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Spectrum and transport properties of interacting carbon nanotubes [Elektronische Ressource] / vorgelegt von Leonhard Mayrhofer

162 pages
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?Lebenslauf
Leonhard Mayrhofer
Diplom-Physiker
* 26.07.1977 in Augsburg
Zur schönen Gelegenheit 6
93047 Regensburg
Familienstand: ledig
Hochschulbildung
11/1998 – 10/2003 Studium der Physik an der Universität Regensburg
11/2003 – 11/2004 Diplomarbeit in theoretischer Festkörperphysik bei Milena Grifoni
Thema: "Correlated Transport in Carbon Nanotubes"
Abschluss als Diplom-Physiker

seit 12/2004 Promotionsstudium im Graduiertenkolleg 638 "Nichtlinearität und
Nichtgleichgewicht in kondensierter Materie" an der Uni Regensburg
Thema der Dissertation:
"Spectrum and transport properties of interacting carbon nanotubes"
Auslandsstudium
10/2001 – 07/2002 an der ETH in Zürich mit den Schwerpunkten Glaziologie und Rechnergestützte
Physik, DAAD Stipendium
Wehrdienst
09/1997 – 06/1998 Grundwehrdienst
Schulbildung
09/1984 – 07/1988 Grundschule Rain am Lech
09/1988 – 06/1997 Gymnasium Donauwörth
Regensburg, 21.11.2007




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Contents
Introduction 1
Part I
Electronic properties of interacting single wall carbon nanotubes 7
Chapter 1. Electronic properties of noninteracting SWNTs 9
1.1. Band structure of graphene 9
1.2. Morphology of SWNTs 14
1.3. Zone folding 15
1.4. Low energy description of noninteracting armchair SWNTs 17
Chapter 2. Interacting electrons in metallic SWNTs 25
2.1. What is special about interacting SWNTs 27
2.2. Coulomb interaction in metallic SWNTs 30
2.3. The relevant scattering processes 32
2.4. Interlude: The bosonization formalism 37
2.5. Bosonization and diagonalization of the interacting SWNT Hamiltonian 40
2.6. The spectrum of metallic SWNTs 50
2.7. Conclusions 57
Part II
Transport properties of single wall carbon nanotubes 59
Introduction 60
Chapter 3. Quantum Dots 63
3.1. Charge quantization and Coulomb blockade 64
Transport theory for weakly coupled quantum dots 67
3.2. Model Hamiltonian 67
3.3. Dynamics of the reduced density matrix 69
3.4. Current 75
Chapter 4. Metallic SWNT quantum dots with unpolarized leads 77
4.1. Electronic properties of metallic large size SWNTs 77
4.2. Generalized master equation for unpolarized SWNT quantum dots 78
4.3. Excitation lines 86
4.4. Low Bias Regime 88
4.5. High bias regime 92
Chapter 5. Metallic SWNT quantum dots with polarized leads 99
iii CONTENTS
5.1. Experimental realization of SWNT spin valves 100
5.2. The model Hamiltonian 100
5.3. Generalized master equation for the SWNT spin valve 102
5.4. Coordinate transformations in spinor space 106
5.5. Linear regime 108
5.6. Nonlinear regime 114
5.7. Conclusions 117
Summary and outlook 119
Acknowledgements 123
Appendix A. Derivation of the bosonization identity 125
Appendix B. Bosonized form of the kinetic part of the Hamiltonian 129
Appendix C. Bogoliubov transformation 133
Appendix D. Modeling the interaction potential 137
Appendix E. Calculation of the matrix elements 139
Appendix F. Regularization of 145
Appendix G. Invariance of the transport calculation under unitary
transformations 149
Appendix H. The matrix elements of the electron operators 151
Bibliography 155