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ScienceWeek
MATERIALS SCIENCE: ELECTRON-HOLE SYMMETRY IN CARBON NANOTUBES
The following points are made by P. Jarillo-Herrero et al (Nature 2004 429:389):
1) Optical and electronic phenomena in solids arise from the behavior of electrons and holes (unoccupied states in a filled electron sea). Electron-hole symmetry can often be invoked as a simplifying description, which states that electrons with energy above the Fermi sea behave the same as holes below the Fermi energy. In semiconductors, however, electron-hole symmetry is generally absent, because the energy-band structure of the conduction band differs from the valence band(1).
2) Carbon nanotubes can be metallic or semiconducting depending on their chirality(3). Electron transport through individual nanotubes has been studied for both classes(2). Nanotubes of finite length have a discrete energy spectrum. Analogous to studies on semiconducting quantum dots, these discrete states can be filled with electrons, one by one, by means of a voltage applied to a nearby gate electrode(4). Whereas metallic nanotubes have shown clean quantum dot (QD) behavior(5), this has not been achieved in semiconducting single-wall nanotubes (SWNTs). Theory indicates that semiconducting tubes are more susceptible to disorder than metallic ones. Disorder typically divides a semiconducting nanotube into multiple islands, preventing the formation of a single, well-defined QD. Consequently, the electronic spectrum of semiconducting SWNTs has not been resolved before.
3) The authors report on measurements of the discrete, quantized-energy spectrum of electrons and holes in a semiconducting carbon nanotube(2). By applying a voltage to a gate electrode, an individual nanotube is filled controllably with a precise number of either electrons or holes, starting from one. The discrete excitation spectrum for a nanotube with N holes is strikingly similar to the corresponding spectrum for N electrons. This observation of near-perfect electron-hole symmetry(3) demonstrates that a semiconducting nanotube can be free of charged impurities, even in the limit of few electrons or holes. The authors furthermore find an anomalously small Zeeman spin splitting and an excitation spectrum indicating strong electron-electron interactions.
References (abridged):
1. Ashcroft, N. W. & Mermin, N. D. Solid State Physics (Saunders College, Orlando, 1976)
2. Dekker, C. Carbon nanotubes as molecular quantum wires. Phys. Today 52, 22-28 (1999)
3. Dresselhaus, M. S., Dresselhaus, G. & Eklund, P. C. Science of Fullerenes and Carbon Nanotubes (Academic, San Diego, 1996)
4. Kouwenhoven, L. P., Austing, D. G. & Tarucha, S. Few-electron quantum dots. Rep. Prog. Phys. 64, 701-736 (2001)
5. Tans, S. J. et al. Individual single-wall nanotubes as quantum wires. Nature 386, 474-477 (1997)
Nature http://www.nature.com/nature
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Related Material:
STRUCTURE AND PROPERTIES OF CARBON NANOTUBES
The following points are made by H.F. Bettinger et al (J. Am. Chem. Soc. 2001 123:12849):
1) Multiwall carbon nanotubes, a new tubular form of carbon, were discovered in 1991 by S. Iijima. Carbon nanotubes are comprised of a rolled graphite sheet ("graphene") and closed by fullerene-like caps. Depending on the way the graphene is rolled, different chiralities are possible, and are commonly distinguished by their chiral vector (n,m). The (n,n) tubes are called "armchair" and the (n.0) tubes are called "zigzag" nanotubes. A simple analysis imposing appropriate boundary conditions on the graphene band structure predicts that the armchair tubes are metallic (i.e., the band gap is zero due to band crossing), whereas the zigzag tubes are either semimetals or semiconductors, depending on the value of (n). The computations of the band structures using density functional theory (plane-wave pseudopotential local density approximation) indicate that these simple rules need to be refined, at least for narrow zigzag tubes. It was found by these calculations that the rehybridization of the carbon states due to the strong curvature of small tubes introduces low-lying conduction band states into the band gap of insulating tubes.
2) Whereas Iijima's multiwall carbon nanotubes consist of at least 2 concentric tubes, single wall carbon nanotubes are produced by laser vaporization of a metal-graphite (Co, Ni) target. These single-wall nanotubes are comprised of a single rolled graphene sheet, but have a tendency to form "ropes", i.e., bundles of single-wall nanotubes. The tubes produced by the laser-oven technique have very uniform diameters of approximately 1.38 +- 0.02 nanometers, according to x-ray diffraction, and an intertube distance of 0.315 nanometers in the ropes, similar to that in crystalline C(sub60). It has been concluded that the ropes are made up of (10,10) armchair single-wall nanotubes.
J. Am. Chem. Soc. http://pubs.acs.org/JACS
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Related Material:
CARBON NANOTUBES -- THE ROUTE TOWARD APPLICATIONS
The following points are made by R.H. Baughman et al (Science 2002 297:787):
1) There are two main types of carbon nanotubes that can have high structural perfection. Single-walled nanotubes (SWNTs) consist of a single graphite sheet seamlessly wrapped into a cylindrical tube. Multiwalled nanotubes (MWNTs) comprise an array of such nanotubes that are concentrically nested like rings of a tree trunk.
2) Despite structural similarity to a single sheet of graphite, which is a semiconductor with zero band gap, SWNTs may be either metallic or semiconducting, depending on the sheet direction about which the graphite sheet is rolled to form a nanotube cylinder. This direction in the graphite sheet plane and the nanotube diameter are obtainable from a pair of integers (n,m) that denote the nanotube type (1). Depending on the appearance of a belt of carbon bonds around the nanotube diameter, the nanotube is either of the armchair (n = m), zigzag (n = 0 or m = 0), or chiral (any other n and m) variety. All armchair SWNTs are metals; those with n - m = 3k, where k is a nonzero integer, are semiconductors with a tiny band gap; and all others are semiconductors with a band gap that inversely depends on the nanotube diameter (1).
3) The electronic properties of perfect MWNTs are rather similar to those of perfect SWNTs, because the coupling between the cylinders is weak in MWNTs. Because of the nearly one-dimensional electronic structure, electronic transport in metallic SWNTs and MWNTs occurs ballistically (i.e., without scattering) over long nanotube lengths, enabling them to carry high currents with essentially no heating (2,3). Phonons also propagate easily along the nanotube: The measured room temperature thermal conductivity for an individual MWNT (>3000 W/m.K) is greater than that of natural diamond and the basal plane of graphite (both 2000 W/m.K) (4). Superconductivity has also been observed, but only at low temperatures, with transition temperatures of about 0.55 K for 1.4-nm-diameter SWNTs (5) and ~5 K for 0.5-nm-diameter SWNTs grown in zeolites.
4) In summary: Many potential applications have been proposed for carbon nanotubes, including conductive and high-strength composites; energy storage and energy conversion devices; sensors; field emission displays and radiation sources; hydrogen storage media; and nanometer-sized semiconductor devices, probes, and interconnects. Some of these applications are now realized in products. Others are demonstrated in early to advanced devices, and one, hydrogen storage, is clouded by controversy. Nanotube cost, polydispersity in nanotube type, and limitations in processing and assembly methods are important barriers for some applications of single-walled nanotubes.
References (abridged):
1. S. G. Louie, Top. Appl. Phys. 80, 113 (2001)
2. W. Liang, et al., Nature 411, 665 (2001)
3. S. P. Frank et al., Science 280, 1744 (1998)
4. P. Kim et al, Phys. Rev. Lett. 87, 215502 (2001)
5. M. Kociak, et al., Phys. Rev. Lett. 86, 2416 (2001)
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