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
11 - The Hall effect due to small polarons and conduction in narrow energy bands
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 small polaron has proved useful in understanding the transport properties of such low-mobility solids as oxides, glasses, and amorphous semiconductors. Polarons and bipolarons are of interest in high-Tc superconductors. I will first briefly review the basic mechanism for the Hall effect found in the localized regime where transport is due to multi-phonon-assisted transitions between localized small polaron states. The temperature-dependence of the Hall mobility will be reviewed for the non-adiabatic, adiabatic and three- and four site cases. I will then indicate how the magnetic phase factors in the localized regime give the conventional magnetic Lorentz force in a description of polaron band motion or of purely electronic bands of narrow width. This narrow-band regime is more relevant to the normal state of high- Tc materials in which carrier motion is itinerant. I will then survey experimental evidence for the Hall effect due to small polarons and in the narrow-band regime for several materials and conclude with an example of the Hall effect in the normal state of the cuprate superconductors taken from David Emin.
The basic mechanism of the Hall effect in the localized regime
The model used is a straightforward two-dimensional generalization of the molecular crystal model of Holstein [1]. (This case admits only a small-polaron and free-particle solution and no large-polaron solution.) Briefly, the model consists of a site occupied by diatomic molecules with fixed centres of gravity and orientation but variable internuclear separation so that each acts like an Einstein oscillator with fixed frequency, ω0. The oscillators are subject to weak coupling giving rise to dispersion of the vibrational frequencies.
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- Publisher: Cambridge University PressPrint publication year: 1995