Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Part I Condensed Matter Physics
- Part II Quantum Field Theory
- Part III Quantum Field Theory Approach to Condensed Matter Systems
- 13 Quantum Field Theory Methods in Condensed Matter
- 14 Metals, Fermi Liquids, Mott and Anderson Insulators
- 15 The Dynamics of Polarons
- 16 Polyacetylene
- 17 The Kondo Effect
- 18 Quantum Magnets in 1D: Fermionization, Bosonization, Coulomb Gases and “All That”
- 19 Quantum Magnets in 2D: Nonlinear Sigma Model, CP1 and “All That”
- 20 The Spin-Fermion System: a Quantum Field Theory Approach
- 21 The Spin Glass
- 22 Quantum Field Theory Approach to Superfluidity
- 23 Quantum Field Theory Approach to Superconductivity
- 24 The Cuprate High-Temperature Superconductors
- 25 The Pnictides: Iron-Based Superconductors
- 26 The Quantum Hall Effect
- 27 Graphene
- 28 Silicene and Transition Metal Dichalcogenides
- 29 Topological Insulators
- 30 Non-Abelian Statistics and Quantum Computation
- Further Reading
- References
- Index
27 - Graphene
from Part III - Quantum Field Theory Approach to Condensed Matter Systems
Published online by Cambridge University Press: 25 October 2017
- Frontmatter
- Dedication
- Contents
- Preface
- Part I Condensed Matter Physics
- Part II Quantum Field Theory
- Part III Quantum Field Theory Approach to Condensed Matter Systems
- 13 Quantum Field Theory Methods in Condensed Matter
- 14 Metals, Fermi Liquids, Mott and Anderson Insulators
- 15 The Dynamics of Polarons
- 16 Polyacetylene
- 17 The Kondo Effect
- 18 Quantum Magnets in 1D: Fermionization, Bosonization, Coulomb Gases and “All That”
- 19 Quantum Magnets in 2D: Nonlinear Sigma Model, CP1 and “All That”
- 20 The Spin-Fermion System: a Quantum Field Theory Approach
- 21 The Spin Glass
- 22 Quantum Field Theory Approach to Superfluidity
- 23 Quantum Field Theory Approach to Superconductivity
- 24 The Cuprate High-Temperature Superconductors
- 25 The Pnictides: Iron-Based Superconductors
- 26 The Quantum Hall Effect
- 27 Graphene
- 28 Silicene and Transition Metal Dichalcogenides
- 29 Topological Insulators
- 30 Non-Abelian Statistics and Quantum Computation
- Further Reading
- References
- Index
Summary
Graphene is one of the most remarkable materials ever found. Also one of the most studied. It presents a number of unique features that have attracted the attention of both theoreticians and experimentalists. Investigation of its properties has led to breakthroughs, not only from the perspective of fundamental research but also from the point of view of applied science. Theoretically conjectured long ago, it was concretely obtained in 2004 by Geim and Novoselov [243]. Graphene properties include an outstanding mechanical robustness, being orders of magnitude stronger than steel; high electric and thermal conductivities, despite the absence of a Fermi surface; finite resistivity even without impurities, despite the absence of a gap; and relativistic dispersion relation for the active electrons, implying their kinematics are described by the Dirac equation and not by the Schrödinger equation, among others. This last property makes of graphene a concrete realization of the Dirac sea, a concept that in spite of not manifesting itself in nature, in the absence of matter has enabled Dirac to predict the existence of antimatter. The observation of antimatter in vacuo and the subsequent concrete realization of the Dirac sea in a material system such as graphene is an outstanding example of the great unity that exists in physics. Other properties of Dirac particles such as the Klein tunneling have been observed as well in graphene. As a consequence of charge conjugation symmetry, both electrons and holes possess the same mobility in graphene, a feature that is not found, for instance, in regular (Si or Ge based) semiconductors. Further properties of this extraordinary material include, for instance, the occurrence of the integer and fractional quantum Hall effects, in the presence of an external perpendicular magnetic field and the Zitterbewegung.
Crystal Structure and Tight-Binding Approach
Graphene is a one-atom-wide sheet of carbon with a sp2 hybridization, assembled in a honeycomb crystal structure, consisting of a Bravais triangular lattice with spacing a and a base of two atoms, respectively placed at (0, 0) and (0, h), with respect to the Bravais lattice sites.
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- Quantum Field Theory Approach to Condensed Matter Physics , pp. 437 - 457Publisher: Cambridge University PressPrint publication year: 2017