Advances in Polaron Physics (eBook)

Alexandre S. Alexandrov received the MSc ( 1st class honour) , Ph.D. and and the highest post-graduate academic degree D.Sc. ("Doktor nauk") in Theoretical Physics from the Moscow Engineering Physics Institute in 1970, 1973 and 1984, respectively. From 1973 to 1990 he was an Associate Professor, Full Professor, Dean of Theoretical and Experimental Physics Faculty, Head of General Physics Department, and a Vice-Rector of the Moscow Engineering Physics Institute, Russia. He was a Visiting Professor at the Rhein–Westfalische Technische Hochschule (RWTH) Aachen, Germany from 1990 to 1992, and a Research Professor at IRC in Superconductivity, Cavendish, University of Cambridge, United Kingdom from 1992 to 1995. In 1995 he was appointed to a chair of Theoretical Physics in the Department of Physics at Loughborough University, UK, where he was the Head of Physics from 1998 to 2001. He is currently Professor of Theoretical Physics in the Department of Physics at Loughborough University. Professor Alexandrov extended the conventional (BCS) theory of superconductivity towards the strong-coupling regime, now known as the bipolaronic superconductivity, proposed a theory of colossal magnetoresistance and a theory of correlated transport through molecular quantum dots, developed the theory of charged Bose-liquids and predicted novel quantum magneto-oscillations in low-dimensional metals and in nanowires. He was the first Mott By-Fellow of Gonville and Caius College (University of Cambridge, UK), and published 6 books, three of them co-authored with the Nobel Prize Laureate Sir Nevill Mott. Professor Alexandrov is a Fellow of the Institute of Physics (IOP, London) and a member of APS. He was Codirector of a NATO Advanced Research Workshop (2003), a Scientific Convenor of the European Science Foundation (ESF) Workshop (2006), a Guest-Editor for special issues of Physica C (2004) and of Journal of Physics: Condensed Matter (2007)  Jozef T. Devreese received his MSc ( magna cum laude) and Ph.D. (maxima cum laude) in Physics from the KULeuven in 1960 and 1964 respectively. From 1961to 1966 he was reasearch Scientist (and Consultant from 1966 till 1980) at the Nuckear Energy Centre (SCK-CEN) in Mol (Belgium).In 1966 he was appointed Lecturer at the University of Antwerp where he became Full Professor in 1969, first appointed to a chair of Applied Mathematics, later as Theoretical Condensed Matter Physicist. He became head of the Physics Department in 1973. In 1977 Prof. Devreese was appointed Visiting Professor at the Eindhoven University of Technology, a position he held till 2002. In 1980 and in 1983 Prof. Devreese was elected as Chairman of the Condensed Matter Division of the European Physical Society for two consecutive three-year periods. In 1971 he organised an International Advanced Study Institute on the Physics of Polarons in Ionic Crystals and in Polar Semiconductors. He was elected as member of the CMD-EPS- Board from 1978 till 2002.Devreese took the initiative for the General Conference of the Condensed Matter Division of EPS and was the chairman of the first such conference organised in Anrwerp in 1980. This initiative resulted in a series of such CMD-EPS General Conferences, the 22th of which is the Rome-2008 Conference . J.  Devreese was visiting professor at Lehigh University (PA, USA), The University of Western Ontario (Canada), and was invited as lecturer or seminar speaker at numerous universities and research institutions in the USA and in Europe. He was elected Fellow of the European Physical Society (2006) and the American Physical Society (1990) and as active member of the European Academy of Sciences and Arts (2005). Prof. Devreese’s research resulted in contributions to the theory of polarons, bipolarons and excitons in 3D and also in reduced dimensions, reduced dimensionality and in different topologies. He investigated the dynamical response properties of those systems like optical absorption, cyclotron resonance, photoluminescence, Raman-scattering etc Other studies addressed many body problems and superconductivity in mesoscopic systems and in nanostructures. More recently he studied also systems of ultra-cold atoms (bosons and fermions) including the BEC-BCS transition, and vorticity in those systems.In many of those studies the Feynman path integral was a basic mathematical and conceptual tool.

Preface 6
Contents 7
1 Introduction 10
1.1 First-Principle Hamiltonian 10
1.2 Local Density Approximation 11
1.3 Electron–Phonon Interaction in the Bloch Representation 12
1.4 Electron–Phonon Interaction in the Wannier (Site) Representation 14
2 Continuum Polaron 19
2.1 Pekar’s Polaron 20
2.2 Fröhlich Large Polaron 23
2.3 All-Coupling Fröhlich Polaron 26
2.4 Response of Continuum Polarons 35
2.5 Polaron Scaling Relations 58
3 Lattice Polaron 61
3.1 Holstein Model 61
3.2 Lang–Firsov Canonical Transformation 66
3.3 Effect of EPI Range and Phonon Dispersion on Lattice Polaron Dynamics 71
3.4 All-Coupling Lattice Polaron 74
3.5 Isotope Effect on the Polaron Mass 85
3.6 Jahn–Teller Polaron 86
3.7 Trapping of Lattice Polarons by Impurities 89
3.8 Response of Lattice Polarons 91
4 Bipolaron 104
4.1 Polaron–Polaron Interaction 104
4.2 Holstein Bipolaron 106
4.3 Continuum Fröhlich Bipolaron 111
4.4 Discrete Superlight Fröhlich Bipolaron 113
4.5 Discrete All-Coupling Fröhlich Bipolaron 118
4.6 Polaronic Exciton 120
5 Multipolaron Problem 121
5.1 Ground State of a Large-Polaron Gas, Polaron Wigner Crystals, and Ripplopolarons 121
5.2 Breakdown of the Migdal–Eliashberg Theory in the Strong-Coupling Regime 127
5.3 Polaronic Superconductivity 130
5.4 Lattice Bipolarons and Competing Orders 132
5.5 Bipolaronic Superconductivity 135
5.6 Polarons and Spin Effects 137
6 Polarons and Bipolarons in Advanced Materials 141
6.1 Polarons in High-Temperature Superconductors 141
6.2 Polarons in Colossal Magnetoresistance Oxides 145
6.3 Polarons in Nanostructures 147
7 Current Status of Polarons and Open Problems 150
References 154
Index 169