Foundations of Solid State Physics

An essential guide to solid state physics through the lens of dimensionality and symmetry Foundations of Solid State Physics introduces the essential topics of solid state physics as taught globally with a focus on understanding the properties of solids from the viewpoint of dimensionality and symmetry. Written in a conversational manner and designed to be accessible, the book contains a minimal amount of mathematics. The authors?noted experts on the topic?offer an insightful review of the basic topics, such as the static and dynamic lattice in real space, the reciprocal lattice, electrons in solids, and transport in materials and devices. The book also includes more advanced topics: the quasi-particle concept (phonons, solitons, polarons, excitons), strong electron-electron correlation, light-matter interactions, and spin systems. The authors' approach makes it possible to gain a clear understanding of conducting polymers, carbon nanotubes, nanowires, two-dimensional chalcogenides, perovskites and organic crystals in terms of their expressed dimension, topological connectedness, and quantum confinement. This important guide: -Offers an understanding of a variety of technology-relevant solid-state materials in terms of their dimension, topology and quantum confinement -Contains end-of-chapter problems with different degrees of difficulty to enhance understanding -Treats all classical topics of solid state physics courses - plus the physics of low-dimensional systems Written for students in physics, material sciences, and chemistry, lecturers, and other academics, Foundations of Solid State Physics explores the basic and advanced topics of solid state physics with a unique focus on dimensionality and symmetry.

Autorentext

Siegmar Roth is founding director of Sineurop Nanotech GmbH Stuttgart, Germany, a company synthesizing carbon nanotubes, graphene and related materials. He has obtained his PhD in Physics at the University of Vienna, Austria, and his Habilitation at the University of Karlsruhe, Germany. After some years at Siemens in Erlangen, Germany, he joined the Institut Laue Langevin and later on the High Field Magnet Lab in Grenoble, from where he moved to Stuttgart to become leader of the Research Group on Synthetic Nanostructures at the Max Planck Institute for Solid State Research. Between 2009 and 2012 he was visiting professor at the School of Electrical Engineering of Korea University.

David L. Carroll is professor at the Wake Forest University. He is a trained materials scientist and received his PhD from Wesleyan University, Middletown, USA. After a stay as postdoctoral fellow at the department of materials science and engineering, University of Pennsylvania, Philadelphia from 1993-1995, he joined the Max-Planck-Institute for solid state research in Stuttgart, Germany. In 1997 he became Assistant Professor at Clemson University and 2001 Associate Professor. He moved with his group to Wake Forest University in 2003, where he founded the Center for Nanotechnology and Molecular Materials.

Inhalt

Preface xiii

1 Introduction 1

1.1 Dimensionality 2

1.2 Approaching Dimensionality from Outside and from Inside 4

1.3 Dimensionality of Carbon: Solids 8

1.3.1 Three-Dimensional Carbon: Diamond 10

1.3.2 Two-Dimensional Carbon: Graphite and Graphene 10

1.3.3 One-Dimensional Carbon: Cumulene, Polycarbyne, and Polyene 12

1.3.4 Zero-Dimensional Carbon: Fullerene 13

1.4 Something in Between: Topology 14

1.5 More Peculiarities of Dimension: One Dimension 16

1.6 Summary 19

Exploring Concepts 20

References 26

2 One-Dimensional Substances 29

2.1 A15 Compounds 32

2.2 Krogmann Salts 37

2.3 Alchemists' Gold 40

2.4 Bechgaard Salts and Other Charge-Transfer Compounds 42

2.5 Polysulfurnitride 45

2.6 Phthalocyanines and Other Macrocycles 47

2.7 Transition Metal Chalcogenides and Halides 48

2.8 Halogen-Bridged Mixed-Valence Transition Metal Complexes 50

2.9 Returning to Carbon 52

2.9.1 Conducting Polymers 53

2.9.2 Carbon Nanotubes 55

2.10 Perovskites 59

2.11 Topological States 61

2.12 What Did We Forget? 62

2.12.1 Poly-deckers 62

2.12.2 Polycarbenes 63

2.12.3 Isolated, Freestanding Nanowires 63

2.12.4 Templates and Filled Pores 64

2.12.5 Asymmetric Growth Using Catalysts 65

2.12.6 Gated Semiconductor Quantum Wires 66

2.12.7 Few-Atom Metal Nanowires 66

2.13 A Summary of Our Materials 68

Exploring Concepts 69

References 69

3 Order and Symmetry: The Lattice 75

3.1 The Correlation Function 76

3.2 The Real Space Crystal Lattice and Its Basis 77

3.2.1 Using a Coordinate System 81

3.2.2 Surprises in Two-Dimensional Lattices 86

3.2.3 The One-Dimensional Lattice 91

3.2.4 Polymers as One-Dimensional Lattices 92

3.2.5 Carbon Nanotubes as One-Dimensional Lattices 93

3.3 Bonding and Binding 94

3.4 Spatial Symmetries Are Not Enough: Time Crystals 101

3.5 Summary 102

Exploring Concepts 103

References 110

4 The Reciprocal Lattice 111

4.1 Describing Objects Using Momentum and Energy 111

4.1.1 Constructing the Reciprocal Lattice 112

4.1.2 The Unit Cell 114

4.2 The Reciprocal Lattice and Scattering 116

4.2.1 General Scattering 116

4.2.2 Real Systems 120

4.2.3 Applying This to Real One-Dimensional Systems 123

4.3 A Summary of the Reciprocal Lattice 125

Exploring Concepts 126

References 128

5 The Dynamic Lattice 129

5.1 Crystal Vibrations and Phonons 130

5.1.1 A Simple One-Dimensional Model 133

5.1.1.1 A Model 133

5.1.1.2 Long Wavelength Vibrations 136

5.1.1.3 Short Wavelength Vibrations 137

5.1.1.4 More Atoms in the Basis 137

5.1.2 More Dimensions 139

5.2 Quantum Considerations with Phonons 143

5.2.1 Conservation of Crystal Momentum 144

5.2.2 General Scattering 144

5.3 Phonons Yield Thermal Properties 147

5.3.1 Internal Energy and Phonons 148

5.3.2 Models of Energy Distribution: f p(𝜔) and 𝜔K,p 150

5.3.2.1 DuLong and Petit: Equipartition of Energy 150

5.3.2.2 Einstein and Quantum Statistics 151

5.3.2.3 Debye and the Spectral Analysis 152

5.3.3 The Debye Approximation 156

5.3.4 Generalizations of the Density of States 159

5.3.5 Other Thermal Properties: Thermal Transport 161

5.4 Anharmonic Effects 162

5.5 Summary of Phonons 168

Exploring Concepts 168

References 172 **6 Elect...