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Chapter 6. Multilayer graphene and carbon nanotubes 134 Figure 6.13.: Transmission through a (3,0)@(12,0) zigzag telescopic CNT. The overall transmission is three orders higher than in the previous case (Fig. 6.12) due to the stronger hybridization in this extremely lower diameter case. At E = 0.1 eV, the wave vectors are large enough to produce clear resonances at long wavelengths, though they are still less regular than in the armchair case. (Figure taken from Ref. [5])
6.5. Telescopic carbon nanotubes Figure 6.14.: Energy resolved transmission in a zigzag telescopic CNT. The peak at E = 0 at L = 0.5a is caused by the zigzag edge state. (Figure taken from Ref. [5]) Figure 6.15.: Sketch of the model of telescopic quantum wires: two wires run in parallel over length L. Both extend infinitely in opposite directions. In the common region, a coupling causes an energy split of ±δE into one band of even and another band of odd symmetry. At the Fermi energy, this translates into a split of the k vector by ±δk. 135
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Quantum Transport in Carbon-based N
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Contents Introduction 9 1. Carbon-b
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Contents A. Decimation techniques 1
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Introduction Carbon is the most ver
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Chap. 3: Quantum transport The theo
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Chapter 1. Carbon-based nanostructu
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1.1. Hybridization of carbon orbita
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1.1. Hybridization of carbon orbita
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Geometry 1.2. Graphite Figure 1.4.:
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1.3.1. Isolation by exfoliation 1.3
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1.3. Graphene Figure 1.10.: The hon
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1.4. Graphene nanoribbons Figure 1.
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1.5. Carbon nanotubes Figure 1.17.:
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1.6. Fullerenes Figure 1.23.: Struc
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Chapter 2. Electronic structure The
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2.1. The tight-binding approximatio
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2.1. The tight-binding approximatio
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2.2. Band structure of graphene nan
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2.3. Band structure of single-wall
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2.3. Band structure of single-wall
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2.5. Beyond tight-binding: Density
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2.5. Beyond tight-binding: Density
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Chapter 3. Theory of quantum transp
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3.1. Mesoscopic length scales In cr
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3.1. Mesoscopic length scales Figur
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3.2. The transport regimes 3.2. The
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3.4. The quantum mechanical transmi
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3.5. Beyond coherent transport: int
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Chapter 4. Electrical contacts to n
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4.1. Conventional contact models in
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4.2. Extended contacts Figure 4.2.:
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Page 83 and 84: 4.2. Extended contacts Figure 4.10.
Page 89 and 90: 4.2. Extended contacts 4.2.5. Three
Page 91 and 92: 4.2.6. Non-epitaxial contacts 4.2.
Page 93 and 94: 4.2. Extended contacts spacing in g
Page 97 and 98: 4.3. Ferromagnetic contacts and spi
Page 103 and 104: Chapter 5. Disorder and defects The
Page 105 and 106: 5.1. Anderson model for disorder 5.
Page 107 and 108: 5.2. The elastic mean free path Fig
Page 109 and 110: 5.3. Strong localization 5.3. Stron
Page 111 and 112: 5.4. Vacancies and defects Figure 5
Page 113 and 114: to occur in the same unit cell, ℓ
Page 115 and 116: 5.5. Graphene nanoribbons states, b
Page 117 and 118: Chapter 6. Multilayer graphene and
Page 119 and 120: 6.1. Commensurability up of two arm
Page 121 and 122: 6.2. Modeling the interlayer coupli
Page 123 and 124: 6.3. Bilayer graphene Figure 6.3.:
Page 125 and 126: 6.4. Double-wall carbon nanotubes t
Page 127 and 128: 6.4. Double-wall carbon nanotubes s
Page 129 and 130: 6.5. Telescopic carbon nanotubes st
Page 131 and 132: 6.5. Telescopic carbon nanotubes Th
Page 133: 6.5. Telescopic carbon nanotubes Fi
Page 137 and 138: Chapter 7. Magnetoelectronic struct
Page 139 and 140: 7.1. Peierls substitution periodic
Page 141 and 142: 7.2. Hofstadter butterfly Figure 7.
Page 143 and 144: 7.3. Butterfly and anomalous Landau
Page 145 and 146: 7.4. Butterfly of single-wall nanot
Page 147 and 148: 7.5. Graphene nanoribbons for arbit
Page 149 and 150: 7.7. Bilayer graphene total flux pe
Page 151 and 152: 7.8. Butterfly of double-wall nanot
Page 153 and 154: 7.8. Butterfly of double-wall nanot
Page 155 and 156: Conclusions and perspectives In the
Page 157 and 158: periodic and gives little rise to b
Page 159 and 160: Appendix A. Decimation techniques D
Page 161 and 162: From Eq. (A.4) it follows that: G11
Page 163 and 164: A.3. Finite block tridiagonal syste
Page 165 and 166: A.4. Periodic systems the other. Th
Page 167 and 168: A.4. Periodic systems which can be
Page 169 and 170: A.4. Periodic systems Now, it turns
Page 171 and 172: Appendix B. Analytic derivations B.
Page 173 and 174: B.1. Supersymmetric spectrum of gra
Page 175 and 176: B.2. The linear-chain model of exte
Page 177 and 178: B.2. The linear-chain model of exte
Page 179 and 180: B.3. The elastic mean free path in
Page 181 and 182: B.3. The elastic mean free path in
Page 183 and 184: Appendix C. Numerical implementatio
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C.3. Constructing chiral carbon nan
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C.3. Constructing chiral carbon nan
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C.5. Tight-binding interlayer Hamil
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C.6. Decimation of a finite block t
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C.8. Periodic gauge C.8. Periodic g
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Appendix D. Reprints of publication
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180 S. Krompiewski et al.: Spin tra
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182 S. Krompiewski et al.: Spin tra
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PRL 96, 076802 (2006) tion. For bot
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PRL 96, 076802 (2006) contact regio
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NORBERT NEMEC AND GIANAURELIO CUNIB
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Hofstadter butterflies of bilayer g
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HOFSTADTER BUTTERFLIES OF BILAYER G
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Bibliography [1] S. Krompiewski, N.
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Bibliography [31] D. Bethune, C. Kl
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Bibliography [66] S. Datta. Electri
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Bibliography [100] F. Guinea, A. H.
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Bibliography [135] A. E. Karu and M
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Bibliography [171] A. Maiti and A.
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Bibliography [205] D. Papaconstanto
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Bibliography [239] B. Shan and K. C
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Bibliography [274] S. Wang, M. Grif
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Acknowledgments Although a few word
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