Correlation effects and Pekar bipolaron (arbitrary electron–phonon interaction)

Abstract

The Buimistrov-Pekar method of canonical transformation was used to calculate the energies of the lowest singlet and triplet terms of bipolarons in crystals with ionic binding. An arbitrary electronphonon interaction described by the Fraehlich Hamiltonian was considered. It was shown that, in the whole parametric range of electron-phonon interaction, the value of the free bipolaron ground state energy obtained by the Buimistrov-Pekar method is lower than all those found by Adamowski and Bednarek in the framework of direct variational approaches, and only slightly exceeds (relative error <0.3%) those obtained by Verbist, Peeters, and Devreese by integration over trajectories for a 7. The calculations have shown that any metastable triplet states corresponding to the lowest triplet term of a bipolaron are absent for all the parameters of the electron-phonon interaction, the results being in complete analogy with Hill's theorem about the absence of any bound excited states for an H À ion. Study of a wave function of more general form has demonstrated that a two-center bipolaron is energetically less advantageous than a one-center one for all the parameters of the electron-phonon interaction. Control calculations performed with the system of functions used in this paper have yielded 1.173 a.u. for the hydrogen molecule energy, which is in good agreement with the experimental value.

Translation-invariant bipolarons and the problem of high-temperature superconductivity

“…In this connection the study of conditions at which bipolaron states are stable takes on primary importance. The lowest values of the bipolaron energy were obtained for the electron-phonon coupling constant α < 8 in [3,4,5], and for α > 8 in [5,6,7].…”

Pekar's ansatz and the strong coupling problem in polaron theory

“…Before the publication of [47]- [49] the lowest values of the energy of bipolaron states determined by electron-phonon interaction were obtained in [50]- [52] for α < 8 and in [52]- [55] for α > 8. Attempts to find a translation-invariant solution of the bipolaron problem by varia-tional methods using direct variation of the wave function of the two-electron system [39], [56], [57] yielded higher values of the bipolaron ground state energy as compared to those obtained with the use of a wave function lacking translation invariance [51], [52], [55], [58]. In this section we present the results obtained in [47]- [49] for a bipolaron within the translation-invariant approach.…”

Distinctive Features of Metal-Insulator Transitions, Multiscale Phase Separation, and Related Effects in Hole-Doped Cuprates

“…In these systems, the conditions for the formation of (bi)polarons, as shown in Refs. [44][45][46], are much easier than in other non-polar compounds. Actually, the self-trapping of holes by now has been discovered in different classes of substances (including alkali halides [47,48] and cuprates [5,49]).…”