Graphene Quantum Dots (eBook)

Preface 6
Contents 8
1 Introduction 11
References 12
2 Graphene---Two-Dimensional Crystal 13
2.1 Introduction to Graphene 13
2.2 Fabrication of Graphene 21
2.2.1 Mechanical Exfoliation 21
2.2.2 Chemical Vapor Decomposition 22
2.2.3 Thermal Decomposition of SiC 22
2.2.4 Reduction of Graphite Oxide (GO) 23
2.3 Mechanical Properties 23
2.4 Electronic Band Structure of Graphene 24
2.4.1 Tight-Binding Model 24
2.4.2 Effective Mass Approximation, Dirac Fermions and Berry's Phase 28
2.4.3 Chirality and Absence of Backscattering 31
2.4.4 Bilayer Graphene 32
References 34
3 Graphene Nanostructures and Quantum Dots 38
3.1 Fabrication Methods 38
3.2 The Role of Edges 41
3.3 Size Quantization Effects 44
References 45
4 Single-Particle Properties of Graphene Quantum Dots 48
4.1 Size, Shape and Edge Dependence of Single Particle Spectrum 48
4.1.1 One-Band Empirical Tight-Binding Model 48
4.1.2 Effective Mass Model of Graphene Quantum Dots 55
4.1.3 Graphene Quantum Dots in a Magnetic Field in the Effective Mass Approximation 58
4.2 Spin-Orbit Coupling in Graphene Quantum Dots 62
4.2.1 Four-Band Tight-Binding Model 64
4.2.2 Inclusion of Spin-Orbit Coupling into Four-Band Tight-Binding Model 65
4.2.3 Kane-Mele Hamiltonian and Quantum Spin Hall Effect in Nanoribbons 67
4.3 Triangular Graphene Quantum Dots with Zigzag Edges 71
4.3.1 Energy Spectrum 71
4.3.2 Analytical Solution for Zero-Energy States 72
4.3.3 Zero-Energy States in a Magnetic Field 77
4.3.4 Classification of States with Respect to Irreducible Representations of C3v Symmetry Group 77
4.3.5 The Effect of Spin-Orbit Coupling 85
4.4 Bilayer Triangular Graphene Quantum Dots with Zigzag Edges 86
4.5 Triangular Mesoscopic Quantum Rings with Zigzag Edges 88
4.5.1 Energy Spectrum 89
4.6 Hexagonal Mesoscopic Quantum Rings 90
4.6.1 Energy Spectrum 91
4.7 Nanoribbon Rings 95
4.7.1 Möbius and Cyclic Nanoribbon Rings 96
References 98
5 Electron--Electron Interactions in Graphene Quantum Dots 100
5.1 Introduction 100
5.2 Many-Body Hamiltonian 102
5.3 Two-body Scattering---Coulomb Matrix Elements 103
5.4 Mean-Field Hartree-Fock Approximation 104
5.4.1 Hartree-Fock State in Graphene Quantum Dots 105
5.4.2 Semimetal-Mott Insulator Transition in Graphene Quantum Dots 108
5.4.3 Hubbard Model---Mean-Field Approximation 109
5.5 Ab Inito Density Functional Approach 110
5.6 Configuration Interaction Method 112
5.6.1 Many-Body Configurations 112
5.6.2 Diagonalization Methods for Large Matrices 115
5.7 TB+HF+CI Method 116
References 117
6 Magnetic Properties of Gated Graphene Nanostructures 120
6.1 Triangular Graphene Quantum Dots with Zigzag Edges 120
6.1.1 Filling Factor Dependence of the Total Spin of TGQD 120
6.1.2 Size Dependence of Magnetic Properties of TGQD: Excitons, Trions and Lieb's Theorem 123
6.1.3 Pair-Correlation Function of Spin Depolarized States 128
6.1.4 Coulomb and Spin Blockades in TGQD 129
6.1.5 Comparison of Hubbard, Extended Hubbard and Full CI Results 131
6.1.6 Edge Stability from Ab Initio Methods 134
6.2 Bilayer Triangular Graphene Quantum Dots with Zigzag Edges 139
6.3 Triangular Mesoscopic Quantum Rings with Zigzag Edges 141
6.3.1 Properties of the Charge-Neutral TGRQ 142
6.3.2 Filling Factor Dependence of Mesoscopic TGQRs 145
6.4 Hexagonal Mesoscopic Quantum Rings 147
6.4.1 Dependence of Magnetic Moment in Hexagonal GQRs on Size 147
6.4.2 Analysis as a Function of Filling Factor 149
6.5 Nanoribbon Rings 149
References 152
7 Optical Properties of Graphene Nanostructures 154
7.1 Size, Shape and Type of Edge Dependence of the Energy Gap 154
7.2 Optical Joint Density of States 156
7.3 Triangular Graphene Quantum Dots With Zigzag Edges 158
7.3.1 Excitons in Graphene Quantum Dots 158
7.3.2 Charged Excitons in Interacting Charged Quantum Dots 161
7.3.3 Terahertz Spectroscopy of Degenerate Shell 161
7.4 Optical Spin Blockade and Optical Control of Magnetic Moment in Graphene Quantum Dots 163
7.5 Optical Properties of Colloidal Graphene Quantum Dots 168
7.5.1 Optical Selection Rules for Triangular Graphene Quantum Dots 168
7.5.2 Band-edge Exciton 171
7.5.3 Low-Energy Absorption Spectrum 173
7.5.4 Effects of Screening ? and Tunneling t 173
7.5.5 Comparison With Experiment 176
References 177
Index 178