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Register a new userTheory of superconductivity of carbon nanotubes and graphene
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We present a new mechanism of carbon nanotube superconductivity that originates from edge states which are specific to graphene. Using on-site and boundary deformation potentials which do not cause bulk superconductivity, we obtain an appreciable transition temperature for the edge state. As a consequence, a metallic zigzag carbon nanotube having open boundaries can be regarded as a natural superconductor/normal metal/superconductor junction system, in which superconducting states are developed locally at both ends of the nanotube and a normal metal exists in the middle. In this case, a signal of the edge state superconductivity appears as the Josephson current which is sensitive to the length of a nanotube and the position of the Fermi energy. Such a dependence distinguishs edge state superconductivity from bulk superconductivity.
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The electron-phonon matrix element for edge states of carbon nanotubes and graphene at zigzag edges is calculated for obtaining renormalized energy dispersion of the edge states. Self-energy correction by electron-phonon interaction contributes to the energy dispersion of edge states whose energy bandwidth is similar to phonon energy. Since the energy-uncertainty of the edge state is larger than temperature, we conclude that the single-particle picture of the edge state in not appropriate when the electron-phonon interaction is taken into account. The longitudinal acoustic phonon mode contributes to the matrix element through the on-site deformation potential because the wavefunction of the edge state has an amplitude only on one of the two sublattices. The on-site deformation potentials for the longitudinal and in-plane tangential optical phonon modes are enhanced at the boundary. The results of local density of states are compared with the recent experimental data of scanning tunneling spectroscopy.
A single-wall carbon nanotube possesses two different types of plasmons specified by the wavenumbers in the azimuthal and axial directions. The azimuthal plasmon that is caused by interband transitions has been studied, while the effect of charge doping is unknown. In this paper, we show that when nanotubes are heavily doped, intraband transitions cause the azimuthal plasmons to appear as a plasmon resonance in the near-infrared region of the absorption spectra, which is absent for light doping due to the screening effect. The axial plasmons that are inherent in the cylindrical waveguide structures of nanotubes, account for the absorption peak of the metallic nanotube observed in the terahertz region. The excitation of axial (azimuthal) plasmons requires a linearly polarized light parallel (perpendicular) to the tubes axis.
We review recent studies of coherent phonons (CPs) corresponding to the radial breathing mode (RBM) and G-mode in single-wall carbon nanotubes (SWCNTs) and graphene. Because of the bandgap-diameter relationship, RBM-CPs cause bandgap oscillations in SWCNTs, modulating interband transitions at terahertz frequencies. Interband resonances enhance CP signals, allowing for chirality determination. Using pulse shaping, one can selectively excite speci!c-chirality SWCNTs within an ensemble. G-mode CPs exhibit temperature-dependent dephasing via interaction with RBM phonons. Our microscopic theory derives a driven oscillator equation with a density-dependent driving term, which correctly predicts CP trends within and between (2n+m) families. We also find that the diameter can initially increase or decrease. Finally, we theoretically study the radial breathing like mode in graphene nanoribbons. For excitation near the absorption edge, the driving term is much larger for zigzag nanoribbons. We also explain how the armchair nanoribbon width changes in response to laser excitation.
Allotropes of carbon, including one-dimensional carbon nanotubes and two-dimensional graphene sheets, continue to draw attention as promising platforms for probing the physics of electrons in lower dimensions. Recent research has shown that the electronic properties of graphene multilayers are exquisitely sensitive to the relative orientation between sheets, and in the bilayer case exhibit strong electronic correlations when close to a magic twist angle. Here, we investigate the electronic properties of a carbon nanotube deposited on a graphene sheet by deriving a low-energy theory that accounts both for rotations and rigid displacements of the nanotube with respect to the underlying graphene layer. We show that this heterostructure is described by a translationally invariant, a periodic or a quasi-periodic Hamiltonian, depending on the orientation and the chirality of the nanotube. Furthermore, we find that, even for a vanishing twist angle, rigid displacements of a nanotube with respect to a graphene substrate can alter its electronic structure qualitatively. Our results identify a promising new direction for strong correlation physics in low dimensions.
We propose a way of making graphene superconductive by putting on it small superconductive islands which cover a tiny fraction of graphene area. We show that the critical temperature, T_c, can reach several Kelvins at the experimentally accessible range of parameters. At low temperatures, T<<T_c, and zero magnetic field, the density of states is characterized by a small gap E_g<T_c resulting from the collective proximity effect. Transverse magnetic field H_g(T) E_g is expected to destroy the spectral gap driving graphene layer to a kind of a superconductive glass state. Melting of the glass state into a metal occurs at a higher field H_{g2}(T).
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