Topology in condensed matter / M. I. Monastyrsky (ed.).

Format:

Book

Contributor:

Monastyrskiĭ, M. I. (Mikhail Ilʹich)

Series:

Springer series in solid-state sciences ; 150.

Springer series in solid-state sciences, 0171-1873 ; 150

Language:

English

Subjects (All):

Condensed matter--Congresses.

Condensed matter.

Topology--Congresses.

Topology.

Genre:

Conference papers and proceedings.

Physical Description:

xiv, 254 pages : illustrations (some color) ; 24 cm.

Place of Publication:

Berlin ; New York : Springer, [2006]

Summary:

This book reports new results in condensed matter physics for which topological methods and ideas are important. It considers, on the one hand, recently discovered systems such as carbon nanocrystals and, on the other hand, new topological methods used to describe more traditional systems such as the Fermi surfaces of normal metals, liquid crystals and quasicrystals. The authors of the book are renowned specialists in their fields and present the results of ongoing research, some of it obtained only very recently and not yet published in monograph form.

Contents:

1 Topology in the Electron Theory of Metals / A.M. Kosevich 3

1.2 Dynamics of Conductivity Electrons and the Fermi Surface 4

1.3 Geometry of the Fermi Surface in Crystal 8

1.4 Quantum Magnetic Oscillations and the Shape of the Fermi Surface 11

1.5 Magnetic Breakdown 16

1.6 Band Electrons in the Electric Field and Bloch Oscillations 17

1.7 Topology of the Fermi Surfaces and Low-Temperature Magnetoresistivity of Metals 19

1.8 Berry's Phase and the Topology of the Electron Trajectories in the Magnetic Field 23

2 Topology, Quasiperiodic Functions, and the Transport Phenomena / A. Ya. Maltsev, S.P. Novikov 31

2.1.1 Galvanomagnetic Phenomena in Normal Metals: Classical Results, GSMF Limit 31

2.1.2 Modern Ideas: The GSMF Limit, Topology and Dynamical Systems 36

2.1.3 Transport in 2D Electron Gas and Topology of Quasiperiodic Functions 39

2.2 The Classification of Fermi Surfaces and the "Topological Quantum Numbers" 41

2.3 Quasiperiodic Modulations of 2D Electron Gas and the Generalized Novikov Problem 49

3 The Role of Topology in Growth and Agglomeration / R. Kerner 61

3.2 Topology and Geometry of Polygon Tilings and Networks 62

3.3 Dynamical Model of Polygon Agglomeration in Two Dimensions 69

3.4 Application: How the Fullerene Molecules are Formed 74

3.5 Onion Fullerenes and Carbon Tubes 79

3.6 Rigidity and Local Structure in Covalent Glasses 85

4 Topological Defects in Carbon Nanocrystals / V.A. Osipov 93

4.2 Geometry and Topology of Carbon Nanoparticles 94

4.3 Electronic Properties 98

4.3.1 Theory: Basic Assumptions 99

4.4 Spherical Molecules 102

4.4.1 The Model 102

4.4.2 Extended Electron States 104

4.4.3 Numerical Results 105

4.4.4 Zero-Energy Modes 106

4.5 Nanocones 107

4.5.1 The Model 107

4.5.2 Electron States 108

4.5.3 Numerical Results 110

4.6 Hyperboloid Geometry 110

4.6.1 The Model 110

4.6.2 Electron States 111

4.6.3 Numerical Results 113

5 Physics from Topology and Structures / J. Yi 117

5.2 Quantum Hall Effect 118

5.3 Shapiro Steps in Josephson Junctions 122

5.4 Charge Density Waves 126

5.5 Quantum Phases 129

5.6 Carbon Nanotubes 132

6 Phason Dynamics in Aperiodic Crystals / T. Jannsen 139

6.1.1 Quasiperiodic Crystals 139

6.1.2 Examples of Quasiperiodic Crystals 140

6.1.3 Symmetry 141

6.2 Embedding in Superspace 143

6.3 Simple Models for Incommensurate Structures 145

6.3.1 Displacively Modulated Phases 145

6.3.2 The Double-Chain Model for Incommensurate Composites 147

6.3.3 The Ground State of the DCM 147

6.4 Phonons and Phasons 148

6.4.1 Phonons in Aperiodic Crystals 148

6.4.2 Phason Excitations 151

6.4.3 The Phason Content of Phonons 153

6.5 Nonlinear Phason Dynamics 154

6.5.1 Modulated Phases 154

6.5.2 Incommensurate Composites 155

6.6 Sliding on a Quasiperiodic Substrate 160

6.6.1 A Model 160

6.6.2 Nonlinear Dynamics and Friction 162

7 Hamiltonian Monodromy as Lattice Defect / B. Zhilinskii 165

7.2 Integrable Classical Singular Fibrations and Monodromy 165

7.3 Quantum Monodromy 167

7.4 Elementary Defects of Lattices 168

7.4.1 Vacations and Linear Dislocations 169

7.4.2 Angular Dislocations as Elementary Monodromy Defect 170

7.4.3 About the Sign of the Elementary Monodromy Defect 171

7.4.4 Rational Cuts and Rational Line Defects 172

7.5 Defects with Arbitrary Monodromy 175

7.5.1 Topological Description of Unimodular Matrices 175

7.5.2 Classes of Conjugated Elements and "Normal Form" of SL(2, Z) Matrices 177

7.5.3 Several Elementary Monodromy Defects 177

7.5.4 Several Rational Line Defects 181

7.6 Is There Mutual Interest in Defect - Monodromy Correspondence? 183

8 Two-Qubit and Three-Qubit Geometry and Hopf Fibrations / R. Mosseri 187

8.2 From the S[superscript 3] Hypersphere to the Bloch Sphere Representation 188

8.3 Two Qubits, Entanglement, and the S[superscript 7] Hopf Fibration 190

8.3.1 The Two-Qubit Hilbert Space 190

8.3.2 The S[superscript 7] Hopf Fibration 190

8.3.3 Generalized Bloch Sphere for the Two-Qubit Case 192

8.4 Three Qubits and the S[superscript 15] Hopf Fibration 197

8.4.1 Three Qubits 197

8.4.2 The S[superscript 15] Hopf Fibration 197

9 Defects, Surface Anchoring, and Three-Dimensional Director Fields in the Lamellar Structure of Cholesteric Liquid Crystals as Studied by Fluorescence Confocal Polarizing Microscopy / I.I. Smalyukh, O.D. Lavrentovich 205

9.2 Experimental Methods and Materials 207

9.2.1 Materials and Cell Preparation 207

9.2.2 Fluorescence Confocal Polarizing Microscopy 208

9.3 Directors and Defects in Cholesteric Liquid Crystals 209

9.4 Elastic and Surface Properties of Cholesterics 210

9.4.1 Elasticity of Cholesteric Liquid Crystals 211

9.4.2 Surface Anchoring Energy 213

9.5 Dislocation-Interface Interaction and Three-Dimensional Director Structures in the Weakly Anchored Cholesterics 216

9.5.1 Anchoring-Mediated Dislocation-Interface Interaction 216

9.5.2 Layers Profiles of Isolated Edge Dislocations 220

9.6 The Equilibrium Defects and Structures in Strongly Anchored Cholesteric Wedges 222

9.6.1 Experimental Observations 223

9.6.2 Far-Field Energy of an Isolated Dislocation 226

9.6.3 Dislocation Core Energy 227

9.6.4 Effect of Confinement on the Dislocation Energy 228

9.6.5 Equilibrium Lattice of Dislocation in a Cholesteric Wedge 228

9.7 Metastable Structures, Oily Streaks, Turns and Nodes of Defects 230

9.7.1 Metastable Structures and Oily Streaks 230

9.7.2 Dislocation Turns 234

9.7.3 Nodes of Line Defects 235

9.8 Dynamics of Defects, Glide and Climb of Dislocations, and Their Kinks 237

9.8.1 Peach and Koehler Force 238

9.8.2 Climb 238

9.8.3 Glide 239

9.8.4 Experimental Observations 240

9.8.5 Peierls-Nabarro Friction 244

9.8.6 Kink Structure Versus Peierls-Nabarro Energy Barrier 246.

Notes:

"This volume is based on the talks and lectures given by participants of the 3-month seminar program 'Topology in Condensed Matter,' which was held in the MPIPKS Dresden, 8 May-31 July 2002."--Preface.

Includes bibliographical references and index.

ISBN:

3540234063

OCLC:

62700949

Publisher Number:

9783540234067