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Register a new userValley coupling in finite-length metallic single-wall carbon nanotubes
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Degeneracy of discrete energy levels of finite-length, metallic single-wall carbon nanotubes depends on type of nanotubes, boundary condition, length of nanotubes and spin-orbit interaction. Metal-1 nanotubes, in which two non-equivalent valleys in the Brillouin zone have different orbital angular momenta with respect to the tube axis, exhibits nearly fourfold degeneracy and small lift of the degeneracy by the spin-orbit interaction reflecting the decoupling of two valleys in the eigenfunctions. In metal-2 nanotubes, in which the two valleys have the same orbital angular momentum, vernier-scale-like spectra appear for boundaries of orthogonal-shaped edge or cap-termination reflecting the strong valley coupling and the asymmetric velocities of the Dirac states. Lift of the fourfold degeneracy by parity splitting overcomes the spin-orbit interaction in shorter nanotubes with a so-called minimal boundary. Slowly decaying evanescent modes appear in the energy gap induced by the curvature of nanotube surface. Effective one-dimensional model reveals the role of boundary on the valley coupling in the eigenfunctions.
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Using the real-time diagrammatic technique and taking into account both the sequential and cotunneling processes, we analyze the transport properties of single-wall metallic carbon nanotubes coupled to nonmagnetic and ferromagnetic leads in the full range of parameters. In particular, considering the two different shell filling schemes of the nanotubes, we discuss the behavior of the differential conductance, tunnel magnetoresistance and the shot noise. We show that in the Coulomb diamonds corresponding to even occupations, the shot noise becomes super-Poissonian due to bunching of fast tunneling processes resulting from the dynamical channel blockade, whereas in the other diamonds the noise is roughly Poissonian, in agreement with recent experiments. The tunnel magnetoresistance is very sensitive to the number of electrons in the nanotube and exhibits a distinctively different behavior depending on the shell filling sequence of the nanotube.
We present a simple technique which uses a self-aligned oxide etch to suspend individual single-wall carbon nanotubes between metallic electrodes. This enables one to compare the properties of a particular nanotube before and after suspension, as well as to study transport in suspended tubes. As an example of the utility of the technique, we study quantum dots in suspended tubes, finding that their capacitances are reduced owing to the removal of the dielectric substrate.
The dynamical conductance of electrically contacted single-walled carbon nanotubes is measured from dc to 10 GHz as a function of source-drain voltage in both the low-field and high-field limits. The ac conductance of the nanotube itself is found to be equal to the dc conductance over the frequency range studied for tubes in both the ballistic and diffusive limit. This clearly demonstrates that nanotubes can carry high-frequency currents at least as well as dc currents over a wide range of operating conditions. Although a detailed theoretical explanation is still lacking, we present a phenomenological model of the ac impedance of a carbon nanotube in the presence of scattering that is consistent with these results.
The possibility of low-energy surface plasmon amplification by optically excited excitons in small-diameter single wall carbon nanotubes is theoretically demonstrated. The nonradiative exciton-plasmon energy transfer causes the buildup of the macroscopic population numbers of coherent localized surface plasmons associated with high-intensity coherent local fields formed at nanoscale throughout the nanotube surface. These strong local fields can be used in a variety of new optoelectronic applications of carbon nanotubes, including near-field nonlinear-optical probing and sensing, optical switching, enhanced electromagnetic absorption, and materials nanoscale modification.
Semiconducting single-wall carbon nanotubes are classified into two types by means of orbital angular momentum of valley state, which is useful to study their low energy electronic properties in finite-length. The classification is given by an integer $d$, which is the greatest common divisor of two integers $n$ and $m$ specifying the chirality of nanotubes, by analyzing cutting lines. For the case that $d$ is equal to or greater than four, two lowest subbands from two valleys have different angular momenta with respect to the nanotube axis. Reflecting the decoupling of two valleys, discrete energy levels in finite-length nanotubes exhibit nearly fourfold degeneracy and its small lift by the spin-orbit interaction. For the case that $d$ is less than or equal to two, in which two lowest subbands from two valleys have the same angular momentum, discrete levels exhibit lift of fourfold degeneracy reflecting the coupling of two valleys. Especially, two valleys are strongly coupled when the chirality is close to the armchair chirality. An effective one-dimensional lattice model is derived by extracting states with relevant angular momentum, which reveals the valley coupling in the eigenstates. A bulk-edge correspondence, relationship between number of edge states and the winding number calculated in the corresponding bulk system, is analytically shown by using the argument principle, which enables us to estimate the number of edge states from the bulk property. The number of edge states depends not only on the chirality but also on the shape of boundary.
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