Ultrashort optical pulses in carbon nanotubes and graphene with periodic impurities

The dispersion law for electrons has been derived by the Green’s function method using the Anderson periodic model, which has been proposed to describe the electron subsystem in carbon nanotubes and graphene with impurities. The combined dynamics of electrons and an electromagnetic field has been considered in the low-temperature limit, and the effective equation describing the propagation of ultrashort optical pulses has been obtained. The solutions to this equation as functions of the parameters of the problem have been presented.     

Electromagnetic solitons in carbon nanotubes at low temperatures

The propagation of a variable electromagnetic field in arrays of “zigzag” carbon nanotubes at low temperatures is considered. The electronic system of carbon nanotubes is analyzed using the Hamilton formalism with ignoring interactions with the phonon subsystem because the electromagnetic field pulse is extremely short. An effective equation for the amplitude of the electromagnetic field vector-potential was obtained. Solutions-analogues of solitons were revealed; these solutions corresponded to solitons for the cosine electronic subsystem dispersion law. The dependences of the nonlinear solutions obtained on problem parameters were analyzed.     

Interaction of few-cycle optical pulses in nonmetallic carbon nanotubes

Collision of two few-cycle optical pulses propagating in the medium of nonmetallic carbon nanotubes is described using joint solution of the Maxwell equations for the electromagnetic field and the Boltzmann equation for the electron subsystem.     

Collision of extremely short optical pulses in semiconductor carbon nanotubes

The interaction of extremely short optical pulses in semiconductor carbon nanotubes is discussed. An equation is derived for the dynamics of the electromagnetic field in a system of semiconductor carbon nanotubes at low temperatures, whose solutions are analogs to the solitons of the sine-Gordon equation. The behavior of extremely short optical pulses in semiconductor carbon nanotubes on collision is analyzed.     

Helical modes in carbon nanotubes generated by strong electric fields

Helical modes, conducting opposite spins in opposite directions, are shown to exist in metallic armchair nanotubes in an all-electric setup. This is a consequence of the interplay between spin-orbit interaction and strong electric fields. The helical regime can also be obtained in chiral metallic nanotubes by applying an additional magnetic field. In particular, it is possible to obtain helical modes at one of the two Dirac points only, while the other one remains gapped. Starting from a tight-binding model we derive the effective low-energy Hamiltonian and the resulting spectrum.     

Direct space time-characterization of the electric fields of ultrashort optical pulses

We report the complete spatiotemporal characterization of ultrashort light pulses by use of a self-referencing device based on shearing interferometry in the space and frequency domains. The apparatus combines a spatially resolved spectral shearing interferometer with a spectrally resolved spatial shearing interferometer. The electric field as a function of one transverse spatial coordinate and time is obtained from a single experimental trace by means of a direct and fast algebraic phase reconstruction algorithm. The method has been tested in several common laboratory situations.     

Extremely short two-dimensional optical pulses in an array of carbon nanotubes in the presence of a constant electric field

The interaction between the electromagnetic fields of extremely short two-dimensional optical pulses propagating in an array of zigzag-type carbon nanotubes and an external constant electric field is investigated. The evolution of the investigated system’s electromagnetic field is described by Maxwell’s equations.     

Ultimately short optical pulses in carbon nanotubes in dispersive nonmagnetic dielectric media

We consider Maxwell’s equations for an electromagnetic field propagating in carbon nanotubes placed in dispersive nonmagnetic dielectric media. An effective equation having the form of an analog of the classical sine-Gordon equation was obtained and analyzed numerically. The dependence of the pulse on the type of carbon nanotubes, initial pulse amplitude, and dispersion constants of the medium was revealed.     

Contacting single bundles of carbon nanotubes with alternating electric fields

Single bundles of carbon nanotubes have been selectively deposited from suspensions onto sub-micron electrodes with alternating electric fields. We show that it is possible to control the trapping of a single bundle by the use of Ag as electrode material which, unlike Au, strongly interacts with the carboxyl functionalized carbon nanotubes. Excellent alignment of the bundles between Au or Ag electrodes occurs at frequencies above 1 kHz, with superior contacts being formed with Ag electrodes. Received: 22 May 2002 / Accepted: 21 June 2002 / Published online: 28 October 2002 RID="*" ID="*"Corresponding author. Fax: +49-7247/82-6368, E-mail: ralph.krupke@int.fzk.de     

Dislocation dynamics in multiwalled carbon nanotubes at high temperatures

Dislocation dynamics dictate the mechanical behavior of materials. Dislocations in periodic crystalline materials have been well documented. On the contrary, dislocations in cylindrical carbon nanotubes, particularly in multiwalled carbon nanotubes (MWCNTs), remain almost unexplored. Here we report that a room temperature 1/2<0001> sessile dislocation in a MWCNT becomes highly mobile, as characterized by its glide, climb, and the glide-climb interactions, at temperatures of about 2000 degrees C. The dislocation glide leads to the cross-linking of different shells; dislocation climb creates nanocracks; and the interaction of two 1/2<0001> dislocations creates kinks. We found that dislocation loops act as channels for mass transport. These dislocation dynamics are drastically different from that in conventional periodic crystalline materials due to the cylindrical, highly anisotropic structures of MWCNTs.     

Exciton absorption in silicon at low electric fields

This paper reports for the first time high-resolution transverse EA spectra of Si in low electric fields at liquid-helium temperature. The data conclusively demonstrate that the observed effect is related to the discrete levels of the Wannier exciton and that for the n = 1 level it can be accounted for both qualitatively and quantitatively by means of a Stark approximation where field-induced broadening is phenomenologicaly introduced to allow for weak tunneling-like contributions. The exciton energy levels determined here are in good agreement with the results of wavelength-modulation spectroscopy and all the other parameters of the absorption process are consistent with previous absolute absorption experiments.     

Photoluminescence and electric conductivity in germanium at low temperatures

We have studied the exciton and electron-hole droplet (EHD) luminescence in optically irradiated germanium at temperatures between 1.8 and 4.2 K in the presence of an electric field. Simultaneously the electric conductivity was measured. The sample material was high-purity Ge (N _A –N _D =7·10¹⁰ cm^–3) andp-doped Ge withN _A =3·10¹⁴ cm^–3. In the high-purity Ge samples the exciton and EHD-luminescence intensity decreased nearly linearly as a function of the applied electric current, whereas the dependence upon the electric field was more complicated. Our results could be explained by a model in which carrier annihilation at the contacts following a rapid drifting process plays a dominant role (drift model). In thep-doped Ge samples the current-dependence of the luminescence intensity was qualitatively similar. However, here the drift model is not strictly valid any more because of the reduced carrier mobility and the generation of additional carriers by impurity impact ionization. During variation of the electric field, the luminescence intensity and the electric current show hysteresis. Here the capture of the moving carriers by the EHD appears to play an important role, in addition to the EHD-nucleation process.     

Magnetic properties of multiwall carbon nanotubes and astralenes in strong electric fields

The force interaction between anode and cathode in the process of field-emission current extraction from cathodes based on carbon nanoclusters—carbon nanotubes and astralenes—has been investigated. The measured forces are linear functions of the field-emission current and significantly exceed the forces conditioned by the electrostatic nature of interaction. The observed effect is explained within the framework of a model that suggests the formation of magnetic nanoclusters in the cathode and the emission of polarized electrons.     

Kink formation and motion in carbon nanotubes at high temperatures

We report that kink motion is a universal plastic deformation mode in all carbon nanotubes when being tensile loaded at high temperatures. The kink motion, observed inside a high-resolution transmission electron microscope, is reminiscent of dislocation motion in crystalline materials: namely, it dissociates and multiplies. The kinks are nucleated from vacancy creation and aggregation, and propagate in either a longitudinal or a spiral path along the nanotube walls. The kink motion is related to dislocation glide and climb influenced by external stress and high temperatures in carbon nanotubes.     

Mechanism for superelongation of carbon nanotubes at high temperatures

We report molecular dynamics simulations of the recently discovered superelongation of carbon nanotubes (CNTs) at high temperatures. The nearly simultaneous activation and wide distribution of a large number of defects near the elastic limit play a key role in impeding the formation of localized predominant instability and facilitating large tensile elongation. It suggests new and more complex mechanisms for CNT superelongation in contrast with the previously proposed ideal defect glide and pseudoclimb. Defect interaction and evolution generate multistage necking and kinking and new types of larger defects that dominate the tensile elongation and breaking process. Intricate interplay between CNT sizes and defect nucleation and motion determine the overall deformation pattern.     

Electric resistivity of multi-walled carbon nanotubes at high temperatures

The electric resistivity of a clean multi-walled carbon nanotube (MWNT) mat sample was studied at temperatures T between 300 and 1900 K. We found that the resistivity ρ decreases monotonously with increasing temperature without showing any sign of turn up. Our results can be well fitted with a power law of T^−α within the framework of one dimensional Luttinger liquid theory with α = 0.13 or with a simple thermally activated inter shell hopping model.     

Linear conductance of multiwalled carbon nanotubes at high temperatures

We have studied the electrical conductance of gas-desorbed multiwalled carbon nanotubes (MWNTs) at high temperatures, and found a peculiar linear temperature dependence of conductance over a wide temperature range from 100 to 800 K. We interpret this phenomenon by using a thermal activation picture of conduction channels below the gap in the vicinity of the Dirac points. The result also indicates a very short and temperature-independent electron mean free path in our MWNTs, and provides a way to determine the number of residual conduction channels in the MWNTs.     

Three-dimensional few-cycle optical pulses in an array of carbon nanotubes inside a magnetic field

The behavior of three-dimensional few-cycle optical pulses, propagating in a system of carbon nanotubes inside an external magnetic field applied parallel to the nanotube axes and perpendicular to the direction of pulse propagation, is studied. The evolution of the electromagnetic field is classically derived using Maxwell’s equations.