Narrow-gap Carbon Nanotubes Research Articles

Anomalous screening in narrow-gap carbon nanotubes

The screening of Coulomb interaction controls many-body physics in carbon nanotubes, as it tunes the range and strength of the force that acts on charge carriers and binds electron-hole pairs into excitons. In doped tubes, the effective Coulomb interaction drives the competition between Luttinger liquid and Wigner crystal, whereas in undoped narrow-gap tubes it dictates the Mott or excitonic nature of the correlated insulator observed at low temperature. Here, by computing the dielectric function of selected narrow- and zero-gap tubes from first principles, we show that the standard effective-mass model of screening systematically underestimates the interaction strength at long wavelength, hence missing the binding of low-energy excitons. The reason is that the model critically lacks the full three-dimensional topology of the tube, being adapted from graphene theory. As ab inito calculations are limited to small tubes, we develop a two-band model dielectric function based on the plane-wave expansion of Bloch states and the exact truncated Coulomb cutoff technique. We demonstrate that our -- computationally cheap -- approach provides the correct screening for narrow-gap tubes of any size and chirality. A striking result is that the screened interaction remains long-ranged even in gapless tubes, as an effect of the microscopic local fields generated by the electrons moving on the curved tube surface. As an application, we show that the effective electron-electron force that is felt at distances relevant to quantum transport experiments is super Coulombic.

Interband transitions in narrow-gap carbon nanotubes and graphene nanoribbons

We use the robust nearest-neighbor tight-binding approximation to study the same footing interband dipole transitions in narrow-bandgap carbon nanotubes (CNTs) and graphene nanoribbons (GNRs). It is demonstrated that curvature effects in metallic single-walled CNTs and edge effects in gapless GNRs not only open up bandgaps, which typically correspond to THz frequencies, but also result in a giant enhancement of the probability of optical transitions across these gaps. Moreover, the matrix element of the velocity operator for these transitions has a universal value (equal to the Fermi velocity in graphene) when the photon energy coincides with the bandgap energy. Upon increasing the excitation energy, the transition matrix element first rapidly decreases (for photon energies remaining in the THz range but exceeding two bandgap energies, it is reduced by three orders of magnitude), and thereafter it starts to increase proportionally to the photon frequency. A similar effect occurs in an armchair CNT with a bandgap opened and controlled by a magnetic field applied along the nanotube axis. There is a direct correspondence between armchair GNRs and single-walled zigzag CNTs. The described sharp photon-energy dependence of the transition matrix element, together with the van Hove singularity at the bandgap edge of the considered quasi-one-dimensional systems, makes them promising candidates for active elements of coherent THz radiation emitters. The effect of Pauli blocking of low-energy interband transitions caused by residual doping can be suppressed by creating a population inversion using high-frequency (optical) excitation.

Terahertz transitions in narrow-gap carbon nanotubes and graphene nanoribbons

We show that the curvature effects in quasi-metallic carbon nanotubes and edge effects in narrow-gap graphene nanoribbons not only open band gaps in the THz range but also result in giant enhancement of the transition probabilities across these gaps. This makes these nanostructures perspective candidates for sources and detectors of THz radiation.

Crossovers from excitons to plasmons in narrow-gap carbon nanotubes

Plasmons and excitons, bound states of electrons and holes, are collective charge excitations in solids. In this study, we numerically show that in most metallic carbon nanotubes, which are called narrow-gap carbon nanotubes, excitons cross over to plasmons as the wave vector increases. This indicates that resonance with the excitons changes to that with the plasmons by changing the nanotube length, which can explain the origin of observed peaks in the terahertz or far-infrared region in the optical absorption spectra of metallic carbon nanotubes. In the crossovers from excitons to plasmons, a depolarization effect on the many-body wave functions of the plasmons and excitons is clarified.

Pair states in one-dimensional Dirac systems

Analytic solutions of the quantum relativistic two-body problem are obtained for an interaction potential modeled as a one-dimensional smooth square well. Both stationary and moving pairs are considered and the limit of the {\delta}-function interaction is studied in depth. Our result can be utilized for understanding excitonic states in narrow-gap carbon nanotubes. We also show the existence of bound states within the gap for a pair of particles of the same charge.

Excitons in narrow-gap carbon nanotubes

We calculate the exciton binding energy in single-walled carbon nanotubes with narrow band gaps, accounting for the quasi-relativistic dispersion of electrons and holes. Exact analytical solutions of the quantum relativistic two-body problem are obtain for several limiting cases. We show that the binding energy scales with the band gap, and conclude on the basis of the data available for semiconductor nanotubes that there is no transition to an excitonic insulator in quasi-metallic nanotubes and that their THz applications are feasible.

Spin-orbit effects in carbon-nanotube double quantum dots

We study the energy spectrum of symmetric double quantum dots in narrow-gap carbon nanotubes with one and two electrostatically confined electrons in the presence of spin-orbit and Coulomb interactions. Compared to GaAs quantum dots, the spectrum exhibits a much richer structure because of the spin-orbit interaction that couples the electron's isospin to its real spin through two independent coupling constants. In a single dot, both constants combine to split the spectrum into two Kramers doublets, while the antisymmetric constant solely controls the difference in the tunneling rates of the Kramers doublets between the dots. For the two-electron regime, the detailed structure of the spin-orbit split energy spectrum is investigated as a function of detuning between the quantum dots in a 22-dimensional Hilbert space within the framework of a single-longitudinal-mode model. We find a competing effect of the tunneling and Coulomb interaction. The former favors a left-right symmetric two-particle ground state, while in the regime where the Coulomb interaction dominates over tunneling, a left-right antisymmetric ground state is found. As a result, ground states on both sides of the $(11)$-$(02)$ degeneracy point may possess opposite left-right symmetry, and the electron dynamics when tuning the system from one side of the $(11)$-$(02)$ degeneracy point to the other is controlled by three selection rules (in spin, isospin, and left-right symmetry). We discuss implications for the spin-dephasing and Pauli blockade experiments.

Competition between intertube interactions and external electric fields on a pair of narrow-gap carbon nanotubes

A uniform transverse electric field is applied to a pair of narrow-gap carbon nanotubes with intertube interactions, and the electronic structures at low energy are studied within the tight-binding model. Unlike a single nanotube, the band structures of an aligned pair vary with not only the strength of the electric field but its direction. When the transverse field is applied along the plane containing both tube axes of the pair, the low energy bands are found to have significant changes with the field strength higher than 0.01 V / A ˚ , only a tenth of the order for a single tube. A small energy gap could be opened by the intertube interactions, nevertheless, the hybridization of atomic wave functions between tubes is suppressed by increasing the electric field. By contrast, a field perpendicular to the plane of tube axes alters the band structures at the same level as for a single tube, and the electronic states between tubes are still strongly coupled.

Electronic excitations and deexcitations in narrow-gap carbon nanotubes

The band structures play an important role in excitations and deexcitations innarrow-gap carbon nanotubes. The temperature-induced free carriers exist inthe low energy states and cause the low-frequency intraband and interband e–hexcitations. Such kinds of excitations could be the effective decay channels forthe excited states of the lowest conduction and valence bands. The Coulombdecay rates are sensitive to the changes in radius, wavevector, temperature anddeexcitation mechanisms. Those with interband decay increase as the radius increases,while the others with intraband decay exhibit the opposite behavior except at lowtemperature. The decay rates are dominated by the intraband deexcitations. For theconduction-band states, the decay rates quickly rise and then decline with increasingtemperature, and a linear increase appears as the temperature further increases. Thewavevector dependence, on the other hand, is weak. As to the valence-band states,the decay rates drop rapidly when the initial states deviate from the band-edgestate, and they increase as the temperature becomes higher. Moreover, the decayrates of narrow-gap carbon nanotubes contrast sharply with those of metallic andmoderate-gap ones. For example, they are the largest at room temperature. Thefemtosecond time-resolved spectroscopies could be utilized to verify the predictedresults.

Magnetization of carbon nanotubes

For narrow-gap carbon nanotubes, the curvature effect due to the misorientation of 2 p z orbitals dominates over electronic structures and thus magnetic properties. It significantly changes magnetization and magnetic susceptibility, and creates special structures in them. There exists a critical field direction in changing magnetism. The critical angle strongly depends on the chiral angle, the nanotube radius, and the temperature. One-dimensional carbon nanotubes are quite different from zero-dimensional carbon tori, such as in terms of special structures in magnetization, the strength of the magnetic response, and the critical angle.

Electronic and Optical Properties of Narrow-Gap Carbon Nanotubes

The sp 3 tight-binding model is used to calculate electronic structures of narrow-gap carbon nanotubes. The curvature effects cause a small energy gap, a one-dimensional parabolic bands, and a shift in the Fermi wave vector. The energy gap is described by the approximate relation E g ≃ 5|V ppπ |b 2 cos(3θ)/16R 2 d . It is almost identical to the first-principles result. Due to the curvature effects, the optical spectra exhibit single-particle absorption peaks and a plasmon structure. They are consistent with the experimental results, the absorption peaks in the optical conductivity and the plasmon edge in the reflectance spectrum, thereby verifing the relation between Eg and (R d ,θ).