An Introduction to Condensed Matter Physics for the Nanosciences

Cover
Half Title
Title Page
Copyright Page
Table of Contents
Preface
Chapter 1 Introduction
1.1 Electrical Properties
1.2 Optical Transport and the Interaction of Light with Matter
1.3 Electrons in a Variety of Dimensions
1.4 Semiconductors
1.5 The Landauer Approach to Conductivity
1.6 Photonic Crystals and Metamaterials
1.7 Quantum Optics
1.8 Anderson Localization and Mott Localization
1.9 Quantum Hall Effect
1.10 Phenomena Related to the Hall Effect
1.11 Correlated Electron Systems
1.11.1 Superconductivity
1.12 Josephson Junctions
1.13 Fractional Quantum Hall Effect
1.14 Coulomb Blockade
1.15 Resonance
1.16 Scaling and Renormalization Group
References
Chapter 2 Conductivity
2.1 Basic Ideas of Conductivity
2.2 Quantum Effects
2.3 Magnetic Field Effects
2.3.1 Classical Treatment of a Two-Dimensional Gas in a Harmonic Confining Potential
2.3.2 Orbital and Landau Diamagnetism: Magnetism of a Two-Dimensional Fermi Gas
2.3.3 Magnetic Properties and Landau Diamagnetism of a Slab of Fermi Gas
2.3.4 Pauli Paramagnetism
2.4 Stoner Theory of Permanent Magnetism of Metals
2.5 Localization Properties of the Fermi Gas Model
2.5.1 Periodic Potential
2.5.2 Modes in the Anderson Localized Gas
2.5.3 Phase Coherence in Localization
2.5.4 Dependence of Localization on the System Dimension
2.5.5 Hopping and Variable-Range Hopping Conductivity
2.5.6 Ioffe–Regel Criterion and Minimum Metallic Conductivity
2.6 Mott Transition
2.7 Wigner Crystal
2.8 Superconductivity
2.8.1 Planar Interface Between a Superconductor and Normal Metal
2.8.2 Flux Quantization
2.9 Ahronov–Bohm Effect in Normal Metals
References
Chapter 3 Conductivity: Another View
3.1 The Landauer Formulation
3.2 Scattering within the Waveguide: Ohmic Limit
3.3 Landauer–Buttiker Formula
3.4 Universal Conductance Fluctuations
3.5 Nonzero Temperature
References
Chapter 4 Properties of Periodic Media
4.1 Tight-Binding Model
4.1.1 A One-Dimensional Model of a Chain of Atoms
4.1.2 A Two-Dimensional Tight-Binding Model of Graphene
4.1.2.1 The Tight-Binding Hamiltonian of Graphene
4.1.2.2 Dispersive Properties of the Excitations in Graphene
4.1.3 Graphene Conductivity
4.1.4 Graphene Nanotubes
4.1.5 Some of the Interesting Properties of Graphene
4.2 Quantum Dots, Quantum Wells, and Quantum Wires
4.2.1 Properties of GaAs and Ga[sub(1–x)]Al[sub(x)]As
4.2.2 Effective Mass Approximation
4.2.3 Envelope Function Approximation
4.2.4 Quantum Wells and Heterostructures
4.2.4.1 Quantum Wells
4.2.4.2 Quantum Heterostructures
4.2.5 Quantum Wires and Dots
4.3 Excitons
4.4 Photonic and Phononic Crystals
4.4.1 Properties of Waves in Periodic Media
4.4.2 Examples of Periodic Media in One and Two Dimensions
4.4.2.1 Examples of Two-Dimensional Photonic Crystals
4.4.2.2 Two-Dimensional Semiconducting Photonic Crystal
4.4.3 Applications of Photonic and Phononic Crystals
References
Chapter 5 Basic Properties of Light and its Interactions with Matter
5.1 Quantized Electromagnetic Waves
5.1.1 General Form of 3D Quantized Electromagnetic Waves
5.1.2 Cavity Modes
5.1.3 Coherent States
5.2 Field Interactions with Atoms and Electrons
5.2.1 Jaynes–Cumming Model
5.2.2 Jaynes–Cumming Model: Example of Fock States
5.2.3 Jaynes–Cumming Model: Example of Coherent States
5.2.4 Jaynes–Cumming Model: Temperature Effects
5.3 Optical Correlations and Coherence
References
Chapter 6 Basic Properties of Lasers, Masers, and Spasers
6.1 Stimulated Emission
6.1.1 Deviations of the System From Thermal Equilibrium
6.2 Rate Equation Model of Laser Operations
6.3 Resonator Cavity
6.4 Maser
6.4.1 The Model
6.4.2 The Hamiltonian: Absence of Maser Fields
6.4.3 Density Matrix
6.4.4 Hamiltonian: Phenomenological Dissipative Terms
6.4.5 Development of the Solutions with Dissipative Effects
6.4.6 Density Matrix of the Maser
6.4.7 The General Atomic Passage Maser Processes
6.4.8 The Loss Terms in the Maser Processes
6.4.9 Statistical Properties of Maser Radiation
6.5 Spasers and Atom Lasers
References
Chapter 7 Semiconductor Junctions
7.1 Semiconductor Model
7.1.1 Thermal Occupancy
7.1.2 Extrinsic Semiconductors: n- and p- Type Materials
7.1.3 Positioning of the Chemical Potential
7.2 Semiconductor Junction Model
7.2.1 Electrostatics at the Junction
7.2.2 Application of a Potential Across the Junction
7.2.3 Resulting Current Versus Voltage Relationship of the Junction
References
Chapter 8 Rectifiers and Transistors
8.1 Rectifiers and Transistors
8.1.1 The Transition Region in a p–n Junction
8.1.2 The Transition Region Characteristics
8.2 Field Effect Transistor
8.2.1 p–n–p Transistor
8.2.2 Basic Transistor Circuit
8.2.3 Geometry of the Subregion of Net Positive Charge within the n-Material Layer
8.2.4 Connected Region of Charge-Neutral n-Material Between the Source and Drain
8.2.5 Disconnected Region of Charge-Neutral n-Material Between the Source and Drain
8.2.6 Conditions of Zero Drain Current
8.2.7 Switches and Amplifier Circuits
8.2.8 n–p–n Transistors
8.3 Bipolar Transistor
References
Chapter 9 Toward Single-Electron Transistors: Coulomb Blockade
9.1 A Single Island Device
9.2 Single-Electron Transistor
9.2.1 Electron Transitions Between the Source and the Island
9.2.2 Electron Transitions Between the Drain and the Island
9.2.3 Stability of N Net Uncompensated Electrons on the Island
9.3 Applications of Single-Electron Transistors
References
Chapter 10 Quantum Hall Effect
10.1 Two Quantum Hall Effects
10.1.1 Integer Quantum Hall Effect
10.1.2 Fractional Quantum Hall Effects
10.2 Classical Model of the Hall Effect
10.3 Theory of the Integer Quantum Hall Effect
10.3.1 Transverse Conductivity
10.3.1.1 Another Approach to the Conductivity
10.3.2 Shubnikov-De Hass Effect
10.4 Fractional Quantum Hall Effect
10.4.1 Free Electrons in High Fields
10.4.2 Wave Function for the Fractional Quantum Hall Effect
10.4.3 The Electron–Electron Interactions
10.4.4 Conductivity and Resistivity of the 1/3 Fractional Hall State
10.4.5 Conclusions
10.5 Spin
10.6 Spin Hall Effect and the Spin Hall Effect of Light
References
Chapter 11 Resonance Properties
11.1 Metamaterial Responses and Simple Spatial Resonances
11.2 Standard Resonance Involving Quantum Wells
11.3 Fano Resonance Involving Quantum Wells
11.4 Topological Excitations
References
Chapter 12 Josephson Junction Properties and Basic Applications
12.1 Time-Dependent Ginzburg–Landau Free Energy
12.1.1 Schrodinger Gauge Symmetry
12.1.2 Ginzburg–Landau Form
12.1.2.1 An Example
12.2 Josephson Junction
12.3 Spatial Dependent Effects: Magnetic Fields
12.4 Josephson Junction in a Static Magnetic Field
12.5 Real-World Versus Ideal Josephson Junction
12.6 Josephson Junctions of Finite Cross-Sectional Area
12.6.1 Two Junctions in Parallel
12.7 Type I and Type II Superconductors and Interfaces with Normal Metals
12.8 High-Temperature Superconductors
References
Chapter 13 Scaling and Renormalization
13.1 One-Dimensional Ferromagnet
13.2 Second-Order Phase Transitions
13.3 First-Order Phase Transitions
13.4 Scaling Theory
13.4.1 Examples of the Two-Dimensional Ising Model and Landau Theory
13.4.2 Natural Length Scales
13.5 Renormalization Group Approach
13.6 Application of the Renormalization Group to the Landau Formulation
Appendix
References
Index