Güçlü / Potasz / Korkusinski Graphene Quantum Dots

2014
ISBN: 978-3-662-44611-9
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 181 Seiten

Reihe: NanoScience and Technology

This book reflects the current status of theoretical and experimental research of graphene based nanostructures, in particular quantum dots, at a level accessible to young researchers, graduate students, experimentalists and theorists. It presents the current state of research of graphene quantum dots, a single or few monolayer thick islands of graphene. It introduces the reader to the electronic and optical properties of graphite, intercalated graphite and graphene, including Dirac fermions, Berry's phase associated with sublattices and valley degeneracy, covers single particle properties of graphene quantum dots, electron-electron interaction, magnetic properties and optical properties of gated graphene nanostructures. The electronic, optical and magnetic properties of the graphene quantum dots as a function of size, shape, type of edge and carrier density are considered. Special attention is paid to the understanding of edges and the emergence of edge states for zigzag edges. Atomistic tight binding and effective mass approaches to single particle calculations are performed. Furthermore, the theoretical and numerical treatment of electron-electron interactions at the mean-field, HF, DFT and configuration-interaction level is described in detail.

Autoren/Hrsg.

Güçlü, Alev Devrim

Potasz, Pawel

Korkusinski, Marek

Hawrylak, Pawel

Inhaltsverzeichnis

1;Preface;6
2;Contents;8
3;1 Introduction;11
3.1;References;12
4;2 Graphene---Two-Dimensional Crystal;13
4.1;2.1 Introduction to Graphene;13
4.2;2.2 Fabrication of Graphene;21
4.2.1;2.2.1 Mechanical Exfoliation;21
4.2.2;2.2.2 Chemical Vapor Decomposition;22
4.2.3;2.2.3 Thermal Decomposition of SiC;22
4.2.4;2.2.4 Reduction of Graphite Oxide (GO);23
4.3;2.3 Mechanical Properties;23
4.4;2.4 Electronic Band Structure of Graphene;24
4.4.1;2.4.1 Tight-Binding Model;24
4.4.2;2.4.2 Effective Mass Approximation, Dirac Fermions and Berry's Phase;28
4.4.3;2.4.3 Chirality and Absence of Backscattering;31
4.4.4;2.4.4 Bilayer Graphene;32
4.5;References;34
5;3 Graphene Nanostructures and Quantum Dots;38
5.1;3.1 Fabrication Methods;38
5.2;3.2 The Role of Edges;41
5.3;3.3 Size Quantization Effects;44
5.4;References;45
6;4 Single-Particle Properties of Graphene Quantum Dots;48
6.1;4.1 Size, Shape and Edge Dependence of Single Particle Spectrum;48
6.1.1;4.1.1 One-Band Empirical Tight-Binding Model;48
6.1.2;4.1.2 Effective Mass Model of Graphene Quantum Dots;55
6.1.3;4.1.3 Graphene Quantum Dots in a Magnetic Field in the Effective Mass Approximation;58
6.2;4.2 Spin-Orbit Coupling in Graphene Quantum Dots;62
6.2.1;4.2.1 Four-Band Tight-Binding Model;64
6.2.2;4.2.2 Inclusion of Spin-Orbit Coupling into Four-Band Tight-Binding Model;65
6.2.3;4.2.3 Kane-Mele Hamiltonian and Quantum Spin Hall Effect in Nanoribbons;67
6.3;4.3 Triangular Graphene Quantum Dots with Zigzag Edges;71
6.3.1;4.3.1 Energy Spectrum;71
6.3.2;4.3.2 Analytical Solution for Zero-Energy States;72
6.3.3;4.3.3 Zero-Energy States in a Magnetic Field;77
6.3.4;4.3.4 Classification of States with Respect to Irreducible Representations of C3v Symmetry Group;77
6.3.5;4.3.5 The Effect of Spin-Orbit Coupling;85
6.4;4.4 Bilayer Triangular Graphene Quantum Dots with Zigzag Edges;86
6.5;4.5 Triangular Mesoscopic Quantum Rings with Zigzag Edges;88
6.5.1;4.5.1 Energy Spectrum;89
6.6;4.6 Hexagonal Mesoscopic Quantum Rings;90
6.6.1;4.6.1 Energy Spectrum;91
6.7;4.7 Nanoribbon Rings;95
6.7.1;4.7.1 Möbius and Cyclic Nanoribbon Rings;96
6.8;References;98
7;5 Electron--Electron Interactions in Graphene Quantum Dots;100
7.1;5.1 Introduction;100
7.2;5.2 Many-Body Hamiltonian;102
7.3;5.3 Two-body Scattering---Coulomb Matrix Elements;103
7.4;5.4 Mean-Field Hartree-Fock Approximation;104
7.4.1;5.4.1 Hartree-Fock State in Graphene Quantum Dots;105
7.4.2;5.4.2 Semimetal-Mott Insulator Transition in Graphene Quantum Dots;108
7.4.3;5.4.3 Hubbard Model---Mean-Field Approximation;109
7.5;5.5 Ab Inito Density Functional Approach;110
7.6;5.6 Configuration Interaction Method;112
7.6.1;5.6.1 Many-Body Configurations;112
7.6.2;5.6.2 Diagonalization Methods for Large Matrices;115
7.7;5.7 TB+HF+CI Method;116
7.8;References;117
8;6 Magnetic Properties of Gated Graphene Nanostructures;120
8.1;6.1 Triangular Graphene Quantum Dots with Zigzag Edges;120
8.1.1;6.1.1 Filling Factor Dependence of the Total Spin of TGQD;120
8.1.2;6.1.2 Size Dependence of Magnetic Properties of TGQD: Excitons, Trions and Lieb's Theorem;123
8.1.3;6.1.3 Pair-Correlation Function of Spin Depolarized States;128
8.1.4;6.1.4 Coulomb and Spin Blockades in TGQD;129
8.1.5;6.1.5 Comparison of Hubbard, Extended Hubbard and Full CI Results;131
8.1.6;6.1.6 Edge Stability from Ab Initio Methods;134
8.2;6.2 Bilayer Triangular Graphene Quantum Dots with Zigzag Edges;139
8.3;6.3 Triangular Mesoscopic Quantum Rings with Zigzag Edges;141
8.3.1;6.3.1 Properties of the Charge-Neutral TGRQ;142
8.3.2;6.3.2 Filling Factor Dependence of Mesoscopic TGQRs;145
8.4;6.4 Hexagonal Mesoscopic Quantum Rings;147
8.4.1;6.4.1 Dependence of Magnetic Moment in Hexagonal GQRs on Size;147
8.4.2;6.4.2 Analysis as a Function of Filling Factor;149
8.5;6.5 Nanoribbon Rings;149
8.6;References;152
9;7 Optical Properties of Graphene Nanostructures;154
9.1;7.1 Size, Shape and Type of Edge Dependence of the Energy Gap;154
9.2;7.2 Optical Joint Density of States;156
9.3;7.3 Triangular Graphene Quantum Dots With Zigzag Edges;158
9.3.1;7.3.1 Excitons in Graphene Quantum Dots;158
9.3.2;7.3.2 Charged Excitons in Interacting Charged Quantum Dots;161
9.3.3;7.3.3 Terahertz Spectroscopy of Degenerate Shell;161
9.4;7.4 Optical Spin Blockade and Optical Control of Magnetic Moment in Graphene Quantum Dots;163
9.5;7.5 Optical Properties of Colloidal Graphene Quantum Dots;168
9.5.1;7.5.1 Optical Selection Rules for Triangular Graphene Quantum Dots;168
9.5.2;7.5.2 Band-edge Exciton;171
9.5.3;7.5.3 Low-Energy Absorption Spectrum;173
9.5.4;7.5.4 Effects of Screening ? and Tunneling t;173
9.5.5;7.5.5 Comparison With Experiment;176
9.6;References;177
10;Index;178