Electron pairing and Coulomb repulsion in one-dimensional anharmonic lattices

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

doi:10.1103/physrevb.85.245105

Cited by 26 publications

(10 citation statements)

References 50 publications

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“…can be approximated near the minimum with high degree of precision by the anharmonic potential U c (see (12.42)) (for more details see [5]). …”

Section: Comparison With Numerical Simulationsmentioning

confidence: 99%

“…In view of the above here we explicitly analyze how the lattice anharmonicity added to the electron-phonon interaction facilitates electron pairing in a one-dimensional lattice and also helps overcoming Coulomb repulsion. It has been shown that anharmonic lattices also favor pairing of electrons (holes) in a singlet localized state [5,44,45]. While in harmonic lattices the nonlinearity in the system is due to the electron-lattice interaction, in anharmonic lattices there are two nonlinearities: the nonlinearity of the lattice itself, and the electron-lattice interaction.…”

Section: Introductionmentioning

confidence: 98%

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Bound States of Electrons in Harmonic and Anharmonic Crystal Lattices

et al. 2015

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The pairing of electrons in harmonic and anharmonic one-dimensional lattices is studied with account of the electron-lattice interaction. It is shown that in harmonic lattices binding of electrons in a bound localized state called bisoliton, takes place. It is also shown that bisolitons in harmonic lattices can propagate with velocity below the velocity of the sound. Similarly, binding of electrons in singlet spin state, called bisolectron, takes place in anharmonic lattices. It is shown that the account of the lattice anharmonicity leads to the stabilization of bisolectron dynamics: bisolectrons are dynamically stable up to the sound velocity in lattices with cubic or quartic anharmonicities and can also be supersonic. They have finite values of energy and momentum in the whole interval of bisolectron velocities. The bisolectron binding energy and critical value of the Coulomb repulsion at which the bisolectron becomes unstable and decays into two independent solectrons, are calculated. The analytical results are in a good agreement with the results of numerical simulations in a broad interval of the parameter values.

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“…can be approximated near the minimum with high degree of precision by the anharmonic potential U c (see (12.42)) (for more details see [5]). …”

Section: Comparison With Numerical Simulationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Bound States of Electrons in Harmonic and Anharmonic Crystal Lattices

et al. 2015

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“…A generalization of the polaron to solectron, which is the bound state of the crowdion or DB and electron has been proposed () to discuss the peculiarities of electron transport in crystals .…”

Section: Possible Applications Of Discrete Breathersmentioning

confidence: 99%

Discrete breathers in 2D and 3D crystals

Chetverikov

Velarde

2015

Physica Status Solidi (b)

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Discrete breathers (DB) are spatially localized, large‐amplitude vibrational modes in defect‐free nonlinear lattices. Recent numerical and experimental studies have confirmed that DB exist in crystals. In the present work, we briefly describe the well‐known existence conditions of DB in crystals and present our recent results on DB in 2D crystals such as graphene and graphane and in 3D crystals such as alkali halide crystals and pure metals. The possible role of DB in solid state physics and materials science is discussed. Stroboscopic picture of atomic motions in the vicinity of discrete breather excited in graphene homogeneously strained with ϵxx=0.3, ϵyy=−0.1. Displacements of atoms from the equilibrium lattice positions are multiplied by the factor 4 for clarity. The discrete breather is of high spatial localization, so that only two atoms oscillate with a large amplitude.

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“…To calculate it, let us consider, for simplicity, the case of a bisolectron at rest, V = 0. Substituting function (64) (or (65) ) and the corresponding lattice deformation (30) into the Hamiltonian H and expanding the result with respect to l in the assumption l < µ = 2π/κ ν , we obtain, after the integration, the total energy of the system including the Coulomb repulsion (62):…”

Section: Bisolectron With Account Of the Coulomb Repulsionmentioning

confidence: 99%

Stabilizing Role of Lattice Anharmonicity in the Bisoliton Dynamics

Brizhik¹,

Chetverikov²,

Ébeling

et al. 2013

Ukr. J. Phys.

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We show that, in anharmonic one-dimensional lattices, the pairing of electrons or holes in a localized bisoliton (called also bisolectron) state is possible due to a coupling between the charges and the lattice deformation that can overcome the Coulomb repulsion. We show that bisolitons are dynamically stable up to the sound velocities in lattices with cubic or quartic anharmonicities, and have finite values of energy and momentum in the whole interval of bisoliton velocities up to the sound velocity in the chain. We calculate the bisoliton binding energy and the critical value of Coulomb repulsion at which the bisoliton becomes unstable and decays into two independent electrosolitons. We estimate these energies for chain parameters that are typical of biological macromolecules and some quasi-one-dimensional conducting systems and show that the Coulomb repulsion in such systems is relatively weak as compared with the binding energy. Our analytical results are in a good agreement with the results of numerical simulations in a broad interval of the parameter values. K e y w o r d s: lattice anharmonicity, bisoliton, bisolectron, Coulomb repulsion, electron, hole, exciton, polaron, model Hamiltonian.

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Electron pairing and Coulomb repulsion in one-dimensional anharmonic lattices

Cited by 26 publications

References 50 publications

Bound States of Electrons in Harmonic and Anharmonic Crystal Lattices

Bound States of Electrons in Harmonic and Anharmonic Crystal Lattices

Discrete breathers in 2D and 3D crystals

Stabilizing Role of Lattice Anharmonicity in the Bisoliton Dynamics

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