1 Introduction... 1 Hassan Raza 1.1 Overview Book Summary Outlook References... 11

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1 Contents 1 Introduction... 1 Hassan Raza 1.1 Overview Book Summary Outlook References Part I Metrology and Synthesis 2 Raman Spectroscopy: Characterization of Edges, Defects, and the Fermi Energy of Graphene and sp 2 Carbons M.S. Dresselhaus, A. Jorio, L.G. Cançado, G. Dresselhaus, and R. Saito 2.1 Introduction to the Resonance Raman Spectra of Graphene The Raman Spectra of sp 2 Carbons Edge Structure of Graphene The Multiple-Resonance Raman Scattering Process Concept of the Kohn Anomaly Introduction to Near-Field Raman Spectroscopy Characterization of Defects Point Defects Induced by Ion Bombardment Model for the D-Band Activated Region Line Defects at the Edges of Nanographene Characterization of Edges Overview of Graphene Edges The Characterization of Graphene Edges from Their D-Band Scattering Mode assignments of the Raman Spectra of Graphene Nanoribbons Polarization Dependence of the Raman Intensity ix

2 x Contents 2.4 The Fermi Energy Dependence: The Kohn Anomaly Effect of Gate Doping on the G-Band of Single-Layer Graphene Effect of Gate Doping on the G Band of Double-Layer Graphene Near-Field Raman Spectroscopy The Spatial Resolution in Optical Microscopes The Principle of TERS Mechanism of Near-Field Enhancement Application to Carbon Nanotubes Summary and Perspective References Scanning Tunneling Microscopy and Spectroscopy of Graphene Guohong Li and Eva Y. Andrei 3.1 Introduction STM/STS Techniques Sample Preparation Hallmarks of Graphene in STM/STS Line Shape of Landau Levels Electron phonon Coupling Coupling Between Graphene Layers Twist Between Graphene Layers Appearance of Moiré Pattern Saddle Point Van Hove Singularities Single Layer-like Behavior and Velocity Renormalization Graphene on SiO Three Types of Corrugations Scanning Tunneling Spectroscopy Quantum Interference and Fermi Velocity Trapped Charges in SiO Edges, Defects and Magnetism SPM-based Nano-lithography Signs of Invasiveness of an STM Tip Folding Graphene Layers Cutting Graphene Layers Surface Modification Summary and Perspectives References The Electronic Properties of Adsorbates on Graphene Eli Rotenberg 4.1 Introduction: What Are Adsorbates on Graphene Good for? Angle-Resolved Photoemission Spectroscopy Introduction... 96

3 Contents xi Band Structure Determination of Graphene Self-energy Determination The Zoology of Adsorbates Adsorption of Nontransition-Metal Atoms Adsorption of Transition Metal Atoms Adsorbate Graphene Interactions: General Symmetry Considerations Hydrogen on Graphene As a Prototype Adsorbate System Introduction Hydrogen on Graphene: Experimental Evidence for Anderson Localization Potassium on Graphene: The Coulomb Interaction in Graphene, Revealed K Adsorption on Epitaxial Graphene on SiC(0001) K Adsorption on Quasi-free-Standing Epitaxial Graphene on SiC(0001) Calcium Adsorption: Superconducting Instability of Graphene Conclusions and Outlook References Epitaxial Graphene on SiC(0001) Thomas Seyller 5.1 Introduction Silicon Carbide and Its Polar Surfaces Growth of Epitaxial Graphene on SiC(0001) in Ultra-High Vacuum The.6 p 3 6 p 3/R30 ı Reconstruction Electronic Structure of Monolayer and Bilayer Graphene at the K-point State-of-the Art Graphene Growth in Argon Atmosphere Transport Properties of Graphene on SiC(0001) Engineering the Interface Between Graphene and SiC(0001) by Hydrogen Intercalation Conclusion References Magneto-Transport on Epitaxial Graphene Peide D. Ye, Michael Capano, Tian Shen, Yanqing Wu, and Michael L. Bolen 6.1 Introduction Epitaxial Graphene Synthesis Dielectric Integration on Epitaxial Graphene Top-Gate Graphene Field-Effect Transistors Half-Integer Quantum Hall-Effect in Epitaxial Graphene Ballistic and Coherent Transport on Epitaxial Graphene

4 xii Contents 6.7 Spin Transport on Epitaxial Graphene Summary References Epitaxial Graphene on Metals Yuriy Dedkov, Karsten Horn, Alexei Preobrajenski, and Mikhail Fonin 7.1 Introduction Methods of Graphene Preparation on Metal Surfaces Experimental Methods Graphene on Lattice-Matched 3d-Metal Surfaces Atomic Structure of Graphene Layer on Ni(111) and Co(0001) Electronic Structure of Graphene on Lattice-Matched Surfaces Magnetism of Graphene on the Ni(111) Surface Graphene on Lattice-Mismatched 4d;5d-Metal Surfaces Structure of Graphene on Ir(111), Ru(0001), and Rh(111) Electronic Structure of Graphene on Lattice-Mismatched Surfaces Hybrid Structures on the Basis of Graphene Layers on Metal Surfaces Intercalation-like Systems Growth of Noble Metal Clusters on Graphene Moirè Growth of Magnetic Metal Clusters on Graphene Moirè Chemical Functionalization of Graphene on Transition Metal Surfaces Conclusions and Outlook References Part II Electronic-structure and Transport Properties 8 Electronic Properties of Monolayer and Bilayer Graphene Edward McCann 8.1 Introduction The Crystal Structure of Monolayer Graphene The Real Space Structure The Reciprocal Lattice of Graphene The Atomic Orbitals of Graphene The Tight-Binding Model The Tight-Binding Model of Monolayer Graphene Diagonal Matrix Elements Off-Diagonal Matrix Elements

5 Contents xiii The Low-Energy Electronic Bands of Monolayer Graphene Massless Chiral Quasiparticles in Monolayer Graphene The Dirac-Like Hamiltonian Pseudospin and Chirality in Graphene The Tight-Binding Model of Bilayer Graphene Massive Chiral Quasiparticles in Bilayer Graphene The Low-Energy Bands of Bilayer Graphene The Two-Component Hamiltonian of Bilayer Graphene Pseudospin and Chirality in Bilayer Graphene The Integer Quantum Hall Effect in Graphene The Landau Level Spectrum of Monolayer Graphene The Integer Quantum Hall Effect in Monolayer Graphene The Landau Level Spectrum of Bilayer Graphene The Integer Quantum Hall Effect in Bilayer Graphene Trigonal Warping in Graphene Trigonal Warping in Monolayer Graphene Trigonal Warping and Lifshitz Transition in Bilayer Graphene Tuneable Band Gap in Bilayer Graphene Asymmetry Gap in the Band Structure of Bilayer Graphene Self-Consistent Model of Screening in Bilayer Graphene Summary References Electronic Properties of Graphene Nanoribbons Katsunori Wakabayashi 9.1 Introduction Electronic States of Graphene Tight-Binding Model and Edge States Massless Dirac Equation Edge Boundary Condition and Intervalley Scattering Electronic Transport Properties One-Way Excess Channel System Model of Impurity Potential Perfectly Conducting Channel: Absence of Anderson Localization

6 xiv Contents 9.4 Universality Class Graphene Nanoribbons with Generic Edge Structures Transport Properties Through Graphene Nanojunction Summary References Mesoscopics in Graphene: Dirac Points in Periodic Geometries H.A. Fertig and L. Brey 10.1 Graphene Ribbons Hamiltonian Zigzag Nanoribbons Armchair Nanoribbons Graphene Quantum Rings Chirality in Armchair Nanoribbons Phase Jumps at Corner Junctions Numerical Results Graphene in a Periodic Potential Counting Dirac Points Numerical Solutions of the Dirac Equation Conductivity Conclusion References Electronic Properties of Multilayer Graphene Hongki Min 11.1 Introduction Stacking Arrangements Orbital Continuum Model Energy Band Structure Preliminaries Monolayer Graphene AA Stacking AB Stacking ABC Stacking Arbitrary Stacking Landau-Level Spectrum Preliminaries AA Stacking AB Stacking ABC Stacking Arbitrary Stacking Low-Energy Effective Theory Introduction Pseudospin Hamiltonian

7 Contents xv Stacking Diagrams Partitioning Rules Degenerate State Perturbation Theory Limitations of the Minimal Model Effects of the Consecutive Stacking Applications Quantum Hall Conductivity Optical Conductivity Electrical Conductivity Conclusions References Graphene Carrier Transport Theory Shaffique Adam 12.1 Introduction Graphene Boltzmann Transport Screening: Random Phase Approximation (RPA) Coulomb Scatterers Gaussian White Noise Disorder Yukawa Potential Gaussian Correlated Impurities Midgap States Transport at Low Carrier Density Self-Consistent Approximation Effective Medium Theory Magneto-Transport and Temperature Dependence of the Minimum Conductivity Quantum to Classical Crossover Summary of Theoretical Predictions for Coulomb Impurities Comparison with Experiments Magnetotransport: Dependence of xx and xy on Carrier Density Dependence of min and Mobility on Impurity Concentration Dependence of min and Mobility on Dielectric Environment Conclusion References Exploring Quantum Transport in Graphene Ribbons with Lattice Defects and Adsorbates George Kirczenow and Siarhei Ihnatsenka 13.1 Landauer Theory of Transport Subband Structure and Transport in Ideal Ribbons Quantized Ballistic Conductance

8 xvi Contents 13.4 Electron Transport in Graphene Ribbons Discovery of Quantized Conductance in Strongly Disordered Graphene Ribbons The Roles of Different Classes of Defects Tight Binding Model of Ribbons with Edge Disorder, Interior Vacancies, and Long-Ranged Potentials Numerical Simulations of Quantum Transport Disorder-Induced Conductance Suppression, Fluctuations and Destruction of the Ballistic Quantized Conductance Plateaus Conductance Dips at the Edges of Ribbon Subbands The Role of Temperature From Ballistic Transport to Anderson Localization The Quantized Conductance in Disordered Ribbons: Theory vs. Experiment Adsorbates on Graphene and Dirac Point Resonances Tight Binding Hamiltonian for Adsorbates on Graphene Effective Hamiltonian for Adsorbates on Graphene The T-matrix Formalism Dirac Point Scattering Resonances due to H, F, and O Atoms and OH Molecules Adsorbed on Graphene Electron Quantum Transport in Graphene Ribbons with Adsorbates Building Efficient Tight-Binding Models Results of Numerical Simulations of Quantum Transport in Ribbons with Adsorbates Summary References Graphene Oxide: Synthesis, Characterization, Electronic Structure, and Applications Derek A. Stewart and K. Andre Mkhoyan 14.1 Introduction Understanding Bulk Graphite Oxide and Graphene Oxide Monolayers Fabrication of Graphite Oxide and Graphene Oxide Traditional Approaches to Fabricate Graphite Oxide New Fabrication Techniques for Graphite Oxide and Graphene Oxide

9 Contents xvii 14.4 Characterization Approaches Optical Microscopy Scanning Transmission Electron Microscopy Electron Energy Loss Spectroscopy Atomic Force Microscopy X-ray Photoelectron Spectroscopy Raman Spectroscopy of Graphene Oxide and Reduced Graphene Insight from Simulations Using Epoxy Groups to Unzip Graphene Graphene Oxide Electronic Structure Electron Mobility and Transport Applications for Graphene Oxide Graphene Oxide Electronics Sensors Carbon-Based Magnetism Future Perspectives References Part III From Physics and Chemistry of Graphene to Device Applications 15 Graphene pn Junction: Electronic Transport and Devices Tony Low 15.1 Introduction Transport in the Absence of a Magnetic Field Dirac Equation, Pseudospin, and Chirality Abrupt pn Junction and Analogy with Optics Tunneling for Dirac and Schr Rodinger Fermions Quantum Transport Modeling Experiments: Asymmetry and odd Resistances Transport in the Presence of Magnetic Fields Weak Magnetic Field Regime Edge States, Snake States, and Valley Isospin Quantum Hall Regime: The Ballistic Case Experiments: Ballistic to Ohmic Transition Transport in the Presence of Strain-Induced Pseudo-Magnetic Fields Strain-Induced Pseudo-Magnetic Field Edge States and Transport Gap Magnetic and Electric Snake States Discussions Devices: Current Status and Outlook Conclusions References

10 xviii Contents 16 Electronic Structure of Bilayer Graphene Nanoribbon and Its Device Application: A Computational Study Kai-Tak Lam and Gengchiau Liang 16.1 Introduction Methodology Electronic Structure of Monolayer Graphene Nanoribbon Armchair Edges Zigzag Edges Dopant Effect Electronic Structure of Bilayer Graphene Nanoribbon Armchair Edges Zigzag Edges with Dopants Interlayer Distance Bilayer Graphene Nanoribbon Device Bilayer ZGNR NEM Switch Conclusion References Field-Modulation Devices in Graphene Nanostructures Hassan Raza 17.1 Introduction Electronic Structure Theoretical Framework: Extended Hückel Theory Bilayer Graphene A B Q stacking Strain Engineering Misalignment Armchair Graphene Nanoribbons Pristine Edges Periodic edge roughness effects Zigzag Graphene Nanoribbons with Periodic Edge Roughness Novel Applications Conclusions References Graphene Nanoribbons: From Chemistry to Circuits F. Tseng, D. Unluer, M.R. Stan, and A.W. Ghosh 18.1 The Innermost Circle: The Atomistic View Flatland: A Romance in Two Dimensions Whither Metallicity? Edge Chemistry: Benzene or Graphene? Whither Chirality? The Next Circle: Two Terminal Mobilities and I Vs Current Voltage Characteristics (I Vs)

11 Contents xix Low Bias Mobility-Bandgap Tradeoffs: Asymptotic Band Constraints The Third Level: Active Three-Terminal Electronics Wide Narrow Wide: All Graphene Devices Solving Quantum Transport and Electrostatic Equations Improved Electrostatics in 2-D Three-Terminal I Vs Pinning vs. Quasi-Ohmic Contacts The Penultimate Circle: GNR Circuits Geometry of An All Graphene Circuit Compact Model Equations Digital Circuits How Good is a Graphene-based Invertor? Physical Domain Issues: Monolithic Device-Interconnect Structures Conclusions References Index

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