Imaging Electron Wave Functions of Quantized Energy Levels in Carbon Nanotubes

Carbon nanotubes provide a unique system to study one-dimensional quantization phenomena. Scanning tunneling microscopy is used to observe the electronic wave functions that correspond to quantized energy levels in short metallic carbon nanotubes. Discrete electron waves are apparent from periodic oscillations in the differential conductance as a function of the position along the tube axis, with a period that differs from that of the atomic lattice. Wave functions can be observed for several electron states at adjacent discrete energies. The measured wavelengths are in good agreement with the calculated Fermi wavelength for armchair nanotubes.Comment: 11 pages, 4 figures in seperate PDF fil

``X-Ray Edge'' Singularities in Nanotubes and Quantum Wires with Multiple Subbands

Band theory predicts an inverse square root van Hove singularity in the tunneling density of states at the minimum energy of an unoccupied subband in a one-dimensional quantum wire. With interactions, an orthogonality catastrophe analogous to the x-ray edge effect for core levels in a metal strongly reduces this singularity by a power B of the energy above threshold, with B approximately 0.3 for typical carbon nanotubes. Despite the anomalous tunneling characteristic, good quasiparticles corresponding to the unoccupied subband states do exist.Comment: 4 page

Fermi level quantum numbers and secondary gap of conducting carbon nanotubes

For the single-wall carbon nanotubes conducting in the simplest tight binding model, the complete set of line group symmetry based quantum numbers for the bands crossing at Fermi level are given. Besides linear (k), helical (k'} and angular momenta, emerging from roto-translational symmetries, the parities of U axis and (in the zig-zag and armchair cases only) mirror planes appear in the assignation. The helical and angular momentum quantum numbers of the crossing bands never vanishes, what supports proposed chirality of currents. Except for the armchair tubes, the crossing bands have the same quantum numbers and, according to the non-crossing rule, a secondary gap arises, as it is shown by the accurate tight-binding calculation. In the armchair case the different vertical mirror parity of the crossing bands provides substantial conductivity, though kF is slightly decreased.Comment: 6 pages, 2 figure

Effects of magnetic field and disorder on electronic properties of Carbon Nanotubes

Electronic properties of metallic and semiconducting carbon nanotubes are investigated in presence of magnetic field perpendicular to the CN-axis, and disorder introduced through energy site randomness. The magnetic field field is shown to induce a metal-insulator transition (MIT) in absence of disorder, and surprisingly disorder does not affect significantly the MIT. These results may find confirmation through tunneling experimentsComment: 4 pages, 6 figures. Phys. Rev. B (in press

Subband population in a single-wall carbon nanotube diode

We observe current rectification in a molecular diode consisting of a semiconducting single-wall carbon nanotube and an impurity. One half of the nanotube has no impurity, and it has a current-voltage (I-V) charcteristic of a typical semiconducting nanotube. The other half of the nanotube has the impurity on it, and its I-V characteristic is that of a diode. Current in the nanotube diode is carried by holes transported through the molecule's one-dimensional subbands. At 77 Kelvin we observe a step-wise increase in the current through the diode as a function of gate voltage, showing that we can control the number of occupied one-dimensional subbands through electrostatic doping.Comment: to appear in Physical Review Letters. 4 pages & 3 figure

Quantum states and specific heat of low-density He gas adsorbed within the carbon nanotube interstitial channels: Band structure effects and potential dependence

We calculate the energy-band structure of a He atom trapped within the interstitial channel between close-packed nanotubes within a bundle and its influence on the specific heat of the adsorbed gas. A robust prediction of our calculations is that the contribution of the low-density adsorbed gas to the specific heat of the nanotube material shows pronounced nonmonotonic variations with temperature. These variations are shown to be closely related to the band gaps in the adsorbate density of states

Electronic structure and dynamics of optically excited single-wall carbon nanotubes

We have studied the electronic structure and charge-carrier dynamics of individual single-wall carbon nanotubes (SWNTs) and nanotube ropes using optical and electron-spectroscopic techniques. The electronic structure of semiconducting SWNTs in the band-gap region is analyzed using near-infrared absorption spectroscopy. A semi-empirical expression for $E_{11}^{\rm S}$ transition energies, based on tight-binding calculations is found to give striking agreement with experimental data. Time-resolved PL from dispersed SWNT-micelles shows a decay with a time constant of about 15 ps. Using time-resolved photoemission we also find that the electron-phonon ({\it e-ph}) coupling in metallic tubes is characterized by a very small {\it e-ph} mass-enhancement of 0.0004. Ultrafast electron-electron scattering of photo-excited carriers in nanotube ropes is finally found to lead to internal thermalization of the electronic system within about 200 fs.Comment: 10 pages, 10 figures, submitted to Applied Physics

van der Waals interaction in nanotube bundles : consequences on vibrational modes

We have developed a pair-potential approach for the evaluation of van der Waals interaction between carbon nanotubes in bundles. Starting from a continuum model, we show that the intertube modes range from $5 cm^{-1}$ to $60 cm^{-1}$. Using a non-orthogonal tight-binding approximation for describing the covalent intra-tube bonding in addition, we confirme a slight chiral dependance of the breathing mode frequency and we found that this breathing mode frequency increase by $\sim$ 10 % if the nanotube lie inside a bundle as compared to the isolated tube.Comment: 5 pages, 2 figure

Bandgap Change of Carbon Nanotubes: Effect of Small Tensile and Torsional Strain

We use a simple picture based on the $\pi$ electron approximation to study the bandgap variation of carbon nanotubes with uniaxial and torsional strain. We find (i) that the magnitude of slope of bandgap versus strain has an almost universal behaviour that depends on the chiral angle, (ii) that the sign of slope depends on the value of $(n-m) \bmod 3$ and (iii) a novel change in sign of the slope of bandgap versus uniaxial strain arising from a change in the value of the quantum number corresponding to the minimum bandgap. Four orbital calculations are also presented to show that the $\pi$ orbital results are valid.Comment: Revised. Method explained in detai

Analysis of quantum conductance of carbon nanotube junctions by the effective mass approximation

The electron transport through the nanotube junctions which connect the different metallic nanotubes by a pair of a pentagonal defect and a heptagonal defect is investigated by Landauer's formula and the effective mass approximation. From our previous calculations based on the tight binding model, it has been known that the conductance is determined almost only by two parameters,i.e., the energy in the unit of the onset energy of more than two channels and the ratio of the radii of the two nanotubes. The conductance is calculated again by the effective mass theory in this paper and a simple analytical form of the conductance is obtained considering a special boundary conditions of the envelop wavefunctions. The two scaling parameters appear naturally in this treatment. The results by this formula coincide fairly well with those of the tight binding model. The physical origin of the scaling law is clarified by this approach.Comment: RevTe