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GrapheneA New Paradigm in Condensed Matter and Device Physics$
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E. L. Wolf

Print publication date: 2013

Print ISBN-13: 9780199645862

Published to Oxford Scholarship Online: January 2014

DOI: 10.1093/acprof:oso/9780199645862.001.0001

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Electron bands of graphene

Electron bands of graphene

Chapter:
(p.86) 4 Electron bands of graphene
Source:
Graphene
Author(s):

E. L. Wolf

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199645862.003.0004

The Schrödinger tight-binding band theory of solids is applied to graphene. The symmetry of the honeycomb lattice leads to cancellation of terms in the conventional approach, such that the Hamiltonian simplifies to two offset versions of the Dirac Hamiltonian. (It is established that a chemical bond approach, as advocated by L. Pauling, is inadequate for graphene.) The spinor wavefunction casts carrier backscattering as a forbidden “spin flip” transition, consistent with observations of exceedingly high carrier mobility. These circumstances make ordinary electrons behave as chiral particles, analogs of neutrinos. Bilayer graphene is treated at the same level, recovering a semimetal with parabolic bands corresponding to conventional effective mass carriers. A voltage across the bilayer opens a small bandgap between two parabolic energy bands. This is of interest for field-effect switching FET transistors that conventionally need an energy gap for a suitably large increase of resistance in the ‘off’ state.

Keywords:   Schrödinger, tight-binding, Hamiltonian, Dirac, spinor wavefunction, bilayer, energy gap

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