiro, Leonor; Ébeling, W.; Röpke, G.

doi:10.1002/qua.23008

Cited by 14 publications

(19 citation statements)

References 51 publications

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“…To consider the behavior near x = 0, we have φ(x) ∝ x+e 2 m/(2 2 ǫ)x 2 . Therefore, both electrons are kept apart by a distance of the order x 0 given by the value (38). Comparing this expression with the result (27), it should be mentioned that now the deformation of the lattice remains fixed when the distance between the electrons changes.…”

Section: Wave Function For the Two-electron Relative Motion Includsupporting

confidence: 52%

“…Thus we find a lattice soliton binding two electrons together [38] in the lattice deformation potential well (15). The bisolectron solution is stable when its binding energy is larger than the Coulomb repulsion that means with Eq.…”

Section: Limit Case Of Weak Coulomb Repulsionmentioning

confidence: 72%

“…The corresponding values are given in Ref. [38]. For instance, typical values for macromolecules like polypeptides (see [17]) are:…”

Section: Dynamics Of the Coupled Electron-lattice Systemmentioning

confidence: 99%

“…In [38] we discuss the solution φ(x) of the Schrödinger equation for the relative motion using a variational approach. Taking into account the properties we already discussed, we consider the normalized function φ 1 (x; β) = 2 2β…”

Section: Wave Function For the Two-electron Relative Motion Includmentioning

confidence: 99%

“…Both generalize the polaron concept [25][26][27][28][29][30][31]. It has been shown that anharmonic lattices can support the formation of two-component solitons [32][33][34] and pairing of two excess electrons or holes [35][36][37][38][39] may be enhanced bringing strong correlation both in momentum space and in real space.…”

Section: Introductionmentioning

confidence: 99%

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Electron pairing and Coulomb repulsion in one-dimensional anharmonic lattices

et al. 2012

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We show that in anharmonic one-dimensional crystal lattices pairing of electrons or holes in a localized bisolectron state is possible due to coupling between the charges and the lattice deformation that can overcompensate the Coulomb repulsion. Such localized soliton-like states appear as traveling ground bound singlet states of two extra electrons in the potential well created by the local lattice deformation. We also find the first excited localized state of two electrons in a soliton-like lattice deformation potential well given by a triplet state of two electrons. The results of the analytical study of interacting electrons in a lattice with cubic anharmonicity are compared with the numerical simulations of two electrons in an anharmonic lattice taking into account of the (local) Hubbard electron-electron repulsion. We qualitative agreement between both approaches for a broad interval of parameter values. For illustration we give expressions for the bisolectron binding energy with parameter values that are typical for biological macromolecules. We estimate critical values of Coulomb repulsion where the bisolectron becomes unbound.

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Section: Wave Function For the Two-electron Relative Motion Includsupporting

confidence: 52%

Section: Limit Case Of Weak Coulomb Repulsionmentioning

confidence: 72%

“…The corresponding values are given in Ref. [38]. For instance, typical values for macromolecules like polypeptides (see [17]) are:…”

Section: Dynamics Of the Coupled Electron-lattice Systemmentioning

confidence: 99%

Section: Wave Function For the Two-electron Relative Motion Includmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Electron pairing and Coulomb repulsion in one-dimensional anharmonic lattices

et al. 2012

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Quartic lattice interactions, soliton‐like excitations, and electron pairing in one‐dimensional anharmonic crystals

Velarde

Brizhik

Chetverikov

et al. 2011

Int J of Quantum Chemistry

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In this study, it is shown that two added, excess electrons with opposite spins in one-dimensional crystal lattices with quartic anharmonicity may form a bisolectron, which is a localized bound state of the paired electrons to a soliton-like lattice deformation. It is also shown that when the Coulomb repulsion is included, the wave function of the bisolectron has two maxima, and such a state is stable in lattices with strong enough electron (phonon/ soliton)-lattice coupling. Furthermore, the energy of the bisolectron is shown to be lower than the energy of the state with two separate, independent electrons, as even with account of the Coulomb repulsion the bisolectron binding energy is positive.

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Two-Dimensional Anharmonic Crystal Lattices: Solitons, Solectrons, and Electric Conduction

Velárde

Ébeling

Chetverikov

2014

Springer Proceedings in Physics

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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. Soliton assisted electron transfer in 1d lattices.

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Electron pairing in one‐dimensional anharmonic crystal lattices

Cited by 14 publications

References 51 publications

Electron pairing and Coulomb repulsion in one-dimensional anharmonic lattices

Electron pairing and Coulomb repulsion in one-dimensional anharmonic lattices

Quartic lattice interactions, soliton‐like excitations, and electron pairing in one‐dimensional anharmonic crystals

Two-Dimensional Anharmonic Crystal Lattices: Solitons, Solectrons, and Electric Conduction

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