Interplay of bandstructure and quantum interference in multiwall carbon nanotubes [Elektronische Ressource] / vorgelegt von Bernhard Stojetz

Sujets

• Physik

Informations

• Publié par: universitat_regensburg
• Publié le: 01 janvier 2005
• Nombre de lectures: 9
• Langue: English
• Poids de l'ouvrage: 5 Mo

Extrait

Interplay of Bandstructure and
Quantum Interference in
Multiwall Carbon Nanotubes
Dissertation
zur Erlangung des Doktorgrades der Naturwissenschaften
(Dr. rer. nat.)
der naturwissenschaftlichen Fakult¨at II – Physik
der Universit¨at Regensburg
vorgelegt von
Bernhard Stojetz
aus Vilshofen
Dezember 2004Die Arbeit wurde von Prof. Dr. Ch. Strunk angeleitet.
Das Promotionsgesuch wurde am 22. 12. 2004 eingereicht.
Das Kolloquium fand am 10. 2. 2005 statt.
Pru¨fungsausschuss: Vorsitzender: Prof. Dr. Ch. Back
1. Gutachter: Prof. Dr. Ch. Strunk
2. Gutachter: Prof. Dr. M. Grifoni
weiterer Pru¨fer: Prof. Dr. M. MaierI found it hard
Its hard to find
Oh well, whatever,
Nevermind
Kurt CobainContents
1 Introduction 1
2 Electronic Bandstructure of Carbon Nanotubes 5
2.1 Graphene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Tight Binding Method for Graphene . . . . . . . . . . . . . . . . . . 6
2.3 Zone Folding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.4 Density of States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.5 Magnetic Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.5.1 Parallel Field: Aharonov-Bohm effect . . . . . . . . . . . . . . 12
2.5.2 Perpendicular Field: Quantum Oscillations . . . . . . . . . . . 12
3 Transport Properties of Carbon Nanotubes 13
3.1 Quantum Interference . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.1.1 Weak Localization . . . . . . . . . . . . . . . . . . . . . . . . 13
3.1.2 Aharonov-Bohm effect . . . . . . . . . . . . . . . . . . . . . . 15
3.1.3 Universal Conductance Fluctuations . . . . . . . . . . . . . . 16
3.2 Coulomb Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.2.1 Nyquist Dephasing . . . . . . . . . . . . . . . . . . . . . . . . 17
3.2.2 Zero Bias Anomalies . . . . . . . . . . . . . . . . . . . . . . . 18
3.2.3 Coulomb Blockade . . . . . . . . . . . . . . . . . . . . . . . . 20
4 Sample Preparation and Measurement Setup 23
4.1 Nanotube Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.2 Device Fabrication by Random Dispersion . . . . . . . . . . . . . . . 23
4.3 Device Fabrication by Electrostatic Trapping . . . . . . . . . . . . . . 24
4.4 Measurement Circuitry and Cryostats . . . . . . . . . . . . . . . . . . 26ii Contents
5 Motivation and Preliminary Measurements 29
5.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
5.2 Preliminary Measurements . . . . . . . . . . . . . . . . . . . . . . . . 30
6 Bandstructure Effects in Multiwall Carbon Nanotubes 35
6.1 Gate Efficiency and Transport Regimes . . . . . . . . . . . . . . . . . 35
6.2 Irregular Coulomb Blockade . . . . . . . . . . . . . . . . . . . . . . . 37
6.3 Magnetoconductance . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
6.4 Relation to Electronic Bandstructure . . . . . . . . . . . . . . . . . . 41
6.5 Contribution of Weak Localization . . . . . . . . . . . . . . . . . . . 43
6.6 Dephasing Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . 44
6.7 Elastic Mean Free Path . . . . . . . . . . . . . . . . . . . . . . . . . . 47
6.8 Zero Bias Anomalies . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
6.9 Critical Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
7 Aharonov-Bohm Effect and Landau Levels 55
7.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
7.2 Sample Characterization and Doping State . . . . . . . . . . . . . . . 57
7.3 Conductance Oscillations in a Parallel Field . . . . . . . . . . . . . . 59
7.4 Field Dependence of the Magnetic Bandstructure . . . . . . . . . . . 61
7.5 Density of States vs. Measured Conductance . . . . . . . . . . . . . . 63
7.6 Contribution of Quantum Interference . . . . . . . . . . . . . . . . . 66
7.7 Conductance Variations in a Perpendicular Field . . . . . . . . . . . . 69
7.8 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
8 Summary and Outlook 75
Bibliography 77Chapter 1
Introduction
Metallic wires as used in standard microelectronic devices nowadays allow to be
fabricated with widths and heights of several tens of nanometers. Despite these
small dimensions, their electronic transport properties can be understood to a large
extent in terms of classical diffusive motion.
Recently, metalliccontactscouldbeattachedalsotosinglemolecules[1]. Incontrast
to diffusive metal wires, molecules are well defined systems, both with respect to
their atomic structure and their electronic conduction properties: all molecules of
a given structure are identical on atomic scale, and electronic transport through a
single molecule is determined solely by it’s overall, coherent wavefunction.
Since their discovery in 1991, multiwall carbon nanotubes (MWNTs) take an in-
termediate position between the world of identical molecules and disordered solids.
[2]. On one hand, they can be considered as a set of seamlessly rolled up graphene
sheets (referred to as ’shells’), which are put one into another. With this respect,
they have to be classified as perfect molecules.
On the other hand, their typical length of several micrometers and diameters up to
50 nm exceed by far the dimensions of most other molecular systems. Their large
size allows the occurrence of imperfections of the atomic structure, without turning
the molecule into a completely different one, what would be the case for smaller
systems. Such imperfections are for example introduced by atomic displacements
and adsorbates on the outermost nanotube shell. In this sense MWNTs represent
a disordered molecular system, in which electronic transport is influenced both by
the molecular wavefunctions and the imperfections of the atomic structure.
In the last years, large effort has been made in order to clarify and characterize the
transport properties of MWNTs (for an overview see Ref. [3]). One main reason for
that is the fundamental interest in electronic transport on a molecular scale, which
ismosteasily accessed withMWNTs. Furthermore, alsoavariety ofmicroelectronic
12 Chapter 1. Introduction
devices bear the perspective of being assembled by nanotubes, either completely or
by using the tubes as connection wires [4, 5].
Despite the large efforts, the electronic properties of MWNTs could not be clarified
to a satisfying extent. For example, the interaction of adjacent nanotube shells is
not clear, since in the measurement only the outermost shell is contacted. Here, the
question arises, to which extent electric current is carried also by the inner shells
[6].
Thus,themaingoalofthisthesisistoshedsomemorelightontransportinMWNTs.
Especially the question of a possible interplay between the molecular structure and
the disorder is addressed, as well as the resulting consequences for the electronic
transport.
Experimentally, the main investigation tool in this work are conductance measure-
ments on single MWNTs at low temperatures and high magnetic fields. A very
efficient gate is used for a considerable variation of the nanotube’s Fermi level. The
results are compared to numerical tight-binding calculations, as performed by our
collaborators S. Roche and F. Triozon [7].
The thesis is organized as follows: A review of the electronic bandstructure within
the tight binding approach is given in Chapter 2. The tight-binding method repre-
sents a very efficient and successful tool for a basic understanding of the conduction
properties of carbon nanotubes. Furthermore, it allows a comparatively easy inclu-
sion of magnetic fields and disorder.
Subsequently, several mesoscopic transporteffects aredescribed, which areobserved
in MWNTs (Chapter 3). Here only those effects are considered, which are crucial
for the interpretation of the measurements in this work.
After an overview on the sample-fabrication methods and the measurement setup
(Chapter 4), the first experimental results are presented (Chapter 5). These results
serve as a motivation for more extensive investigations, which are presented and
discussed in the following sections.
In Chapter 6, the intricate interplay between the electronic bandstructure and the
disorder of the system is addressed. This is done by means of magnetoconductance
measurements, wheretheFermilevelinthenanotubeischangedwithinalargerange
by means of a highly efficient backgate. The latter offers the possibility of tuning
the Fermi level across several nanotube subbands, which in turn strongly affects the
conduction properties.
Finally, Chapter 7 is concerned with the conduction properties of MWNTs with
large diameters of about 30 nm. If for such tubes the magnetic field is aligned with
the tube axis, it’s cylindrical shape is predicted to cause a variety of effects in the
conductance. All of these effects are closely related to the fundamental Aharonov-
Bohm effect [8], which predicts conductance oscillations of a ring-shaped conductor3
as a function of the magnetic flux through the surface enclosed by the ring. The
predictions are investigated again by magnetotransport measurements.
Fornanotubesoflargediameterinperpendicularfields,thereexistseveralcontradic-
tory theoretical models, predicting the occurence of Landau levels and conductance
oscillations. Thus, in the last section o