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

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

doi:10.1002/qua.23282

Cited by 10 publications

(4 citation statements)

References 39 publications

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“…where the kernel of the integral for both types of anharmonic potentials K ν in view of the explicit form of G ν is very close to unity (see the numerical solution in [15,16]). From Eq.…”

Section: Model Hamiltonian and Dynamic Equationsmentioning

confidence: 88%

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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“…where the kernel of the integral for both types of anharmonic potentials K ν in view of the explicit form of G ν is very close to unity (see the numerical solution in [15,16]). From Eq.…”

Section: Model Hamiltonian and Dynamic Equationsmentioning

confidence: 88%

Stabilizing Role of Lattice Anharmonicity in the Bisoliton Dynamics

Brizhik¹,

Chetverikov²,

Ébeling

et al. 2013

Ukr. J. Phys.

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“…where the kernel of the integral for both types of anharmonic potentials K v in view of the explicit form of G v is very close to unity (see numerical solution in [44,45]). From (12.46) after integration we find that the deformation of the lattice is given by the soliton solutions of the B-KdV equation [12,18,19,29,33,36,41,42] which coincides with the solution of the Davydov system of nonlinear equations [19,38]:…”

Section: Bisolectrons In Anharmonic Latticesmentioning

confidence: 97%

“…of the function (12.105) is the leading one, and the type of the solution is determined by the asymptotics of the electron wave function depending on ρ. Let us consider the parameter L which is determined as the limit has finite values of energy and momentum for the positive lattice anharmonicity (see [44,45]). This solution can be supersonic for strong lattice anharmonicity u anh .…”

Section: Supersonic Bisolectronsmentioning

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

Cited by 10 publications

References 39 publications

Stabilizing Role of Lattice Anharmonicity in the Bisoliton Dynamics

Stabilizing Role of Lattice Anharmonicity in the Bisoliton Dynamics

Bound States of Electrons in Harmonic and Anharmonic Crystal Lattices

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

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