Metallic Zigzag Carbon Nanotubes Research Articles

Possibility of the magnitude of the chiral vector having an effect on the terahertz radiation generation by hot electrons in zigzag carbon nanotubes driven by DC-AC fields

The possibility that the magnitude of a chiral or circumferential vector (Chv) influences the generation of terahertz radiations (T-rays) by hot electrons in zigzag carbon nanotubes (z-CNTs) driven by direct current (DC) and alternating current (AC) fields is taken into consideration. The study conducted a semiclassical theoretical analysis by using the Boltzmann kinetic equation to determine current density in relation to high AC field frequency (ω) and z-CNT circumference (|Chv|) when hot electrons were present. A numerical analysis was performed by varying the magnitude of the circumference of the tube at a fixed temperature and the strong hot electron injection rate at a predetermined value. When the circumference of the semiconducting zigzag carbon nanotubes (sz-CNTs) is increased, the current density's lowest and highest peaks are also enhanced (i.e., large amplitudes). This increases positive differential conductivity (PDC), necessitating enhanced domain suppression for higher potential generation of T-rays. In contrast, it was observed that reducing the tube's circumference in metallic zigzag carbon nanotubes (mz-CNTs) resulted in an increase in both the lowest and highest peaks of current density, which enhanced the PDC. These findings imply that larger circumferential sz-CNTs and smaller circumferential mz-CNTs may be more suitable candidates for a higher potential generation of T-rays with applications pertinent to modern science and technology.

A metal-semiconductor-metal transform appeared in the metallic single-walled carbon nanotubes, controlled by the combined effect of magnetic field and uniaxial strain

As known to us, the metallic zigzag tubes will open a band gap by applying the magnetic field or uniaxial strain. The exciton states of the nearest band to Fermi level (M00) in the metallic carbon nanotubes are calculated by a tight-binding model, under the combined effect of the magnetic field and uniaxial strain. It is found that the excitation energy and binding energy of the metallic zigzag carbon nanotube (24, 0) have the similar variation tendency, which are split into M00+ and M00− excitons by the applied magnetic field and strain. When the uniaxial strain is applied, for M00+, it increases with increasing magnetic field, while for M00−, it decreases. However, it is interesting to find that as the magnetic field increases, the M00− exciton will decrease to be zero and a metal-semiconductor-metal change will appear, which is expected to be confirmed by experiments. The obtained result provides some useful information for future THz applications by controlling the magnetic field and uniaxial strain.

Effect of electron-RBM phonon interaction on conductance of metallic zigzag carbon nanotubes

We use the energy analysis as a perturbative method to study the effect of electron-radial breathing mode (RBM) phonon interaction on the electrical conductance of long metallic zigzag carbon nanotubes (CNTs). The band structure of zigzag CNTs is calculated by exerting zone-folding method on relations derived by using the nearest neighbor approximation of tight-binding expression for the π bands of graphene. The small hollow cylinder model, with two different approximations, is used to obtain the RBM frequency in our calculation. As the result, we have calculated the effects of electron−RBM phonon interaction on the conductance of zigzag CNTs. It has been observed that current is a step−like function of bias voltage due to the absorption or emission by electron injection in the system. Moreover, the dependence of the conductance to the temperature in low bias and high bias voltages has been studied. In this paper, we propose a simple and useful method for phonon spectroscopy. Also, since RBM mode determines the geometry and structure of CNT, this approach can be used for characterization of CNTs.

First-principles study on electron transport through BN-dimer embedded zigzag carbon nanotubes

First-principles calculations are performed for electron transmission through a metallic zigzag carbon nanotube with substitutional BN dimers parallel to the nanotube axis. The transmission coefficient is calculated in the energy range (around the charge neutrality point) in which there exist two degenerate subbands for each spin. Wave functions in the circumferential direction of one of the degenerate subbands can be chosen so as to have nodes at the position of a carbon dimer parallel to the nanotube axis. It is shown that the transmission probability of an incident wave with such wave-function nodes depends crucially on positions of BN dimers relative to the nodes. By placing each of dimers at one of the nodes, the transmission probability is substantially enhanced and is well described by the Born approximation in spite of spatially extended scattering potential due to ionized B and N. This suggests that the arrangement in the circumferential direction of various impurities influences transport through metallic zigzag carbon nanotubes.

Electronic properties of disordered zigzag carbon nanotubes

We study the density of states of zigzag carbon nanotube (CNT) doped with both Boron and nitrogen atoms as donor and acceptor impurities, respectively. The effect of scattering of the electrons on the electronic spectrum of the system can be obtained via adding random on-site energy term to the tight binding model Hamiltonian which describes the clean system. Green's function approach has been implemented to find the behavior of electronic density. Due to Boron (Nitrogen) doping, Fermi surface tends to the valence (conduction) band of semiconductor CNT so that the energy gap width reduces. Furthermore the density of states of disordered metallic zigzag CNTs includes a peak near the Fermi energy.

Electronic features induced by Stone–Wales defects in zigzag and chiral carbon nanotubes

It has been recently shown [P. Partovi-Azar, A. Namiranian, J. Phys.: Condens. Matter, 24 (2012) 035301.] that Stone–Wales (SW) defects induce different electronic features when they are formed with different angels with respect to the axis of armchair carbon nanotubes. However, the electronic features introduced by SW defects in metallic zigzag and chiral carbon nanotubes is less considered in the literature. In this paper, by means of density functional calculations, we study the electronic effects induced by SW defects in metallic zigzag and chiral tubes. We inspect how these effects change with defect orientation and concentration. We show that two and three distinctive orientations of SW defects, respectively in the case of zigzag and chiral tubes, unlike those in armchair ones, behave the same and both introduce a semiconducting gap and an electron-rich region around the defects. For zigzag tubes, the longitudinal defects open wider band gaps than circumferential ones. The value of the gaps in zigzag and chiral tubes are attributed to the degree of deformation caused by the defects.

High frequency conductivity in carbon nanotubes

We report on theoretical analysis of high frequency conductivity in carbon nanotubes. Using the kinetic equation with constant relaxation time, an analytical expression for the complex conductivity is obtained. The real part of the complex conductivity is initially negative at zero frequency and become more negative with increasing frequency, until it reaches a resonance minimum at ω ∼ ωB for metallic zigzag CNs and ω < ωB for armchair CNs. This resonance enhancement is indicative for terahertz gain without the formation of current instabilities induced by negative dc conductivity. We noted that due to the high density of states of conduction electrons in metallic zigzag carbon nanotubes and the specific dispersion law inherent in hexagonal crystalline structure result in a uniquely high frequency conductivity than the corresponding values for metallic armchair carbon nanotubes. We suggest that this phenomenon can be used to suppress current instabilities that are normally associated with a negative dc differential conductivity.

Electrical conductivity of zigzag carbon nanotubes including Holstein polarons

Electrical conductivity of metallic zigzag carbon nanotube is investigated in the context of Holstein model using Green’s function approach. The effects of radius of carbon nanotube, temperature and electron phonon coupling strength on the electrical conductivity of zigzag nanotubes are investigated. It is seen that electrical conductivity increases as a function of temperature at low temperature and gets a maximum value then decays at high temperature. Moreover electrical conductivity increases when CNT diameter increases and decreases with electron phonon interaction strength.

Study of third-harmonic generation in zigzag carbon nanotubes using the Green function approach

We study the frequency behavior of third-order nonlinear optical harmonic of metallic and semiconductor zigzag carbon nanotubes. The tight binding model Hamiltonian is considered for electrons on the rolled honeycomb lattice. Based on the relation between nonlinear optical susceptibility and four current correlation function, the third harmonic can be obtained using Green’s function. The effect of the radius of the nanotube on the susceptibility has been investigated. Furthermore, the role of temperature on the behavior of third-order harmonic is studied. The contribution of interband transitions due to the quantum aspects has been brought within the nonlinear response theory as a generalization of the Kubo formalism.

Polaron effects on the thermal conductivity of zigzag carbon nanotubes

Thermal conductivity of metallic zigzag carbon nanotube is investigated in the context of Holstein model. Green's function approach is implemented to calculate the electronic contribution of thermal conductivity as a function of radius of carbon nanotube, temperature and electron phonon coupling strength. Our results show that electronic thermal conductivity increases as a function of temperature at low temperature and gets a maximum value then decays at high temperature. Also the effect of radius of both metallic and semiconductor zigzag carbon nanotube on the thermal conductivity is studied. Our results show thermal conductivity increases when CNT diameter increases and decreases with electron phonon interaction strength.

Theoretical phonon dispersion of armchair and metallic zigzag carbon nanotubes beyond the adiabatic approximation

AbstractThe dynamic corrections to the phonon dispersion of armchair and metallic zigzag carbon nanotubes are studied systematically within a non‐orthogonal tight‐binding model. These corrections were found to be important in the vicinity of the Kohn anomaly of the phonon dispersion at two points of the Brillouin zone. The first point is the zone‐centre and the dynamic corrections are large for the longitudinal optical phonons, which give rise to the G−‐band in the Raman spectra. The obtained frequencies of these phonons for a large number of metallic nanotubes are in good agreement with previous estimations and available experimental data. The second point is inside the zone for armchair nanotubes and at the zone centre for zigzag nanotubes. In this case, the dynamic effects are also studied and discussed in view of their importance for modelling of double‐resonance scattering processes.

Electronic properties of multi-defected zigzag carbon nanotubes

Electronic properties of multi-defected zigzag single-walled carbon nanotubes are investigated by use of the tight-binding Green’s function method. The Stone-Wales defects and the vacancies are considered. We find that the conductance sensitively depends on the realistic defect configurations for the metallic zigzag carbon nanotubes. Interestingly, the electronic transport properties of the nanotubes with three vacancies can be considered as the sum effect of two double-vacancies, while those with Stone-Wales defects can not. The electron interference along the longitudinal axis and the transport blocking are observed, which may be useful for understanding the electron transport behavior of carbon nanotube in experiments.

Chirality Effects in Atomic Vacancy-Limited Transport in Metallic Carbon Nanotubes

We use first principles density functional theory combined with nonequilibrium Green's function technique to investigate the electronic and transport properties of metallic armchair and zigzag carbon nanotubes (CNTs) with different kinds of multivacancy defects. While the existence of a small band gap in pristine zigzag (12,0) CNTs lowers its conductance compared to pristine armchair (7,7) CNTs, transport properties in the presence of multi (hexa)-vacancy are superior in the former nanostructure, that is more sensitive to defect size and topology than the latter. In addition, in the zigzag structures hexavacancy nanotubes have higher conductance than divancancy nanotubes, which is due to the presence of midgap states that reduce the transmission gap and enhance the conductance.

Conductance through a single impurity in the metallic zigzag carbon nanotube

We investigate the conductance through a single impurity in the metallic zigzag carbon nanotube and find that it sensitively depends on the impurity strength and the bias voltage. The interplay between the current-carrying scattering states and the evanescent modes lead to rich phenomena including resonant backward scattering, perfect tunneling, and charge accumulations. In addition to the Friedel sum rule, we also find an exact relation between the conductance and the scattering phase. Finally, relevance of our findings to the realistic transport in carbon nanotubes is discussed.

Impurity-induced conductance anomaly in zigzag carbon nanotubes

Impurities in carbon nanotubes give rise to rich physics due to the honeycomb lattice structure. We concentrate on the conductance through a point-like defect in metallic zigzag carbon nanotube via the Landauer-Büttiker approach. At low bias, the conductance is suppressed due to the presence of an additional impurity state existing only on one of the sublattices. In consequence, the suppression is exactly half of the perfect conductance without impurity. Furthermore, there exists a transport resonance at larger bias where the perfect conductance is recovered as if the impurity were absent. Implications of these conductance anomalies are elaborated and experimental detections in realistic carbon nanotubes are also discussed.

Phase diagrams of the metallic zigzag carbon nanotube

We investigate a metallic zigzag carbon nanotube by means of a Hubbard model, which includes both on-site and nearest-neighbor interactions. Assuming weak interactions, a renormalization group analysis of the equivalent two-leg ladder followed by bosonization and refermionization results in a Gross-Neveu model with an enlarged symmetry relative to the original Hamiltonian. For the undoped case the symmetry of the Gross-Neveu model is SO(8), but for the doped case the particle-hole symmetry is broken and the symmetry reduces to SO(6). Four ground-state phases are found in the undoped carbon nanotube with repulsive interactions, a $d$-wave Mott insulator, an $s$-wave Mott insulator, a $p$-density wave, and a charge density wave. The doped case has two ground-state phases, a $d$-wave superconductor and a phase where a $p$ density wave and a charge density wave coexist. We also explore the global phase diagram with a general interaction profile and find several additional states, including a chiral current phase where current flows around the nanotube along the zigzag bonds.

Aharanov-Bohm effect for the edge states of zigzag carbon nanotubes

Two delocalized states of metallic zigzag carbon nanotubes near the Dirac point can be localized by the Aharanov-Bohm magnetic field around $20\phantom{\rule{0.3em}{0ex}}\mathrm{T}$. The dependence of the localization on the length and diameter of the nanotubes shows that the localization-delocalization transition can be observed for $2\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ diameter tube. The mechanism of the localization is explained in terms of the deformation-induced gauge field, which shows a topological nature of the localization. The transition from the delocalized states to the localized states can be observed by scanning tunneling microscopy and spectroscopy. A similarity between the transition and the spin Hall effect is discussed.

Interaction induced dimerization in zigzag single wall carbon nanotubes

We derive a low-energy effective model of metallic zigzag carbon nanotubes at half filling. We show that there are three important features characterizing the low-energy properties of these systems: the long-range Coulomb interaction, umklapp scattering, and an explicit dimerization generated by interactions. The ratio of the dimerization induced gap and the Mott gap induced by the umklapp interactions is dependent on the radius of the nanotube and can drive the system upon increasing dimerization strength from a Haldane spin-liquid phase through a quantum phase transition with $\mathrm{SU}{(2)}_{1}$ quantum symmetry to a dimerized phase. We consider the physical properties of the phases on either side of this transition, which should be relevant for realistic nanotubes.

Physical mechanism of transport blocking in metallic zigzag carbon nanotubes

Physical mechanism of transport blocking in metallic zigzag carbon nanotubes

Theory of Superconductivity of Carbon Nanotubes and Graphene

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.