144
7 Carbon Allotropes
as atomic-force microscope tips [2], cathode field emitters [3, 4], electronic circuit
devices [5, 6], hydrogen storage [7–10], chemical sensors [11, 12], energy storage and
management [10, 13–15], and phonon and electronic transportation devices [16–19].
Unrolling a single-walled CNT (SWCNT) generates a graphene nanoribbon
(GNR) [20, 21] with high fraction of undercoordinated carbon atoms located at the
open edges. The undercoordinated edge atoms and the abnormal performances of
electrons surrounding the edges have inspired even more increasing interest because
of the edge-associated intriguing phenomena. The edge associated anomalies can
be seen from neither the SWCNTs nor the infinitely large graphene sheets (LGSs)
[22–30].
Graphene is a wonder material with many superlatives to its name. It is the thinnest
known material in the universe and the strongest ever measured. Its charge carriers
or Dirac fermions (or call them Dirac-Fermi polaritons as will be justified in later
section) exhibiting giant intrinsic mobility can travel for micrometers without scattering at room temperature. Graphene can sustain current densities six orders of
magnitude higher than that of copper, shows record thermal and electric conductivity, is impermeable to gases, and reconciles such conflicting qualities as brittleness
and ductility.
Serving as vehicles for the quantum spin Hall-effect in topological insulators [27,
31–37], Dirac-Fermi polaritons [38, 39] exhibit unique electrical supercurrent properties [40] on account of its reduced dimensionality and “relativistic” band structure
[41]. When contacted with two superconducting electrodes, graphene can support
Cooper pair transport, resulting in the well-known Josephson effect [42]. STM/S
measurements [43–45] have uncovered the Dirac-Fermi polaritons as high protrusions in image and as sharp resonant peak at E F in spectrum from sites surrounding
atomic vacancies, the edges of monolayer graphite terrace and graphene nanoribbons [46–49]. These polaritons demonstrate anomalies including the extremely low
effective mass [50], extremely high group velocity, and a net ½ spin [51, 52], following the Dirac equation, and a nearly linear dispersion (Dirac cone) with energies
crossing Fermi energy [27, 31–34, 53–60]. Electron transport in graphene allows the
investigation of relativistic quantum phenomena in a bench top experiment. These
phenomena and the strip-width-induced band gap expansion demonstrated by the
AGNR can never be observed in the SWCNT, graphene or graphite crystal [23, 61].
7.1.2 Challenges and Objectives
Overwhelming experimental efforts have been exerted primarily in the CNTs and
GNRs growth, characterization, and functioning for practical applications. Considerable theoretical efforts have been made on the performance of the Dirac fermions
that follow the relativistic Dirac equations and the energetic and structural optimization. However, physical insight into the origin behind the fascinations and their
interdependence of the CNTs and the GNRs remain challenging. Opening questions
may be exampled as the following:
7 Carbon Allotropes
as atomic-force microscope tips [2], cathode field emitters [3, 4], electronic circuit
devices [5, 6], hydrogen storage [7–10], chemical sensors [11, 12], energy storage and
management [10, 13–15], and phonon and electronic transportation devices [16–19].
Unrolling a single-walled CNT (SWCNT) generates a graphene nanoribbon
(GNR) [20, 21] with high fraction of undercoordinated carbon atoms located at the
open edges. The undercoordinated edge atoms and the abnormal performances of
electrons surrounding the edges have inspired even more increasing interest because
of the edge-associated intriguing phenomena. The edge associated anomalies can
be seen from neither the SWCNTs nor the infinitely large graphene sheets (LGSs)
[22–30].
Graphene is a wonder material with many superlatives to its name. It is the thinnest
known material in the universe and the strongest ever measured. Its charge carriers
or Dirac fermions (or call them Dirac-Fermi polaritons as will be justified in later
section) exhibiting giant intrinsic mobility can travel for micrometers without scattering at room temperature. Graphene can sustain current densities six orders of
magnitude higher than that of copper, shows record thermal and electric conductivity, is impermeable to gases, and reconciles such conflicting qualities as brittleness
and ductility.
Serving as vehicles for the quantum spin Hall-effect in topological insulators [27,
31–37], Dirac-Fermi polaritons [38, 39] exhibit unique electrical supercurrent properties [40] on account of its reduced dimensionality and “relativistic” band structure
[41]. When contacted with two superconducting electrodes, graphene can support
Cooper pair transport, resulting in the well-known Josephson effect [42]. STM/S
measurements [43–45] have uncovered the Dirac-Fermi polaritons as high protrusions in image and as sharp resonant peak at E F in spectrum from sites surrounding
atomic vacancies, the edges of monolayer graphite terrace and graphene nanoribbons [46–49]. These polaritons demonstrate anomalies including the extremely low
effective mass [50], extremely high group velocity, and a net ½ spin [51, 52], following the Dirac equation, and a nearly linear dispersion (Dirac cone) with energies
crossing Fermi energy [27, 31–34, 53–60]. Electron transport in graphene allows the
investigation of relativistic quantum phenomena in a bench top experiment. These
phenomena and the strip-width-induced band gap expansion demonstrated by the
AGNR can never be observed in the SWCNT, graphene or graphite crystal [23, 61].
7.1.2 Challenges and Objectives
Overwhelming experimental efforts have been exerted primarily in the CNTs and
GNRs growth, characterization, and functioning for practical applications. Considerable theoretical efforts have been made on the performance of the Dirac fermions
that follow the relativistic Dirac equations and the energetic and structural optimization. However, physical insight into the origin behind the fascinations and their
interdependence of the CNTs and the GNRs remain challenging. Opening questions
may be exampled as the following: