Spatial configuration of the bipolaron and the virial theorem

Kashirina, N. I.; Лахно, В. Д.

doi:10.1134/s1063783408010034

Cited by 6 publications

(22 citation statements)

References 13 publications

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“…In 2D systems, the spatial configuration of bipolaron is similar to the configuration of the twodimensional helium atom. The one-center configuration of bipolaron is also realized in three-dimensional (3D) crystals [21,22]. The two-center configuration in 3D crystals, as well as in 2D systems, corresponds to a shallow minimum, which disappears when sufficiently flexible WF is chosen.…”

Section: Discussion Of the Obtained Resultsmentioning

confidence: 99%

Energy of interaction between polarons and spatial configuration of bipolaron in two-dimensional systems

Kashirina¹,

Kashirina²,

Korol³

et al. 2020

SPQEO

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The work is aimed at studying the influence of correlation effects on the interaction energy of two-dimensional (2D) polarons. The two-center configuration of 2D bipolaron corresponds to a shallow secondary minimum, which occurs when only the correlations associated with the permutation symmetry of the system are taken into account. The correlations associated with the direct dependence of the electron wave function on the distance between electrons lead to stabilization of the one-center configuration, and the secondary minimum corresponding to the two-center configuration disappears. Variational calculations were performed using a multiparameter Gaussian functions with correlation multipliers. The ground state energy of bipolaron is E 2 =-0.542169 E h * for η = ε ∞ /ε 0 = 0, where ε ∞ and ε 0 are the high-frequency and static dielectric constants of the crystal, respectively, E h * is the effective Hartree energy. The binding energy of bipolaron was calculated with respect to the double energy of 2D polaron obtained for wave function, consisting of 5 Gaussian exponents. The ground state energy of 2D polaron is E 1 =-0.202366 E h * for η = 0. The critical value of the ionicity parameter η corresponds to η с ≈ 0.2. At η > η c , 2D bipolaron breaks up into two 2D polarons.

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Section: Discussion Of the Obtained Resultsmentioning

confidence: 99%

Energy of interaction between polarons and spatial configuration of bipolaron in two-dimensional systems

Kashirina¹,

Kashirina²,

Korol³

et al. 2020

SPQEO

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“…The conditions under which the virial theorem holds true for the polaron functional were considered in [25] in the general case and in [17] as applied to the strong coupling bipolaron functional.…”

Section: Virial Theorem and Interaction Between Polaronsmentioning

confidence: 99%

“…For this reason, the author [16] erroneously claims that the one-center bipolaron configuration corresponds to a formal solution that has no physical meaning. The proof that the virial theorem is fulfilled in the strong coupling limit for the one-center bipolaron configuration was carried out in [17]. In this paper, we performed a study of the virial theorem for the one-center bipolaron configuration in the case of arbitrary electron-phonon coupling.…”

Section: Introductionmentioning

confidence: 99%

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Pekar bipolaron and the virial theorem (arbitrary coupling)

Kashirina¹

2014

Semicond. Phys. Quantum Electron. Optoelectron.

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The work is devoted to issues related with implementation of the virial theorem for one-center bipolaron. The virial theorem expressions have been obtained for an electron system with Coulomb interactions in the phonon field. It is shown that for the bipolaron functional (one-center configuration) virial theorem holds for arbitrary electron-phonon coupling. As a specific example of the virial theorem for one-center bipolaron configuration, the author adduces numerical calculations of the energy of the ground state and the various contributions (kinetic energy, electron-phonon interaction, electron energy, phonon energy) into the energy of bipolaron, performed within the framework of Buimistrov-Pekar method. It is shown that the virial theorem is fulfilled with high accuracy for the two-electron systems with Coulomb interactions for an arbitrary value electron-phonon coupling. The necessary condition for formation of a bipolaron stable state is accounting electron correlations associated with the direct dependence of the trial electron wave function of the system from the interelectron distance.

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“…Therefore, it is important to study the role played by the electron-electron correlations in the stabilization of a large bipolaron and elucidate whether the electron-electron correlations can indeed modify the Hartree-Fock approximation for the model of quasi-independent electrons so strongly that the bipolaron passes from an axially symmetric two-center state to a spherically symmetric one-center state as claimed, for example, in Refs. [7,8]. For this aim we use the well-known principles of the variational method and firmly established the physical consequences due to the influence electronic correlations on the electronic systems.…”

Section: Introductionmentioning

confidence: 99%

Landau-Pekar Bipolaron in Singlet and Triplet States

Mukhomorov

2014

Review of Advances in Physics Theories and Applications

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We give an overview of studies a bipolaron stability by variational method. For bipolaron formations, a relation is established between the variational principle and the virial theorem optimizing the electronic wave functions. We present a large number of qualitative and quantitative arguments, which indicate that the Landau-Pekar bipolaron is an axially-symmetrical formation. Much attention is paid to the analysis of the influence of the Coulomb electron-electron correlations on the stability of a large bipolaron. In detail we analyzed the criteria for determining the optimal wave functions. It is established that a step-by-step increase in the flexibility of the electronic wave function due to the electron correlations does not stabilize a one-center bipolaron. We show after into account of electron-electron correlations a singlet bipolaron retains spatial axially-symmetrical. At the same time, the electron-excited triplet states of Landau-Pekar bipolaron have spherical symmetry. The results of Kasirina and Lakhno are based on the one-center bipolaron model are incorrect. Presented evidence that the correct application of the variational method and correct account of electron-electron correlations only increase the binding energy of the bipolaron but symmetry of Hartree-Fock approximation can not change. We adduce proofs which point to methodological errors of one-center bipolaron model as well as arising from their calculations incorrect physical consequences. As illustrated in this review the axially symmetric Landau-Pekar bipolaron can correctly interpret the experimentally detected spectroscopic data.

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Spatial configuration of the bipolaron and the virial theorem

Cited by 6 publications

References 13 publications

Energy of interaction between polarons and spatial configuration of bipolaron in two-dimensional systems

Energy of interaction between polarons and spatial configuration of bipolaron in two-dimensional systems

Pekar bipolaron and the virial theorem (arbitrary coupling)

Landau-Pekar Bipolaron in Singlet and Triplet States

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