Nonlinear optical properties and phase-relaxation processes in single-walled carbon nanotubes

We have investigated third-order nonlinear optical properties of bundled and isolated semiconducting single-walled carbon nanotubes (SWNTs) by means of Z-scan method, pump-probe method, and two-beam time-resolved degenerate four-wave mixing (DFWM) method. The figures of merit Im χ⁽³⁾/α in both bundled and isolated SWNTs samples were found to be enhanced with increasing tube diameter. The measured Im χ⁽³⁾/α value in the bundled SWNTs was an order of magnitude smaller than that in the isolated SWNTs. Both population relaxation time T₁ and phase-relaxation time T₂ for bundled samples were smaller than those in the isolated samples. These experimental results can be explained by an increase in nonradiative recombination rate and phase-relaxation rate in the bundled sample. The phase-relaxation time T₂ is considered to have a significant role in the enhancement of Im χ⁽³⁾/α.     

Synthesis, integration, and electrical properties of individual single-walled carbon nanotubes

High-quality single-walled carbon nanotubes (SWNTs) are synthesized by chemical vapor deposition (CVD) of methane on silicon-dioxide substrates at controlled locations using patterned catalytic islands. With the synthesized nanotube chips, microfabrication techniques are used to reliably contact individual SWNTs and obtain low contact resistance. The combined chemical synthesis and microfabrication approaches enable systematic characterization of electron transport properties of a large number of individual SWNTs. Results of electrical properties of representative semiconducting and metallic SWNTs are presented. The lowest two-terminal resistance for individual metallic SWNTs (≈5 μm long) is ≈16.5 kΩ measured at 4.2 K. Received: 17 May 1999 / Accepted: 18 May 1999 / Published online: 14 July 1999     

Nonlinear conductivity of single-walled zigzag carbon nanotubes

The conductivity of the single-walled zigzag carbon nanotube system was studied in an alternating electric field with the intensity vector along the axis of nanotubes. The electronic carbon nanotube system was macroscopically considered in terms of the Boltzmann kinetic equation in the constant relaxation time approximation while omitting the interaction with the phonon subsystem. The nonlinear responses to the applied harmonic field were calculated and analyzed.     

Nonlinear size-dependent behaviour of single-walled carbon nanotubes

This paper examines the nonlinear size-dependent behaviour of single-walled carbon nanotubes (SWCNTs) based on the von-Karman nonlinearity and the nonlocal elasticity theory capable of predicting size effects. To this end, based on Hamilton’s principle in the framework of the nonlocal Euler–Bernoulli beam theory, the equation of motion and associated boundary conditions are derived. Then, with the aid of a high-dimensional Galerkin scheme, the nonlinear partial differential equation of motion of the SWCNT is recast into a reduced-order model. The dynamic response of the system is then investigated for two different types of excitation, namely primary and superharmonic excitations. Eventually, the effect of the slenderness ratio, forcing amplitude, and excitation frequency on the motion characteristics of the system is investigated.     

Intrinsic electrical properties of individual single-walled carbon nanotubes with small band gaps

Individual single-walled carbon nanotubes (SWNT) exhibiting small band gaps on the order of 10 meV are observed for the first time in electron transport measurements. Transport through the valence or conduction band of a small-gap semiconducting SWNT (SGS-SWNT) can be tuned by a nearby gate voltage. Intrinsic electrical properties of the Ohmically contacted SGS-SWNT are elucidated. An SGS-SWNT exhibits metal- or semiconductorlike characteristics depending on the Fermi level position in the band structure.     

Anisotropic optical properties of mechanically aligned single-walled carbon nanotubes in polymer

We have prepared aligned single-walled carbon nanotubes in polymer by mechanical stretching. The polarized absorption and Raman spectra of the aligned samples have been investigated. The optical transitions in nanotubes strongly depend on the angle between the polarization of the incident light and the nanotube axis: the absorbance measured at the peak energy shows a maximum at =0°, and they are suppressed at =90°. Raman spectra also show strong polarization dependence, which is mainly determined by the dependence of the oscillator strength of optical transitions in nanotubes. PACS 71.35.Cc; 78.30.-j; 78.67.Ch; 73.22.-f     

Multiphonon Raman scattering from individual single-walled carbon nanotubes

Combinations of up to 6 zone-edge and zone-center optical phonons are observed in the Raman spectra of individual single-walled carbon nanotubes (SWNTs). These multiphonon Raman modes exhibit distinct signatures of the one-dimensional nature of SWNTs and provide information on the phonon structure, exciton-phonon coupling, and excitonic transitions in nanotubes.     

Ultra-fast optical spectroscopy of micelle-suspended single-walled carbon nanotubes

We present results of wavelength-dependent ultra-fast pump–probe experiments on micelle-suspended single-walled carbon nanotubes. The linear absorption and photoluminescence spectra of the samples show a number of chirality-dependent peaks and, consequently, the pump–probe results sensitively depend on the wavelength. In the wavelength range corresponding to the second van Hove singularities (VHSs) we observe subpicosecond decays, as has been seen in previous pump–probe studies. We ascribe these ultra-fast decays to intraband carrier relaxation. On the other hand, in the wavelength range corresponding to the first VHSs, we observe two distinct regimes in ultra-fast carrier relaxation: fast (0.3–1.2 ps) and slow (5–20 ps). The slow component, which has not been observed previously, is resonantly enhanced whenever the pump photon energy resonates with an interband absorption peak, and we attribute it to interband carrier recombination. Finally, the slow component is dependent on the pH of the solution, which suggests an important role played by H⁺ ions surrounding the nanotubes. PACS 78.47.+p; 78.67.Ch; 73.22.-f     

Excitonic effects and optical spectra of single-walled carbon nanotubes

Many-electron effects often dramatically modify the properties of reduced dimensional systems. We report calculations, based on an ab initio many-electron Green's function approach, of electron-hole interaction effects on the optical spectra of small-diameter single-walled carbon nanotubes. Excitonic effects qualitatively alter the optical spectra of both semiconducting and metallic tubes. Excitons are bound by approximately 1 eV in the semiconducting (8,0) tube and by approximately 100 meV in the metallic (3,3) tube. These large many-electron effects explain the discrepancies between previous theories and experiments.     

碳纳米管悬浮液的光限幅特性实验研究

通过超声波降解法制备了多壁碳纳米管的水-表面活性剂悬浮液,测量了其对于1 064 nm,脉宽10 ns Nd:YAG调Q脉冲激光的光限幅曲线。实验发现：入射激光能量密度较低时,出射能量密度随入射能量密度的增加而线性增加;当入射能量密度为160 mJ/cm2时,出射能量不再线性增加并且逐渐趋近于光限幅器的嵌位输出值,约16 mJ,同时,对激光的透过率从71%下降到15%。通过Z扫描和探针光实验以及45°散射角下散射能量、散射率随入射激光能量变化曲线的测量,对碳纳米管悬浮液的光限幅机理进行了研究。结果表明：其限幅机理可能源于碳纳米管吸收激光能量后升华产生的膨胀的碳气泡对入射激光产生的非线性散射;另外,非线性折射对光限幅效果也有一定的作用。     

Exponential decay lifetimes of excitons in individual single-walled carbon nanotubes

The dynamics of excitons in individual semiconducting single-walled carbon nanotubes was studied using time-resolved photoluminescence (PL) spectroscopy. The PL decay from tubes of the same (n,m) type was found to be monoexponential, however, with lifetimes varying between less than 20 and 200 ps from tube to tube. Competition of nonradiative decay of excitons is facilitated by a thermally activated process, most likely a transition to a low-lying optically inactive trap state that is promoted by a low-frequency phonon mode.     

Controlling growth and Raman spectra of individual suspended single-walled carbon nanotubes

Single-walled carbon nanotubes (SWNTs) were prepared with ethanol chemical vapor deposition (CVD) on SiO₂ flat and pillar-patterned Si substrates. The effect of CVD temperatures from 600 to 800 °C on SWNTs yields was investigated. By virtue of its unperturbed environment, an individual suspended SWNT grown between two different SiO₂ pillars provides a possibility to study the phonon band structure of SWNT itself at a single-nanotube level. Raman spectra of individual SWNTs grown between pillars were investigated systematically.     

Fast detection of the metallic state of individual single-walled carbon nanotubes using a transient-absorption optical microscope

In spite of the outstanding properties of single-walled carbon nanotubes (SWNTs), the coexistence of metallic and semiconducting SWNTs as a result of synthesis has hindered their electronic and photonic applications. We demonstrate a pump-probe microscopy method for fast, contact-free mapping of metallicity in individual SWNTs. We employ the phase of transient absorption as a contrast to discriminate metallic and semiconducting SWNTs. Furthermore, we have clarified the phase dependence on the pump or probe wavelengths and the energy structure of SWNTs. Our imaging method holds the potential of serving as a high-speed metallicity-mapping tool to assist the development of SWNT-based nanoelectronics.     

碳纳米管悬浮液的光限幅特性实验研究

 通过超声波降解法制备了多壁碳纳米管的水-表面活性剂悬浮液,测量了其对于1 064 nm,脉宽10 ns Nd:YAG调Q脉冲激光的光限幅曲线。实验发现：入射激光能量密度较低时,出射能量密度随入射能量密度的增加而线性增加;当入射能量密度为160 mJ/cm²时,出射能量不再线性增加并且逐渐趋近于光限幅器的嵌位输出值,约16 mJ,同时,对激光的透过率从71%下降到15%。通过Z扫描和探针光实验以及45°散射角下散射能量、散射率随入射激光能量变化曲线的测量,对碳纳米管悬浮液的光限幅机理进行了研究。结果表明：其限幅机理可能源于碳纳米管吸收激光能量后升华产生的膨胀的碳气泡对入射激光产生的非线性散射;另外,非线性折射对光限幅效果也有一定的作用。     

Surface-enhanced Raman scattering from the individual metallic single-walled carbon nanotubes

A new experimental technique has been presented to investigate the surface-enhanced Raman scattering (SERS) on “individual and untouched” single-walled carbon nanotubes (SWNTs) deposited onto gold or silver film-covered substrate through a direct CVD method. It was found that the radial breathing mode for SERS shows a narrower linewidth than the normal Raman spectroscopy (NRS). Relative to NRS, the SERS spectra also revealed a preferable contribution to some metallic component of the G line. However no obvious difference for D and G′ between SERS and NRS has been revealed, which is different from the previous results on bulk SWNT samples.     

Electronic transport properties of metallic single-walled carbon nanotubes

We have calculated the differential conductance of metallic carbon nanotubes by the scatter matrix methon.It is found that the differential conductance of metallic nanotube-based devices oscillates as a function of the bias voltage between the two leads and the gate voltage.Oscillation period T is directly proportional to the reciprocal of nanotube length.In addition,we found that electronic transport properties are sensitive to variation of the length of the nanotube.     

Polarization dependence of the optical absorption of single-walled carbon nanotubes

Anisotropic optical absorption properties of single-walled carbon nanotubes (SWNTs) are determined from a vertically aligned SWNT film for 0.5-6 eV. Absorption peaks at 4.5 and 5.25 eV are found to exhibit remarkable polarization dependence and have relevance to optical properties of graphite. A method for determining a nematic order parameter for an aligned SWNT film based on the collinear absorption peak at 4.5 eV is presented, followed by the determination of the optical absorption cross section.     

重频激光对多壁碳纳米管悬浮液光限幅特性的影响研究

在激光以不同重复频率入射下,研究了直径分布为10～20 nm的多壁碳纳米管悬浮液对波长为1064 nm激光的光限幅效应,定性分析了不同重复频率激光对多壁碳纳米管悬浮液的光限幅影响。结果表明:碳纳米管悬浮液对波长为532 nm和1064 nm的激光都具有很强的光限幅响应;在多脉冲激光入射时,碳纳米管悬浮液的光限幅效应比单脉冲激光入射时更显著。     

Luminescence decay and the absorption cross section of individual single-walled carbon nanotubes

The absorption cross section of highly luminescent individual single-walled carbon nanotubes is determined using time-resolved and cw luminescence spectroscopy. A mean value of approximately 1 x 10(-17) cm2 per carbon atom is obtained for (6,5) tubes excited at their second optical transition, and corroborated by single tube photothermal absorption measurements. Biexponential luminescence decays are systematically observed, with short and long lifetimes around 45 and 250 ps. This behavior is attributed to the band edge exciton fine structure with a dark level lying a few meV below a bright one.     

Dynamics of individual single-walled carbon nanotubes in water by real-time visualization

Individual single-walled carbon nanotubes (SWNTs) in aqueous suspension are visualized directly by fluorescence video microscopy. The fluorescent tagging is simple, biocompatible, and does not modify the SWNTs. The dynamics of individual SWNTs in water are observed and quantified for the first time. We measure the confined rotational diffusion coefficient and find it in reasonable agreement with predictions based on confined diffusion of dilute Brownian rods. We determine the critical concentration at which SWNTs in suspensions start interacting. By analyzing the fluctuating shape of SWNTs in the 3 to 5 microm range, we determine that their persistence length ranges between 32 and 174 microm, in agreement with theoretical estimates; thus, commonly available SWNTs in liquids can be considered as rigid Brownian rods in the absence of imposed external fields or self-attractive forces.