Polarons and ExcitonsPDF电子书下载

INTRODUCTION TO THE THEORY OF THE POLARON＆H．FROHLICH 1

1．Historical Introduction 1

2．Qualitative Survey 3

2．1．The size of the polaron 5

2．2．Simple theory of the polaron effective mass 7

2．3．Localization 10

3．Macroscopic Model 11

4．Derivation of the Hamiltonian 14

4．1．Example:a classical point charge at rest 20

5．Solutions for Weak Coupling 22

Appendix:Canonical transformation from coordinate and momentum variables to creation and annihilation operators 28

INTERMEDIATE-COUPLING POLARON THEORY＆DAVID PINES 33

1．Introduction 33

2．Canonical Transformations 36

2．1．Elimination of the electron coordinate and momentum 36

2．2．The＂displaced-oscillator＂transformation 37

3．Properties of the Intermediate-Coupling Solutions 40

4．Range of Validity of Intermediate-Coupling Theory 42

STRONG-COUPLING THEORY OF THE POLARON＆G．R．ALLCOCK 45

1．Introduction 45

2．The Adiabatic Approximation 46

2．1．Diagonalization of the interaction 46

2．2．The eigenfunctions of H1 48

2．3．Minimization of H1 49

2．4．The Born-Oppenheimer approximation 51

3．The Harmonic Approximation 53

3．1．The structure of the adiabatic Hamiltonian 53

3．2．Introduction of translational coordinates 54

3．3．Evaluation of the kinetic energy in terms of the translational coordinates 56

3．4．The Hamiltonian in the harmonic approximation 61

3．5．Some properties of the harmonic Hamiltonian 63

3．6．Pekar＇s approximate Hamiltonian 65

3．7．Introduction of three extra oscillators 66

Appendix:Variational derivation of the polaron rest energy and effective mass in the strong-coupling region 67

FEYNMAN＇S PATH-INTEGRAL METHOD APPLIED TO THE EQUILIBRIUM PROPERTIES OF POLARONS AND RELATED PROBLEMS＆T．D．SCHULTZ 71

1．Path-Integral Formulation of Quantum Mechanics 71

1．1．Introduction 71

1．2．Transformation functions and the density matrix 74

A．Transformation functions 74

B．Density matrix in the canonical ensemble 75

1．3．Path-integral formulation of the transformation function 76

A．The composition property 76

B．Transformation function for infinitesimal times 76

C．The path integral 77

D．Some remarks 77

1．4．Evaluation of path integrals 78

A．Free particle,L = 1/2mx2 79

B．Free harmonic oscillator in one dimension,L = 1/2m(x2-w2x2) 79

C．Forced harmonic oscillator in one dimension 82

2．Path-Integral Approach to the Polaron,T = 0 85

2．1．Formulation of the problem in path integrals 85

2．2．The Feynman variational principle 88

2．3．Ground-state energy and effective mass,Feynman approach 90

A．Ground-state energy 90

B．Polaron effective mass 93

2．4．Polaron model corresponding to the Feynman approximation 95

2．5．Perturbation corrections to the Feynman approximation 98

3．The Polaron at Finite Temperatures 99

3．1．Electron-lattice partition function in path-integral formalism 99

3．2．Variational principle and approximate action 101

4．Feynman Approximation for other Electron-Lattice Problems 104

4．1．Polaron bound to a point defect 104

4．2．An exciton interacting with lattice vibrations 107

4．3．Bipolarons 110

4．4．Polaron in a static magnetic field 110

SEMINAR:Polaron Mobility using the Boltzmann Equation 111

THE ELECTRICAL TRANSPORT PROPERTIES OF POLARONS＆P．M．PLATZMAN 123

1．Introduction 123

2．Formulation of the Mobility Problem in terms of the Electron Coordinates alone 124

3．A Method of Approximation 132

4．First Correction Term 135

5．Behaviour of the Impedance 138

5．1．Zero temperature,v<1;effective ass 139

5．2．General expression for dissipation 139

5．3．Dissipation at low temperatures 141

5．4．Behaviour at high temperatures 146

6．Weak-Coupling Limit:The Boltzmann Equation 147

7．Suggestions for Improving Accuracy 150

ELECTRON,PHONON AND POLARON PROPAGATORS＆DAVID PINES 155

1．Introduction 155

2．The One-Electron Green＇s Function 156

2．1．Spectral representation of the one-electron Green＇s function 159

3．The Phonon Propagator 162

4．Electron-Phonon Interactions:Feynman Diagrams 163

APPLICATION OF GREEN＇S FUNCTION TECHNIQUES TO THE POLARON PROBLEM＆R．PUFF and G．D．WHITFIELD 171

1．Introduction 171

2．Definition and General Properties of G 172

3．Equations of Motion 175

4．Approximate Solutions for Small and Intermediate Values of α 178

4．1．Non-interacting case 178

4．2．Perturbation theory 179

4．3．Hartree-Fock approximation 181

5．An Exactly Soluble Model 184

6．Strong Coupling 186

7．Many-Electron Green＇s Functions and the Strong-Coupling Limit 186

SEMINARS ON GREEN＇S FUNCTION METHODS 191

1．Theory of the Propagation of Resonant Radiation in a Gas．＆S．DONIACH 191

2．Electrical Conductivity in Metals．＆J．RANNINGER 202

SELF-TRAPPING OF AN ELECTRON BY THE ACOUSTIC MODE OF LATTICE VIBRATION＆Y．TOYOZAWA 211

1．Introduction and Continuum Model 211

1．1．Elastic continuum model 213

2．The Tight-Binding Model 217

2．1．Discontinuous change in the effective mass 217

2．2．The variation of the effective mass with coupling constant 220

3．Adiabatic Theory of the Self-Trapped State 224

3．1．The results of calculation in the case of a simple cubic lattice 228

SEMINARS ON LOCALIZED (＂SMALL＂) POLARONS 233

1．Model of Thermally-Activated Polaron Motion．＆G．L．SEWELL 233

2．Interaction of a Polarizable KC1 Crystal with a Valence-Band Hole．＆S．J．NETTEL 245

3．Optical Absorption by Small Polarons．＆D．M．EAGLES 255

THEORY OF EXCITONS－I＆R．J．ELLIOTT 269

1．Introduction 269

1．1．Approximations 269

1．2．Formulae for optical properties 271

2．Band Theory 272

2．1．Band-to-band transitions in semiconductors 273

3．Effective-Mass Theory for Excitons 275

4．Transitions to Exciton States 279

4．1．Direct transitions 279

4．2．Indirect transitions 282

5．Effect of a Magnetic Field 284

5．1．Band states in a magnetic field 284

5．2．Band-to-band transitions in a magnetic field 285

5．3．Excitons in a magnetic field 287

6．Effects of Electron Spin 287

7．Exciton Polarization Effects 289

8．Some experimental results 289

8．1．Germanium 289

8．2．Cuprous Oxide 290

Appendix 292

THEORY OF EXCITONS－II＆H．HAKEN 295

1．Introduction 295

2．Variational Calculation of the Interaction of an Exciton with the Lattice Vibrations at T = 0 297

2．1．Symmetry properties of the basic states 297

2．2．Properties of the polaron wave functions 297

2．3．Exciton variational principle 298

2．4．Evaluation of the effective electron-hole potential in the intermediate-coupling region 301

3．Treatment of the Exciton as a Many-Body Problem 303

3．1．Historical introduction 303

3．2．Treatment of the many-body Hamiltonian 305

3．3．Multipole expansion of Coulomb interaction 308

3．4．Diagonalization of the pair-pair interaction 309

3．5．Transition to the effective two-particle Hamiltonian 310

3．6．Summary 313

3．7．Recent literature 313

4．Feynman Methods Applied to the Exciton Problem 313

4．1．Characteristics of Feynman＇s polaron 313

4．2．Extension of this method to the exciton 314

4．3．Generalization to non-zero temperature 315

4．4．On the use of time-ordered operators 316

4．5．Disentangling of phonon operators and elimination of phonon coordinates 317

4．6．Approximation procedure for calculating the temperature-dependent Green＇s function 318

4．7．Use of the trial Hamiltonian to calculate polaron damping and effective mass 320

EXPERIMENTS ON THE POLARON＆F．C．BROWN 323

1．The Measurement of Carrier Mobility in Polar Crystals 323

1．1．Introduction－elementary concepts 323

1．2．Survey of polar crystals 324

1．3．Drift mobility and Hall mobility 326

A．Semiconductors 326

B．Insulating photoconductors 328

2．Temperature-Dependence of Polaron Mobility 335

2．1．Theoretical formulae 335

2．2．Experimental results:semiconductors and weakly polar crystals 337

2．3．Mobility results－ionic crystals 339

A．The alkali halides 339

B．The silver halides 340

3．Cyclotron Resonance in Silver Bromide 345

4．Optical Properties of the Silver Halides 347

4．1．Introduction 347

4．2．Direct transitions 347

4．3．Indirect transitions 349

SEMINARS ON EXPERIMENTAL WORK 357

1．Polarons in Cyclotron Resonance．＆G．ASCARELLI 357

2．Excitons in Germanium．＆T．P．MCLEAN 367

3．The Effects of Perturbations upon the Excitonic Spectrum of Cuprous Oxide．＆M．GROSMANN 373