Book contents
- Frontmatter
- Contents
- Preface
- 1 A polaron theory of high-temperature superconductors
- 2 On the possibility of non-BCS superconductivity
- 3 A bipolaron Bose liquid in high-Tc superconductors
- 4 Spin polarons in high-Tc superconductors
- 5 The polaron scenario for high-Tc superconductors
- 6 Formation, phase separation and superconductivity of large bipolarons
- 7 Polarons and bipolarons in WO3−x and YBa2Cu3O7
- 8 Polaron bands in the far- and mid-infrared spectra of e-doped cuprates
- 9 Electron–phonon interaction of non-equilibrium carriers in the photoinduced state of YBa2Cu3O7−δ
- 10 Experimental evidence of local lattice distortion in superconducting oxides
- 11 The Hall effect due to small polarons and conduction in narrow energy bands
- 12 Static and dynamic conductivity of untwinned Y1Ba2Cu4O8: gaps or condensation?
- 13 The near infrared and optical absorption of high- Tc superconductors using powders
- 14 Polaronic theory of mid-infrared conductivity: a numerical cluster study
- 15 Electromagnetic properties of local pair superconductors
- 16 Electron–hole asymmetric polarons
- 17 On the nature of the superconducting state in high-Tc cuprates
- 18 High- Tc superconductivity with polarons and bipolarons: an approach from the insulating states
- 19 Coexistence of small-polaron and Anderson localization in high- Tc superconducting materials
- 20 Concentration and temperature-dependence of magnetic polaron spectra in the t–J model
- 21 Mass enhancement without band-narrowing in t–t′–J and related models: predictions for Fermi-surface and optical conductivity
- 22 Polarons in Peierls–Hubbard models
- 23 Exact estimates of inter-polaron coupling constants resulting in bipolaron formation
- 24 Coulomb interaction and the criteria for bipolaron formation
- 25 Large bipolarons and high-Tc materials
- 26 Collective excitations in the ground state of a two-dimensional attractive Fermi gas
- 27 Strong two-band electron self-trapping, state hybridization effects and related pressure-induced phenomena in semiconductors
- 28 Bismuth disproportionation in super- and semiconducting barium bismuthates
- 29 Magnetic polarons in concentrated and diluted magnetic semiconductors
- 30 Energy scales of exotic superconductors
- Index
24 - Coulomb interaction and the criteria for bipolaron formation
Published online by Cambridge University Press: 24 November 2009
- Frontmatter
- Contents
- Preface
- 1 A polaron theory of high-temperature superconductors
- 2 On the possibility of non-BCS superconductivity
- 3 A bipolaron Bose liquid in high-Tc superconductors
- 4 Spin polarons in high-Tc superconductors
- 5 The polaron scenario for high-Tc superconductors
- 6 Formation, phase separation and superconductivity of large bipolarons
- 7 Polarons and bipolarons in WO3−x and YBa2Cu3O7
- 8 Polaron bands in the far- and mid-infrared spectra of e-doped cuprates
- 9 Electron–phonon interaction of non-equilibrium carriers in the photoinduced state of YBa2Cu3O7−δ
- 10 Experimental evidence of local lattice distortion in superconducting oxides
- 11 The Hall effect due to small polarons and conduction in narrow energy bands
- 12 Static and dynamic conductivity of untwinned Y1Ba2Cu4O8: gaps or condensation?
- 13 The near infrared and optical absorption of high- Tc superconductors using powders
- 14 Polaronic theory of mid-infrared conductivity: a numerical cluster study
- 15 Electromagnetic properties of local pair superconductors
- 16 Electron–hole asymmetric polarons
- 17 On the nature of the superconducting state in high-Tc cuprates
- 18 High- Tc superconductivity with polarons and bipolarons: an approach from the insulating states
- 19 Coexistence of small-polaron and Anderson localization in high- Tc superconducting materials
- 20 Concentration and temperature-dependence of magnetic polaron spectra in the t–J model
- 21 Mass enhancement without band-narrowing in t–t′–J and related models: predictions for Fermi-surface and optical conductivity
- 22 Polarons in Peierls–Hubbard models
- 23 Exact estimates of inter-polaron coupling constants resulting in bipolaron formation
- 24 Coulomb interaction and the criteria for bipolaron formation
- 25 Large bipolarons and high-Tc materials
- 26 Collective excitations in the ground state of a two-dimensional attractive Fermi gas
- 27 Strong two-band electron self-trapping, state hybridization effects and related pressure-induced phenomena in semiconductors
- 28 Bismuth disproportionation in super- and semiconducting barium bismuthates
- 29 Magnetic polarons in concentrated and diluted magnetic semiconductors
- 30 Energy scales of exotic superconductors
- Index
Summary
Abstract
The possibility of bipolaron formation is studied taking into account both electron–phonon interaction and direct Coulomb repulsion. Starting from the Bethe–Salpeter equation with a rather general interaction of the form V(k,ω) = 4πe2/ε(k,ω), and using spectral representations for both the bipolaron wave function and the interaction, the effective Schrödinger-type equation is obtained with the new effective potential, which is non-local and which parametrically depends on the binding energy. It is shown that, if the static response function l/ε(K:,0) is non-negative, then there is no bound state, i.e. in this case bipolarons do not form (electron–lattice interaction is not sufficient to overcome direct Coulomb repulsion). Possible ways out are discussed, among them the possibility of a negative static dielectric function or more general form of the effective electron–electron interaction.
Introduction
The problem of the state of electrons in crystals with strong electron–phonon interaction is now attracting considerable attention. It is well known that one of the possibilities in this case is the formation of polarons [1,2]. The conditions for their existence and their properties have been studied in numerous publications.
Much less studied (and more controversial) is the next possible step – formation of bipolarons in certain cases. The possibility of bipolaron formation was probably first pointed out by Vinetskii and Giterman [3]; later, bipolrons were suggested as possible candidates to explain some properties of Ti4O7 [4]. The problem of the existence of bipolarons has recently acquired special significance in view of the suggestions that they may exist in cuprates and may possibly explain the phenomenon of high-temperature superconductivity in them (see especially [5–7]).
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- Publisher: Cambridge University PressPrint publication year: 1995