Session Q6: Carbon Nanotubes: Electronic and Thermal Properties

Ultra-short single-wall carbon nanotube NEMS transistors

We study electron transport in clean suspended single-wall carbon nanotube (SWCNT) transistors hosting a single quantum dot (QD) ranging in length from a few tens of nm down to $\approx$ 3 nm. To fabricate these ultra-short QD transistors, we align narrow gold bow-tie junctions on top of individual SWCNTs and suspend the devices. We then use a feedback-controlled electromigration to break the gold junctions and expose nm-sized sections of the SWCNTs. We measure electron transport in these devices at low temperature and show that they form clean and tunable quantum dot transistors. We observe QD excited states which correspond to both the stretching and flexural vibronic modes. The out-of-plane vibron resonances approach the THz range, and show that these ultra-short suspended transistors are promising candidates to develop highly sensitive NEMS and explore the strong electron-vibron coupling regime.   

Measurement of intrinsic resistivity of individual single walled carbon nanotubes with known-chirality

We report the electrical resistivity measured on individual single walled nanotubes (SWNTs) whose atomic structures are characterized by Rayleigh and Raman spectroscopy. Since electrical transport of SWNTs on substrates is predominantly limited by surface polar phonon from substrate at elevated temperatures, intrinsic transport properties of SWNTs limited by nanotube phonons remained to be probed experimentally. Here we present electrical transport measurement of long suspended individual SWNTs with exactly assigned atomic structures. SWNTs are grown by the chemical vapor deposition method on pre-patterned electrodes and their exact chiral indices are obtained using Rayleigh and Raman spectroscopy. We investigate temperature dependent resistivity of metallic SWNTs in the diffusive regime. We will discuss the chirality dependence of the electron-acoustic phonon interaction inferred from the temperature dependent intrinsic resistivity of SWNTs.   

Probing Magnetic Susceptibility Anisotropy of Large-Diameter Armchair Carbon Nanotubes via Magnetic Linear Dichroism Spectroscopy

We studied magnetic susceptibility anisotropy, via magnetic linear dichroism spectroscopy, of aqueous suspensions of single-walled carbon nanotubes in high magnetic fields up to 22T using a unique magnet system (Split-Florida Helix magnet). Specifically, we measured magnetic susceptibility anisotropies, $\Delta \chi$, of several armchair species ranging from (5,5)-(13,13) at room temperature over an excitation wavelength range of 400-900 nm. For large diameter armchairs such as (12,12) and (13,13), we have observed some of the strongest alignment in a static magnetic field due to their large diameters. Results will be discussed in comparison with detailed calculations involving the Aharonov-Bohm effect.   

Helical modes and Majorana fermions in carbon nanotubes

We derive an effective low-energy theory for metallic (armchair and nonarmchair) single-wall nanotubes in the presence of an electric field perpendicular to the nanotube axis, and in the presence of magnetic fields, taking into account spin-orbit interactions and screening effects on the basis of a microscopic tight-binding model [1,2]. The interplay between electric field and spin-orbit interaction allows us to tune armchair nanotubes into a helical conductor in both Dirac valleys. Metallic nonarmchair nanotubes are gapped by the surface curvature, yet helical conduction modes can be restored in one of the valleys by a magnetic field along the nanotube axis. If in proximity with a superconductor, helical modes give rise to Majorana bound states. Furthermore, we discuss electric dipole spin resonance in carbon nanotubes, and find that the Rabi frequency shows a pronounced dependence on the momentum along the nanotube. \\[4pt] [1] J. Klinovaja, M. Schmidt, B. Braunecker, and D. Loss, Phys. Rev. Lett. 106, 156809 (2011).\\[0pt] [2] J. Klinovaja, M. Schmidt, B. Braunecker, and D. Loss, Phys. Rev. B 84, 085452 (2011).   

Extracting Diameter and Chirality Dependences of Optical and Electronic Properties of Semiconducting Single-Wall Carbon Nanotubes from First-Principles Calculations

First-principles methods based on the combination of density-functional theory (DFT) for ground-state properties, GW approximation for quasiparticle properties and Bethe-Salpeter equation (BSE) for optical properties represent the state-of-art for accurate and reliable calculations of optical and electronic properties of solids and molecules. For semiconducting carbon nanotubes (CNTs), they have been applied successfully to selected small-diameter tubes. In this work, we systematically calculate such properties for all zig-zag semiconducting single-wall carbon nanotubes with diameters ranging from (10,0) to (20,0) CNTs, allowing us to extract in a reliable way the diameter and chirality dependence of many properties, such as: (i) optical transition energies; (ii) quasiparticle band gaps; (iii) exciton binding energies; (iv) bright-dark exciton splittings; (v) excited exciton states properties; (vi) transverse-polarized exciton states properties; (vii) electron and hole effective masses (and therefore excitonic reduced masses). All properties are described with good accuracy by diameter- and chirality-dependent analytical formulas, with parameters extracted from the first-principles calculations.   

Modeling the Thermal Conductivity of Nanocomposites Using Monte-Carlo Methods and Realistic Nanotube Configurations

The effective thermal conductivity (K$_{eff})$ of carbon nanotube (CNT) composites is affected by the thermal boundary resistance (TBR) and by the dispersion pattern and geometry of the CNTs. We have previously modeled CNTs as straight cylinders and found that the TBR between CNTs (TBR$_{CNT-CNT})$ can suppress K$_{eff}$ at high volume fractions of CNTs [1]. Effective medium theory results assume that the CNTs are in a perfect dispersion state and exclude the TBR$_{CNT-CNT }$[2]. In this work, we report on the development of an algorithm for generating CNTs with worm-like geometry in 3D, and with different persistence lengths. These worm-like CNTs are then randomly placed in a periodic box representing a realistic state, since the persistence length of a CNT can be obtained from microscopic images. The use of these CNT geometries in conjunction with off-lattice Monte Carlo simulations [1] in order to study the effective thermal properties of nanocomposites will be discussed, as well as the effects of the persistence length on K$_{eff}$ and comparisons to straight cylinder models. \textbf{References} [1] K. Bui, B.P. Grady, D.V. Papavassiliou, Chem. Phys. Let., 508(4-6), 248-251, 2011 [2] C.W. Nan, G. Liu, Y. Lin, M. Li, App. Phys. Let., 85(16), 3549-3551, 2006   

Computational study of the thermal conductivity of defective carbon nanostructures

We use molecular dynamics simulations to study the role of defects on the thermal conductivity in low-dimensional graphitic nanostructures such as schwarzites (3D), graphene (2D), carbon nanotubes and graphene nanoribbons (1D). Since the simulations are very demanding due to the very long phonon mean free path, we describe forces acting on carbon atoms by a parameterized valence force field. Our calculations make use of the non-equilibrium molecular dynamics technique, which incorporates the constant-temperature Nose-Hoover thermostat and non-equilibrium driving forces, which mimic the effect of the heat flow. We study different types of defects, including vacancies and isotope impurities, and show that their importance changes with changing dimension of the system.   

Near-field heat transfer between an array of SWNTs and a quartz substrate

The near-field heat transfer between a quartz substrate and a sparse array of SWNTs oriented normal to the substrate was studied theoretically. The heat power transferred from the hot quartz substrate to the cold SWNTs was expressed through the electric field Green tensor of the system using the fluctuation-dissipation theorem . The integral equation for the Green tensor was obtained and solved numerically. The spectra of the transferred power were calculated and the pronounced resonance lines in the spectra were demonstrated at the frequencies of the polariton resonances in the quartz and antenna resonances of the surface plasmons in the SWNTs. The dependence of the transferred power on separation between the SWNTs and the substrate and on the SWNTs lengths in the array was also studied.   

Ab initio studies of mechanical, electric, and magnetic properties of functionalized carbon nanotubes

We present results of extensive theoretical studies of mechanical, electric, and magnetic properties of functionalized carbon nanotubes (CNTs). Our studies are based on the ab initio calculations in the framework of the density functional theory. We have performed calculations for various metallic and semiconductor single wall CNTs, functionalized with simple organic molecules such as OH, COOH, NH$_{n}$, CH$_{n}$ and metals, Al, Fe, Ni, Cu, Zn, and Pd. We have determined the stability of the functionalized CNTs, their elastic moduli, conductance, and magnetic moments (in the case of CNTs decorated with magnetic ions). These studies shed light on physical mechanisms governing the binding of the adsorbed molecules and also provide valuable quantitative predictions that are of importance for design of novel composite materials and functional devices. In particular, we find out that the Young's modulus of functionalized CNTs is smaller than in the case of bare CNTs, however it is large enough to provide a strong enforcement of composites. The functionalization with molecules leads also to the metallization of semiconducting CNTs, being relevant in the context of CNT interconnects, whereas the functionalization with metals might be used to cut CNTs into ribbons.   

Nanotube based engine

We discuss a mechanism for converting electrical energy into translational motion using a variable-shape bistable carbon nanotube. Clamping one tube end open and the other one closed, we use an applied voltage to switch the tube between mostly collapsed and mostly inflated shapes. Devices based on such a double-pinned tube geometry can operate as a voltage-controlled constant-force spring, a charge-controlled harmonic spring, or an electromechanical engine performing work by coupling to a propagating collapsed/inflated transition region. Making an analogy to ideal-gas thermodynamics, constant-voltage, constant-charge, and constant-geometry operational regimes correspond to isothermal, adiabatic and isochoric processes. Constant-voltage, constant-charge, and constant-geometry processes coupled can be combined into cycles analogous to those of a heat engine. Unlike a heat engine, the tube bistability enables it to collect useful work on both inflation and collapse motions, thus eliminating the need for external forces to restore the system to its initial state during the operational cycle.   

Influence of temperature and adsorbates on a carbon nanotube resonator by molecular dynamics simulations

The bending modes of carbon nanotube have been studied for ultralow mass and force sensing and its tunable resonance frequency. On the other hand, the nonlinear damping of flexural mode has been shown to be vulnerable to temperature and adsorbates. For this reason, we have studied the interaction between mechanical and thermal characteristics in a carbon nanotube cantilever resonator observing the phase space trajectories, strain-stress distributions, and lattice vibrational spectra for various temperatures and adsorbate conditions. The calculation was based on molecular dynamics simulations using the REBO potential, where a carbon nanotube was excited by sinusoidal mechanical forcing at a tube end with constant-temperature boundary condition. The result confirms that the localized strain distribution is in agreement with previous high-resolution transmission electron microscopy result. Based on the simulations, the dynamic Young's modulus and the damping coefficient will be extracted in the frequency domain for different nanotube length and chirality, and will be compared with the continuum theories. In addition, the interaction between the first resonance mode and the background phonons will be discussed based on the obtained dissipated thermal energy and the phonon energy spectra.   

Electron Spin Resonance as a route to Spin-Gap detection in Carbon Nanotubes

The recent observation of a charge-neutral excitation gap in ultraclean carbon nanotubes\footnote[1]{V. V. Deshpande {\it{et al.}}, Science {\bf 323}, 106 (2009)} raises the intriguing possibility of a phase with gapless charge spectrum and gapped spin spectrum: the Luther-Emery liquid. We note that ESR would be an ideal probe to directly test whether the observed gap is a spin-gap, as it probes the non-local correlations of conduction electron spins. We focus on the Luther-Emery point ($K_s=1/2$, also known as free fermion point) where an explicit calculation of relevant spin-spin correlation function is possible, to calculate the ESR signal in a Luther-Emery liquid. At high frequencies of $\omega>2 \Delta_s$ where $\Delta_s$ is the spin-gap, the ESR signal of the Luther-Emery liquid will exhibits a second peak at magnetic fields away from the resonance condition of $B=\omega/\mu_B g K_s$. We discuss how to measure the spin-gap from the location of this additional peak as a function of applied field strength.   

Coherent non-local transport in quantum wires with strongly coupled electrodes

We report a one-dimensional non-local experiment, where the conductance of a section of carbon nanotube shows regular oscillations due to coherent and ballistic transport in an adjacent section. This occurs in spite of wide strongly coupled contact electrodes, which are expected to divide the nanotube into independent sections. Our simulations show that the electrodes form shallow and wide barriers, which maintain quantum coherence between the adjacent sections.   

Nanofissure formation during selective breakdown of m-SWNT in an aligned array

Selective removal of metallic single walled carbon nanotubes (m-SWNT) in an aligned array is needed for restoring semiconducting properties and better device performance. The selective removal is done via electrical breakdown of m-SWNT while applying a large gate voltage to preserve semiconducting SWNT. In this work, we show using electrical measurements and scanning electron microscopy imaging that in a sufficiently dense array, not only the m-SWNT breaks down but also s-SWNT breaks down in a correlated fashion giving rise to a nano fissure pattern. This is in contrast to the established understanding that SWNTs are broken in a random fashion. The origin of the correlated breakdown is due to the electrostatic field of the broken nanotubes that produces locally inhomogeneous current and Joule heating distributions in the neighboring intact nanotubes triggering their breakdowns in the vicinity of the broken nanotubes   

An optically pumped InGaAsP/InP quantum dot rolled-up microtube laser

Rolled-up quantum dot microtubes are a promising candidate for light sources in integrated photonics. We have fabricated InGaAsP/InAs quantum dot rolled-up microtubes from InGaAsP strained bilayers with embedded InAs quantum dots (grown by chemical beam epitaxy). In room-temperature photoluminescence experiments we have observed resonant-mode emission with wavelengths in the telecom range. This resonant emission is consistent with whispering gallery modes. At a temperature of 82 K, we have demonstrated multi-mode lasing under continuous wave optical pumping. We estimate an ultra-low lasing threshold near 1.25 $\mu$Ws of absorbed optical power.