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Appendix B. Analytic derivations 182
Appendix C. Numerical implementations C.1. Programming language, libraries and tools The numerical work presented in this thesis was done using Open Source tools exclusively: • As a programming language, Python (http://www.python.org) by G. Rossum et al. was chosen due to its flexibility. Being an interpreted language, small scripts can be written with minimal overhead, allowing many ideas to be tried out. Yet, unlike other scripting languages, Python encourages the author to write clear and wellstructured code that can be well maintained and reused. • The library NumPy (http://www.numpy.org) by T. Oliphant et al. allows the very efficient and elegant handling of arrays of numerical data within Python. For many numerical problems, this approach completely eliminates the performance penalty of the interpreted language. Handled correctly, the bulk of the computations runs at the full speed of C or Fortran, with the user only writing Python code or, in special situations, small snippets of compiled code. • The library SciPy (http://www.scipy.org) by E. Jones et al. contains a collection of numerical algorithms based on NumPy. • The library pyTables (http://www.pytables.org) by F. Altet et al. was used for the storage of numerical data. This library gives highly efficient and elegant access to HDF5 data files, storing numerical data in full binary precision in flexible hierarchical structures. The library is fully integrated with NumPy. 183
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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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4.2. Extended contacts Figure 4.10.
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4.2. Extended contacts 4.2.5. Three
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4.2.6. Non-epitaxial contacts 4.2.
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4.2. Extended contacts spacing in g
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4.3. Ferromagnetic contacts and spi
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Chapter 5. Disorder and defects The
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5.1. Anderson model for disorder 5.
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5.2. The elastic mean free path Fig
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5.3. Strong localization 5.3. Stron
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5.4. Vacancies and defects Figure 5
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to occur in the same unit cell, ℓ
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5.5. Graphene nanoribbons states, b
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Chapter 6. Multilayer graphene and
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6.1. Commensurability up of two arm
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6.2. Modeling the interlayer coupli
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6.3. Bilayer graphene Figure 6.3.:
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6.4. Double-wall carbon nanotubes t
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6.4. Double-wall carbon nanotubes s
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6.5. Telescopic carbon nanotubes st
Page 131 and 132: 6.5. Telescopic carbon nanotubes Th
Page 133 and 134: 6.5. Telescopic carbon nanotubes Fi
Page 135 and 136: 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
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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: B.3. The elastic mean free path in
Page 185 and 186: C.3. Constructing chiral carbon nan
Page 187 and 188: C.3. Constructing chiral carbon nan
Page 189 and 190: C.5. Tight-binding interlayer Hamil
Page 191 and 192: C.6. Decimation of a finite block t
Page 193 and 194: C.8. Periodic gauge C.8. Periodic g
Page 195 and 196: Appendix D. Reprints of publication
Page 197 and 198: 180 S. Krompiewski et al.: Spin tra
Page 199 and 200: 182 S. Krompiewski et al.: Spin tra
Page 201 and 202: PRL 96, 076802 (2006) tion. For bot
Page 203 and 204: PRL 96, 076802 (2006) contact regio
Page 205 and 206: NORBERT NEMEC AND GIANAURELIO CUNIB
Page 217 and 218: Hofstadter butterflies of bilayer g
Page 219 and 220: HOFSTADTER BUTTERFLIES OF BILAYER G
Page 221 and 222: Bibliography [1] S. Krompiewski, N.
Page 223 and 224: Bibliography [31] D. Bethune, C. Kl
Page 225 and 226: Bibliography [66] S. Datta. Electri
Page 227 and 228: Bibliography [100] F. Guinea, A. H.
Page 229 and 230: Bibliography [135] A. E. Karu and M
Page 231 and 232: 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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