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
8 - The Coulomb problem
Published online by Cambridge University Press: 24 May 2020
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
Summary
Exact solution of two-dimensional Dirac equation for Coulomb potential (Dirac–Kepler problem) is presented. Linear and nonlinear screening of the Coulomb potential is discused. The main focus is on the phenomenon of relativistic collapse of supercritical charges, which was discussed for many years in high-energy physics (this is the process that determines the end of the periodic table) and was at last discovered in graphene. We introduce Hartree–Fock theory for massless Dirac electrons and show that their Coulomb interaction essentially renormalizes Fermi velocity in such a way that Dirac cone is, strictly speaking, no more cone.
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- Information
- The Physics of Graphene , pp. 193 - 212Publisher: Cambridge University PressPrint publication year: 2020