Advances in Polaron Physics

by Alexandrov, Alexandre S.; Devreese, Jozef T.

• ISBN13: 9783642018954
• ISBN10: 3642018955
• Format: Hardcover
• Copyright: 2009-10-01
• Publisher: Springer Verlag

Summary

While basic features of polarons were well recognized a long time ago and have been described in a number of review papers and textbooks, interest in the role of electron-phonon interactions and polaron dynamics in contemporary materials has recently gone through a vigorous revival. Electron-phonon interactions have been shown to be relevant in high-temperature superconductors and colossal magnetoresistance oxides, and transport through nanowires and quantum dots also often depends on vibronic displacements of ions. The continued interest in polarons extends beyond physical description of advanced materials. The field has been a testing ground for analytical, semi-analytical, and numerical techniques, such as path integrals, strong-coupling perturbation expansion, advanced variational, exact diagonalization, density-matrix renormalization group, dynamic mean-field, and quantum Monte Carlo techniques. Single and multi-polaron theories have offered a new insight in our understanding of high-temperature superconductivity, colossal magnetoresistance, and the correlated transport through molecular quantum dots. This book reviews some recent developments in the field of polarons, starting with the basics and covering a number of active directions of research.

Table of Contents

Introduction	p. 1
First-Principle Hamiltonian	p. 1
Local Density Approximation	p. 2
Electron-Phonon Interaction in the Bloch Representation	p. 3
Electron-Phonon Interaction in the Wannier (Site) Representation	p. 5
Continuum Polaron	p. 11
Pekar's Polaron	p. 12
Ground State	p. 12
Effective Mass of Pekar's Polaron	p. 13
Fröhlich Large Polaron	p. 15
Weak-Coupling Regime	p. 15
Lee-Low-Pines Transformation	p. 16
All-Coupling Fröhlich Polaron	p. 18
Feynman Theory	p. 18
Diagrammatic Monte Carlo Algorithm	p. 22
Response of Continuum Polarons	p. 27
Mobility	p. 27
Optical Absorption at Weak Coupling	p. 32
Optical Absorption at Strong Coupling	p. 34
Optical Absorption at Arbitrary Coupling	p. 37
Main Peak Line and Strong-Coupling Expansion	p. 41
Comparison Between Optical Conductivity Spectra Obtained by Different Methods	p. 45
Sum Rules for the Optical Conductivity Spectra of Fröhlich Polarons	p. 46
Polaron Scaling Relations	p. 50
Lattice Polaron	p. 53
Holstein Model	p. 53
Nonadiabatic Holstein Polaron	p. 55
Adiabatic Holstein Polaron	p. 56
Lang-Firsov Canonical Transformation	p. 58
"1/?" Expansion and Polaron Band	p. 59
Temperature Effect on the Polaron Band	p. 61
Effect of EPI Range and Phonon Dispersion on Lattice Polaron Dynamics	p. 63
All-Coupling Lattice Polaron	p. 66
Holstein Model at Any Coupling	p. 66
Short-Range EPI in Infinite Lattices	p. 68
Finite-Range EPI: Mobile Small Polaron	p. 71
Isotope Effect on the Polaron Mass	p. 77
Jahn-Teller Polaron	p. 78
Trapping of Lattice Polarons by Impurities	p. 81
Response of Lattice Polarons	p. 83
Hopping Mobility	p. 83
Optical Conductivity	p. 86
Spectral and Green's Functions	p. 90
Bipolaron	p. 97
Polaron-Polaron Interaction	p. 97
Holstein Bipolaron	p. 99
Continuum Fröhlich Bipolaron	p. 104
Discrete Superlight Fröhlich Bipolaron	p. 106
Discrete All-Coupling Fröhlich Bipolaron	p. 111
Polaronic Exciton	p. 113
Multipolar on Problem	p. 115
Ground State of a Large-Polaron Gas, Polaron Wigner Crystals, and Ripplopolarons	p. 115
Breakdown of the Migdal-Eliashberg Theory in the Strong-Coupling Regime	p. 121
Polaronic Superconductivity	p. 124
Lattice Bipolarons and Competing Orders	p. 126
Bipolaronic Superconductivity	p. 129
Polarons and Spin Effects	p. 131
Polarons and Bipolarons in Advanced Materials	p. 135
Polarons in High-Temperature Superconductors	p. 135
Polarons in Colossal Magnetoresistance Oxides	p. 139
Polarons in Nanostructures	p. 141
Polaron Effects in Semiconductor Quantum Dots	p. 141
Correlated Polaron Transport Through Molecular Quantum Dots	p. 143
Current Status of Polarons and Open Problems	p. 145
References	p. 149
Index	p. 165
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