Description
Graphene is the thinnest known material, a sheet of carbon atoms arranged in hexagonal cells a single atom thick, and yet stronger than diamond. It has potentially significant applications in nanotechnology, 'beyond-silicon' electronics, solid-state realization of high-energy phenomena and as a prototype membrane which could revolutionise soft matter and 2D physics. In this book, leading graphene research theorist Mikhail Katsnelson presents the basic concepts of graphene physics. Topics covered include Berry phase, topologically protected zero modes, Klein tunneling, vacuum reconstruction near supercritical charges, and deformation-induced gauge fields. The book also introduces the theory of flexible membranes relevant to graphene physics and discusses electronic transport, optical properties, magnetism and spintronics. Standard undergraduate-level knowledge of quantum and statistical physics and solid state theory is assumed. This is an important textbook for graduate students in nanoscience and nanotechnology and an excellent introduction for physicists and materials science researchers working in related areas.
Chapter
2: Electron states in a magnetic field
2.1 The effective Hamiltonian
2.2 Landau quantization for massless Dirac fermions
2.3 Topological protection of the zero-energy states
2.4 Semiclassical quantization conditions and Berry’s phase
2.5 Landau levels in bilayer graphene
2.6 The case of bilayer graphene: trigonal warping effects
2.7 A unified description of single-layer and bilayer graphene
2.8 Magnetic oscillations in single-layer graphene
2.9 The anomalous quantum Hall effect in single-layer and bilayer graphene
2.10 Effects of smooth disorder and an external electric field on the Landau levels
3: Quantum transport via evanescent waves
3.1 Zitterbewegung as an intrinsic disorder
3.2 The Landauer-formula approach
3.3 Conformal mapping and Corbino geometry
3.4 The Aharonov–Bohm effect in undoped graphene
4: The Klein paradox and chiral tunnelling
4.2 The massless case: the role of chirality
4.3 Klein tunnelling in single-layer graphene
4.4 Klein tunnelling for a smooth potential barrier and the effect of magnetic fields
4.5 Negative refraction coefficient and Veselago lenses for electrons in graphene
4.6 Klein tunnelling and minimal conductivity
4.7 Chiral tunnelling in bilayer graphene
5: Edges, nanoribbons and quantum dots
5.1 The neutrino billiard model
5.2 A generic boundary condition: valley mixing
5.3 Boundary conditions for a terminated honeycomb lattice
5.4 Electronic states of graphene nanoribbons
5.5 Conductance quantization in graphene nanoribbons
5.6 The band gap in graphene nanoribbons with generic boundary conditions
5.7 Energy levels in graphene quantum dots
5.8 Edge states in magnetic fields and the anomalous quantum Hall effect
6.1 Scattering theory for Dirac electrons
6.2 Scattering by a region of constant potential
6.3 Scattering theory for bilayer graphene in the parabolic-band approximation
6.4 General theory of defects in a honeycomb lattice
6.5 The case of vacancies
6.6 Adsorbates on graphene
6.7 Scanning tunnelling microscopy of point defects on graphene
6.8 Long-range interaction between adatoms on graphene
7: Optics and response functions
7.1 Light absorption by Dirac fermions: visualization of the fine-structure constant
7.2 The optics of Dirac fermions: the pseudospin precession formalism
7.3 The absence of many-body corrections to the universal optical conductivity
7.4 The magneto-optics of Dirac fermions
7.5 Optical properties of graphene beyond the Dirac approximation
7.6 The dielectric function of Dirac fermions
7.9 Transverse response functions and diamagnetic susceptibility
8.1 Scattering of Dirac fermions by point charges
8.2 Relativistic collapse for supercritical charges
8.3 Nonlinear screening of charge impurities
8.4 Inter-electron Coulomb interaction and renormalization of the Fermi velocity
9: Crystal lattice dynamics, structure and thermodynamics
9.1 Phonon spectra of graphene
9.2 The theory of elasticity for thin plates
9.3 The statistical mechanics of flexible membranes
9.4 Scaling properties of membranes and intrinsic ripples in graphene
9.5 The self-consistent screening approximation
9.6 Thermodynamic and other thermal properties of graphene
9.7 Raman spectra of graphene
10: Gauge fields and strain engineering
10.1 Strain-induced pseudomagnetic fields
10.2 Pseudomagnetic fields of frozen ripples
10.3 Pseudomagnetic fields of ripples: the effect of in-plane relaxation
10.4 The zero-field quantum Hall effect by strain engineering
10.5 The pseudo-Aharonov-Bohm effect and transport gap in suspended graphene
10.6 Gap opening by combination of strain and electric field
11: Scattering mechanisms and transport properties
11.1 The semiclassical Boltzmann equation and limits of its applicability
11.2 The Kubo-Nakano-Mori formula for resistivity
11.3 Scattering mechanisms in graphene on a substrate
11.4 Intrinsic mobility and transport properties of suspended graphene flakes
11.5 Nonlocal transport in magnetic fields
11.6 Beyond the Boltzmann equation: localization and antilocalization
12: Spin effects and magnetism
12.1 General remarks on itinerant-electron magnetism
12.2 Defect-induced magnetism in graphene
Graphene
：Carbon in Two Dimensions
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