| Preface vii |
| Acknowledgments ix |
| Authors xi |
| Chapter 1 Fundamentals of quantum mechanics and band structure 1 |
| 1.1 Fundamentals of quantum mechanics 1 |
| 1.1.1 Probability amplitude and interference effects 1 |
| 1.1.2 Uncertainty principle 5 |
| 1.1.3 Wave functions 7 |
| 1.1.4 Operators 8 |
| 1.1.5 Eigenvalue and expected value 10 |
| 1.1.6 Expansion theorem 10 |
| 1.1.7 Schroedinger equation 11 |
| 1.1.8 Principle of superposition 13 |
| 1.1.9 Examples of solutions of the Schroedinger equation 14 |
| 1.1.9.1 Electron in a one-dimensional (1D) box 14 |
| 1.1.9.2 Harmonic oscillator 15 |
| 1.1.9.3 Hydrogen atom 16 |
| 1.1.10 Matrix mechanics and bra-ket (Dirac) notation 18 |
| 1.1.11 Comparison of the Heisenberg and Schroedinger approaches to quantum mechanics 20 |
| 1.1.12 Perturbation theory 22 |
| 1.2 Electronic band structure of solids 27 |
| 1.2.1 Free electron Fermi gas 27 |
| 1.2.2 Nearly free electron model (DOS) 31 |
| 1.2.3 Bloch function 33 |
| 1.2.4 Kroenig-Penny model 33 |
| 1.2.5 Tight binding model 35 |
| 1.2.6 Phase velocity, group velocity, and effective mass 37 |
| 1.2.7 Reciprocal lattice and the Brillouin zone 40 |
| 1.2.8 Energy band structure of silicon (Si) 44 |
| 1.2.9 Tight binding approximation for calculating the band structure of graphene 45 |
| 1.2.10 Electron correlation 51 |
| 1.2.10.1 Hartree-Fock approximation 51 |
| 1.2.10.2 Density functional method 54 |
| 1.3 Material properties with respect to characteristic size in nanostructures 56 |
| Problems 60 |
| References 60 |
| Chapter 2 Electronic states and electrical properties of nanoscale materials 63 |
| 2.1 Outline 63 |
| 2.2 Low dimensionality and energy spectrum 64 |
| 2.2.1 Space for electrons in materials 64 |
| 2.2.2 Electron DOS of 3D materials with macroscopic dimensions 65 |
| 2.2.3 Electron DOS in 2D materials (nanosheets) 67 |
| 2.2.4 Electron DOS in lD materials (nanowires) 72 |
| 2.2.5 Quantized conductance in 1D nanowire systems 74 |
| 2.2.6 Electron DOS in 0D materials (nanodots) 77 |
| 2.3 Quantization 79 |
| 2.3.1 2D square wells 80 |
| 2.3.2 2D cylindrical wells 83 |
| 2.3.3 Shape effect on the quantized states 85 |
| 2.3.4 Finite potential wells 87 |
| 2.3.5 Band dispersion effect 93 |
| 2.4 Edge (surface)-localized states 96 |
| 2.5 Charging effect 100 |
| 2.6 Tunneling phenomena 103 |
| 2.7 Limiting factors for size effects 111 |
| 2.7.1 Thermal fluctuation 111 |
| 2.7.2 Lifetime broadening effect 113 |
| 2.8 Electronically induced stable nanostructures 115 |
| 2.8.1 Magic numbers in clusters 116 |
| 2.8.2 Electronic growth 119 |
| Problems 122 |
| References 123 |
| Chapter 3 Optical properties and interactions of nanoscale materials 125 |
| 3.1 Size-dependent optical properties: Absorption and emission 125 |
| 3.1.1 Basic quantum mechanics of linear optical transitions 126 |
| 3.1.2 General concept of excitons 133 |
| 3.1.3 Wannier excitons 135 |
| 3.1.4 Size effects in high-dielectric-constant materials 136 |
| 3.1.5 Size effects in π-conjugated systems 140 |
| 3.1.6 Strongly interacting π-conjugated systems: A molecular dimer 144 |
| 3.1.7 Molecular Frenkel exciton 149 |
| 3.1.8 Size effects in molecular excitons: Coherence length and cooperative phenomena 153 |
| 3.1.9 Effects of finite number of optical electrons 157 |
| 3.2 Size-dependent optical properties: Absorption and scattering 158 |
| 3.2.1 Basic theory of light scattering 160 |
| 3.2.2 Size-dependent scattering from dielectric spheres: Mie solutions 164 |
| 3.2.3 Optical properties of metal nanoparticles: Plasmonics 169 |
| 3.2.4 Local field enhancement and surface-enhanced Raman scattering 176 |
| 3.3 Size-dependent electromagnetic interactions: Particle-particle 179 |
| 3.3.1 Radiative energy transfer 179 |
| 3.3.2 Foerster resonant energy transfer (FRET) 180 |
| 3.3.3 Electron-exchange (Dexter) energy transfer 187 |
| 3.3.4 Photo-induced electron transfer 190 |
| 3.4 Size-dependent interactions: Particle-light interactions in finite geometries 191 |
| 3.4.1 Optical interactions in microcavities 191 |
| 3.4.2 Effects of dielectric interfaces 198 |
| Problems 201 |
| References 204 |
| Chapter 4 Magnetic and magnetotransport properties of nanoscale materials 207 |
| 4.1 Fundamentals of magnetism 207 |
| 4.1.1 Magnetic ions and magnetic ordering 207 |
| 4.1.2 Exchange interaction 208 |
| 4.1.3 Mean field theory of ferromagnetism 211 |
| 4.2 Size and surface effects in 3D confined systems 213 |
| 4.2.1 Quantization of electronic structures and the Kubo effect 214 |
| 4.2.2 Surface magnetism of transition noble metals 220 |
| 4.3 Ferromagnetic domain-wall-related phenomena 229 |
| 4.3.1 Macroscopic quantum tunneling in magnetic nanostructures 229 |
| 4.3.2 Electron scattering at domain walls: Quantum coherence 233 |
| 4.3.3 Spin current and spin transfer torque-current-induced domain wall motion 235 |
| 4.4 Spin transport in magnetic nanostructures: Magnetic interface effect 240 |
| 4.4.1 GMR and TMR effect: Spin-dependent scattering in multilayers and tunneling junctions 240 |
| 4.4.2 Spin accumulation and current-perpendicular-to-plane (CPP) GMR: Spin diffusion length 245 |
| 4.4.3 Spin Hall effect: Side jump and skew scattering due to spin-orbit coupling 249 |
| Problems 253 |
| References 253 |
| Index 257 |
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