Nano-Physics and Bio-Electronics (eBook)

A New Odyssey

T. Chakraborty, F. Peeters, U. Sivan (Autoren)

eBook Download: PDF | EPUB

2002 | 1. Auflage
362 Seiten
Elsevier Science (Verlag)
978-0-08-053724-5 (ISBN)

Infos

This book is a collection of some of the invited talks presented at the international meeting held at the Max Planck Institut fuer Physik Komplexer Systeme, Dresden, Germany during August 6-30, 2001, on the rapidly developing field of nanoscale science in science and bio-electronics Semiconductor physics has experienced unprecedented developments over the second half of the twentieth century. The exponential growth in microelectronic processing power and the size of dynamic memorie has been achieved by significant downscaling of the minimum feature size. Smaller feature sizes result in increased functional density, faster speed, and lower costs. In this process one is reaching the limits where quantum effects and fluctuations are beginning to play an important role.
This book reflects the achievements of the present times and future directions of research on nanoscopic dimensions.

Inhalt

Front Cover 1
Nano-Physics & Bio-Electronics: A New Odyssey
Copyright Page 5
Contents 8
Preface 6
Chapter 1. Electronic states and transport in carbon nanotubes 10
Chapter 2. Vertical diatomic artificial quantum dot molecules 74
Chapter 3. Optical spectroscopy of self-assembled quantum dots 94
Chapter 4. Generation of single photons using semiconductor quantum dots 120
Chapter 5. Spin, spin-orbit, and electron-electron interactions in mesoscopic systems 156
Chapter 6. Kondo effect in quantum dots with an even number of electrons 196
Chapter 7. From single dots to interacting arrays 222
Chapter 8. Quantum dots in a strong magnetic field: Quasi-classical consideration 246
Chapter 9. Micro-Hall-magnetometry 266
Chapter 10. Stochastic optimization methods for biomolecular structure prediction 290
Chapter 11. Electrical transport through a molecular nanojunction 312
Chapter 12. Single metalloproteins at work: Towards a single-protein transistor 332
Chapter 13. Towards synthetic evolution of nanostructures 350
Subject index 362

Textauszug

Chapter 1

Electronic states and transport in carbon nanotubes

Tsuneya Ando [e-mail]    Institute for Solid State Physics, University of Tokyo 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8581, Japan

Abstract

A brief review is given of electronic and transport properties of carbon nanotubes mainly from a theoretical point of view. The topics include a giant Aharonov-Bohm effect on the band gap and a Landau-level formation in magnetic fields, optical absorption spectra, and exciton effects. Transport properties are also discussed including absence of backward scattering except for scatterers with a potential range smaller than the lattice constant, a conductance quantization in the presence of short-range and strong scatterers such as lattice vacancies, and transport across junctions between nanotubes with different diameters. A continuum model for phonons in the long-wavelength limit and the resistivity determined by phonon scattering is reviewed as well.

1. Introduction   2

2. Electronic states   4

2.1. Two-dimensional graphite   4

2.2. Nanotubes   10

3. Optical properties   19

3.1. Dynamical conductivity   19

3.2. Parallel polarization   21

3.3. Perpendicular polarization   22

3.4. Exciton   25

3.5. Experiments   28

4. Transport properties   29

4.1. Effective Hamiltonian   29

4.2. Absence of backward scattering   30

4.3. Berry’s phase   33

4.4. Experiments   38

4.5. Lattice vacancies – Strong and short-range scatterers   38

5. Junctions and topological defects   43

5.1. Five- and seven-membered rings   43

5.2. Boundary conditions   44

5.3. Conductance   48

6. Phonons and electron-phonon interaction   51

6.1. Long wavelength phonons   51

6.2. Electron-phonon interaction   54

6.3. Resistivity   57

7. Summary   58

Acknowledgements   58

References   59

1 Introduction

Graphite needles called carbon nanotubes (CNs) were discovered recently [1,2] and have been a subject of an extensive study. A CN is a few concentric tubes of two-dimensional (2D) graphite consisting of carbon-atom hexagons arranged in a helical fashion about the axis. The diameter of CNs is usually between 20 and 300 Å and their length can exceed 1 μm. The distance of adjacent sheets or walls is larger than the distance between nearest neighbor atoms in a graphite sheet and therefore electronic properties of CNs are dominated by those of a single layer CN. Single-wall nanotubes are produced in a form of ropes [3,4]. The purpose of this article is to give a brief review of recent theoretical study on electronic and transport properties of carbon nanotubes.

Figure 1 shows a transmission micrograph image of multi-wall nanotubes and Fig. 2 a computer graphic image of a single-wall nanotube. Carbon nanotubes can be either a metal or semiconductor, depending on their diameters and helical arrangement. The condition whether a CN is metallic or semiconducting can be obtained based on the band structure of a 2D graphite sheet and periodic boundary conditions along the circumference direction. This result was first predicted by means of a tight-binding model ignoring the effect of the tube curvature [5–14].

Fig. 1 Some examples of transmission micrograph images of carbon nanotubes [1]. The diameter is 67, 55, and 65 Å from left to right.

Fig. 2 A computer graphic image of a single-wall armchair nanotube.

These properties can be well reproduced in a k·p method or an effective-mass approximation [15]. In fact, the effective-mass scheme has been used successfully in the study of wide varieties of electronic properties of CN. Some of such examples are magnetic properties [16] including the Aharonov-Bohm effect on the band gap [15], optical absorption spectra [17,18], exciton effects [19], lattice instabilities in the absence [20] and presence of a magnetic field [21,22], and magnetic properties of ensembles of nanotubes [23].

Transport properties of CNs are interesting because of their unique topological structure. There have been some reports on experimental study of transport in CN bundles [24] and ropes [25,26]. Transport measurements became possible for a single multi-wall nanotube [27–31] and a single single-wall nanotube [32–36]. Single-wall nanotubes usually exhibit large charging effects presumably due to nonideal contacts [37–41].

In this article we shall mainly discuss electronic states and transport properties of nanotubes obtained theoretically in the k·p method combined with a tight-binding model. It is worth mentioning that several papers giving general reviews of electronic properties of nanotubes were published already [42–47].

In Sect. 2, electronic states are discussed first in a nearest-neighbor tight-binding model. Then, the effective mass equation is introduced and the band structure is discussed with a special emphasis on Aharonov-Bohm effects and formation of Landau levels in magnetic fields. In Sect. 3, optical absorption is discussed in the effective-mass scheme and the nanotube is shown to behave differently in light polarization parallel or perpendicular to the axis. The importance of exciton effects is emphasized and some related experiments are discussed.

In Sect. 4, effects of impurity scattering are discussed and the total absence of backward scattering is pointed out except for scatterers with a potential range smaller than the lattice constant. Further, the conductance quantization in the presence of lattice vacancies, i.e., strong and short-range scatterers, is also discussed. In Sect. 5, the transport across a junction of nanotubes with different diameters through a pair of topological defects such as five- and seven-member rings is discussed. In Sect. 6, a continuum model for phonons in the long-wavelength limit is introduced and effective Hamiltonian describing electron-phonon interaction is derived. A short summary is given in Sect. 7.

2 Electronic states

2.1 Two-dimensional graphite

The structure of 2D graphite sheet is shown in Fig. 3. We have the primitive translation vectors a = a(1, 0) and =a(−(1/2),3/2), and the vectors connecting between nearest neighbor carbon atoms →1=a(0,1/3), →2=a(−1/2,−1/23), and →3=a(1/2,−1/23). Note that a·b = – a2/2.

Fig. 3 (a) The lattice structure of a 2D graphite sheet and various quantities. a|=|b|=a. (b) The reciprocal lattice vectors and the first Brillouin zone.

The primitive reciprocal lattice vectors a* and b* are given by *=(2π/a)(1,1/3) and *=(2π/a)(0,2/3). The K and K’ points are given as =(2π/a)(1/3,1/3) and K′ = (2π/a)(2/3, 0), respectively. We then have the relations, (iK⋅τ→1)=ω, (iK⋅τ→2)=ω−1, (iK⋅τ→3)=1, (iK′⋅τ→1)=1, (iK′⋅τ→2)=ω−1, and (iK′⋅τ→3)=ω, with ω = exp(2πi/3).

In a tight-binding model, the wave function is written...

Produkt-Details

• Erscheint lt. Verlag: 16.4.2002
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Festkörperphysik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Quantenphysik
• Themenwelt: Technik ► Elektrotechnik / Energietechnik
• Themenwelt: Technik ► Maschinenbau
• Themenwelt: Technik ► Umwelttechnik / Biotechnologie
• ISBN-10: 0-08-053724-3 / 0080537243
• ISBN-13: 978-0-08-053724-5 / 9780080537245