Book contents
- The Physics of Graphene
- The Physics of Graphene
- Copyright page
- Dedication
- Contents
- Preface to the second edition
- Preface to the first edition
- 1 The electronic structure of ideal graphene
- 2 Electron states in a magnetic field
- 3 Quantum transport via evanescent waves
- 4 The Klein paradox and chiral tunneling
- 5 Edges, nanoribbons, and quantum dots
- 6 Point defects
- 7 Optics and response functions
- 8 The Coulomb problem
- 9 Crystal lattice dynamics, structure, and thermodynamics
- 10 Gauge fields and strain engineering
- 11 Scattering mechanisms and transport properties
- 12 Spin effects and magnetism
- 13 Graphene on hexagonal boron nitride
- 14 Twisted bilayer graphene
- 15 Many-body effects in graphene
- References
- Index
5 - Edges, nanoribbons, and quantum dots
Published online by Cambridge University Press: 24 May 2020
- The Physics of Graphene
- The Physics of Graphene
- Copyright page
- Dedication
- Contents
- Preface to the second edition
- Preface to the first edition
- 1 The electronic structure of ideal graphene
- 2 Electron states in a magnetic field
- 3 Quantum transport via evanescent waves
- 4 The Klein paradox and chiral tunneling
- 5 Edges, nanoribbons, and quantum dots
- 6 Point defects
- 7 Optics and response functions
- 8 The Coulomb problem
- 9 Crystal lattice dynamics, structure, and thermodynamics
- 10 Gauge fields and strain engineering
- 11 Scattering mechanisms and transport properties
- 12 Spin effects and magnetism
- 13 Graphene on hexagonal boron nitride
- 14 Twisted bilayer graphene
- 15 Many-body effects in graphene
- References
- Index
Summary
Boundary conditions for electron wave functions in graphene are discussed, both in Dirac approximation and for the honeycomb lattice. We start with the model of "neutrino billiard." Then, we discuss typicality of zigzag boundary conditions for the terminated honeycomb lattice, existence of zero-energy edge mode for these conditions, electronic states and conductance quantization in graphene nanoribbons, level statistics for graphene quantum dots, explanation of quantum Hall effects in terms of topologically protected edge modes, and Aharonov–Bohm effect in multiconnected graphene flakes. The latter case is used as an example of the general topological concept of spectral flow.
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- Information
- The Physics of Graphene , pp. 108 - 140Publisher: Cambridge University PressPrint publication year: 2020