``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

Random walks on finite lattice tubes

Exact results are obtained for random walks on finite lattice tubes with a single source and absorbing lattice sites at the ends. Explicit formulae are derived for the absorption probabilities at the ends and for the expectations that a random walk will visit a particular lattice site before being absorbed. Results are obtained for lattice tubes of arbitrary size and each of the regular lattice types; square, triangular and honeycomb. The results include an adjustable parameter to model the effects of strain, such as surface curvature, on the surface diffusion. Results for the triangular lattice tubes and the honeycomb lattice tubes model diffusion of adatoms on single walled zig-zag carbon nano-tubes with open ends.Comment: 22 pages, 4 figure

Van Hove Singularities in disordered multichannel quantum wires and nanotubes

We present a theory for the van Hove singularity (VHS) in the tunneling density of states (TDOS) of disordered multichannel quantum wires, in particular multi-wall carbon nanotubes. We assume close-by gates which screen off electron-electron interactions. Diagrammatic perturbation theory within a non-crossing approximation yields analytical expressions governing the disorder-induced broadening and shift of VHS's as new subbands are opened. This problem is nontrivial because the (lowest-order) Born approximation breaks down close to the VHS. Interestingly, compared to the bulk case, the boundary TDOS shows drastically altered VHS, even in the clean limit.Comment: 4 pages, 2 figures, accepted with revisions in PR

Charge Screening Effect in Metallic Carbon Nanotubes

Charge screening effect in metallic carbon nanotubes is investigated in a model including the one-dimensional long-range Coulomb interaction. It is pointed out that an external charge which is being fixed spatially is screened by internal electrons so that the resulting object becomes electrically neutral. We found that the screening length is given by about the diameter of a nanotube.Comment: 11 pages, 6 figure

Superconductivity in carbon nanotube ropes

We investigate the conditions in which superconductivity may develop in ropes of carbon nanotubes. It is shown that the interaction among a large number of metallic nanotubes favors the appearance of a metallic phase in the ropes, intermediate between respective phases with spin-density-wave and superconducting correlations. These arise in samples with about 100 metallic nanotubes or more, where the long-range Coulomb interaction is very effectively reduced and it may be overcome by the attractive interaction from the exchange of optical phonons within each nanotube. We estimate that the probability for the tunneling of Cooper pairs between neighboring nanotubes is much higher than that for single electrons in a disordered rope. The effect of pair hopping is therefore what establishes the intertube coherence, and the tunneling amplitude of the Cooper pairs dictates the scale of the transition to the superconducting state.Comment: 12 page

Vacuum structure of Toroidal Carbon Nanotubes

Low energy excitations in carbon nanotubes can be described by an effective field theory of two components spinor. It is pointed out that the chiral anomaly in 1+1 dimensions should be observed in a metallic toroidal carbon nanotube on a planar geometry with varying magnetic field. We propose an experimental setup for studying this quantum effect. We also analyze the vacuum structure of the metallic toroidal carbon nanotube including the Coulomb interactions and discuss some effects of external charges on the vacuum.Comment: 10 pages, 11 figure

Thermoelectric effects of an Aharonov-Bohm interferometer with an embedded quantum dot in the Kondo regime

Thermoelectric effects are studied in an Aharonov-Bohm (AB) interferometer with an embedded quantum dot in the Kondo regime. The AB flux-dependent transmission probability has an asymmetrical shape arising from the Fano interference between the direct tunneling path and the Kondo-resonant tunneling path through a quantum dot. The sign and magnitude of thermopower can be modulated by the AB flux and the direct tunneling amplitude. In addition, the thermopower is anomalously enhanced by the Kondo correlation in the quantum dot near the Kondo temperature ($T_K$). The Kondo correlation in the quantum dot also leads to crossover behavior in diagonal transport coefficients as a function of temperature. The amplitude of an AB oscillation in electric and thermal conductances is small at temperatures far above $T_K$, but becomes enhanced as the system is cooled below $T_K$. The AB oscillation is strong in the thermopower and Lorenz number within the crossover region near the Kondo temperature.Comment: 16 pages, 10 figure

Aharonov-Bohm spectral features and coherence lengths in carbon nanotubes

The electronic properties of carbon nanotubes are investigated in the presence of disorder and a magnetic field parallel or perpendicular to the nanotube axis. In the parallel field geometry, the $\phi_{0}(=hc/e)$-periodic metal-insulator transition (MIT) induced in metallic or semiconducting nanotubes is shown to be related to a chirality-dependent shifting of the energy of the van Hove singularities (VHSs). The effect of disorder on this magnetic field-related mechanism is considered with a discussion of mean free paths, localization lengths and magnetic dephasing rate in the context of recent experiments.Comment: 22 pages, 6 Postscript figures. submitted to Phys. Rev.

W=0 Pairing in (N,N)(N,N) Carbon Nanotubes away from Half Filling

We use the Hubbard Hamiltonian $H$ on the honeycomb lattice to represent the valence bands of carbon single-wall $(N,N)$ nanotubes. A detailed symmetry analysis shows that the model allows W=0 pairs which we define as two-body singlet eigenstates of $H$ with vanishing on-site repulsion. By means of a non-perturbative canonical transformation we calculate the effective interaction between the electrons of a W=0 pair added to the interacting ground state. We show that the dressed W=0 pair is a bound state for resonable parameter values away from half filling. Exact diagonalization results for the (1,1) nanotube confirm the expectations. For $(N,N)$ nanotubes of length $l$, the binding energy of the pair depends strongly on the filling and decreases towards a small but nonzero value as $l \to \infty$. We observe the existence of an optimal doping when the number of electrons per C atom is in the range 1.2$\div$1.3, and the binding energy is of the order of 0.1 $\div$ 1 meV.Comment: 16 pages, 6 figure

Aggregate structure of hydroxyproline-rich glycoprotein (HRGP) and HRGP assisted dispersion of carbon nanotubes

Hydroxyproline-rich glycoproteins (HRGP) comprise a super-family of extracellular structural glycoproteins whose precise roles in plant cell wall assembly and functioning remain to be elucidated. However, their extended structure and repetitive block co-polymer character of HRGPs may mediate their self-assembly as wall scaffolds by like-with-like alignment of their hydrophobic peptide and hydrophilic glycopeptide modules. Intermolecular crosslinking further stabilizes the scaffold. Thus the design of HRGP-based scaffolds may have practical applications in bionanotechnology and medicine. As a first step, we have used single-molecule or single-aggregate atomic force microscopy (AFM) to visualize the structure of YK20, an amphiphilic HRGP comprised entirely of 20 tandem repeats of: Ser-Hyp4-Ser-Hyp-Ser-Hyp4-Tyr-Tyr-Tyr-Lys. YK20 formed tightly aggregated coils at low ionic strength, but networks of entangled chains with a porosity of ~0.5–3 μm at higher ionic strength. As a second step we have begun to design HRGP-carbon nanotube composites. Single-walled carbon nanotubes (SWNTs) can be considered as seamless cylinders rolled up from graphene sheets. These unique all-carbon structures have extraordinary aromatic and hydrophobic properties and form aggregated bundles due to strong inter-tube van der Waals interactions. Sonicating aggregated SWNT bundles with aqueous YK20 solubilized them presumably by interaction with the repetitive, hydrophobic, Tyr-rich peptide modules of YK20 with retention of the extended polyproline-II character. This may allow YK20 to form extended structures that could potentially be used as scaffolds for site-directed assembly of nanomaterials