Luttinger-liquid behaviour in carbon nanotubes

Bockrath, Marc; Cobden, David; Lu, Jia Grace; Rinzler, Andrew G.; Smalley, R. E.; Balents, Leon; McEuen, Paul L.

doi:10.1038/17569

Cited by 1,507 publications

(1,630 citation statements)

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“…At high bias voltages, the electrons have enough energy to emit optical phonons, dramatically reducing the mean-freepath and modifying equation (2) to the more general equation (1). Our measurements clearly show that equation (1) is still valid up to 10 GHz.…”

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confidence: 79%

Microwave Transport in Metallic Single-Walled Carbon Nanotubes

Burke

2005

Nano Lett.

118

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The dynamical conductance of electrically contacted single-walled carbon nanotubes is measured from dc to 10 GHz as a function of source-drain voltage in both the low-field and high-field limits. The ac conductance of the nanotube itself is found to be equal to the dc conductance over the frequency range studied for tubes in both the ballistic and diffusive limit. This clearly demonstrates that nanotubes can carry high-frequency currents at least as well as dc currents over a wide range of operating conditions. Although a detailed theoretical explanation is still lacking, we present a phenomenological model of the ac impedance of a carbon nanotube in the presence of scattering that is consistent with these results.There are two reasons to study single-walled carbon nanotubes (SWNT) 1 : physics and technology. For physics, single walled nanotubes represent nearly ideal 1d electronic structures which allow for experimental studies of interaction effects and Luttinger liquid behavior 2 , ballistic transport at room temperature 3 , quantum confinement effects, Coulomb blockade at room temperature 4 , and spin transport 5 . For technology, nanotube transistors are predicted to be extremely fast 6 , especially if the nanotubes can be used as the interconnects themselves in future integrated nanosystems. The extremely high mobilities found in semiconducting nanowires 7 and nanotubes 8 are important for high speed operations, one of the main predicted advantages of nanotube and nanowire devices in general 9 . Nanotubes may also have a role to play as high frequency interconnects in the long term between active nanotube transistors or in the short term between conventional transistors because of their capacity for large current densities.Early theoretical work 10 , as well as our recent circuit modeling work 11 , predict significant frequency dependence in the nanotube dynamical impedance in the absence of scattering and contact resistance. The origin of this predicted frequency dependence is in the collective motion of the electrons, which can be thought of as 1d plasmons. Our equivalent circuit description shows that the nanotube forms a quantum transmission line, with distributed kinetic inductance and both quantum and geometric capacitance. (One of us recently verified the 2d analog of this effect 12 .) In the absence of damping, standing waves on this transmission line can give rise to resonant frequencies in the microwave range (1-10 GHz) for nanotube lengths between 10 and 100 µm. We also proposed an ad-hoc damping model, relating the damping to the dc resistance per unit length. To date, there have been no measurements of the microwave frequency conductance of a SWNT to either confirm or deny these theoretical predictions or equivalent circuit models.In this Letter, we present the first measurements of the high frequency conductance of a single walled nanotube. We find experimentally that the ac conductance is equal to the dc conductance up to at least 10 GHz. This clearly demonstrates for the first time that the...

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confidence: 79%

Microwave Transport in Metallic Single-Walled Carbon Nanotubes

Burke

2005

Nano Lett.

118

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“…Physically, each of the absorption features corresponds to an interband transition of a particular armchair species whose energy position varies roughly with inverse tube diameter. 5 The implication of this symmetric lineshape is that interband transitions in armchair SWCNTs are excitonic, contrary to expectations from their metallic character. Band-to-band optical transitions in SWCNTs should have an asymmetric absorption lineshape due to the one-dimensional van Hove singularities in the density of states.…”

Section: Introductionmentioning

confidence: 91%

Section: Introductionmentioning

confidence: 99%

“…4 At the same time, their one-dimensional characteristics combined with their linear band dispersions have attracted much fundamental interest for exploring many-body phenomena. 5 However, systematic studies of macroscopic ensembles of armchair nanotubes have been impossible due to the coexistence of different (n,m) species of nanotubes in asgrown samples.Recent years have seen impressive progress in post-growth separation of SWCNTs using a variety of methods. One of the most successful methods has been density gradient ultracentrifugation (DGU), 6-10 which can sort out different species of SWCNTs in bulk quantities according to their diameters, chiralities, and electronic types, enabling studies of (n,m)-dependent properties using standard macroscopic characterization measurements.…”

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confidence: 99%

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Unique Origin of Colors of Armchair Carbon Nanotubes

Hároz

Duque

et al. 2012

J. Am. Chem. Soc.

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ABSTRACT:The colors of suspended metallic colloidal particles are determined by their size-dependent plasma resonance, while those of semiconducting colloidal particles are determined by their size-dependent band gap. Here, we present a novel case for armchair carbon nanotubes, suspended in aqueous medium, for which the color depends on their sizedependent excitonic resonance, even though the individual particles are metallic. We observe distinct colors of a series of armchair-enriched nanotube suspensions, highlighting the unique coloration mechanism of these one-dimensional metals.The size-dependent colors of suspended colloidal particles have fascinated researchers, engineers, and artists for centuries. While quantum confinement always plays a fundamental role, the coloration mechanism can differ depending on whether the particles are metallic or semiconducting. For metallic nanoparticles, their colors are determined by the freecarrier plasma resonance whose frequency depends on the electron density as well as the particle size and shape. 1 For semiconducting nanoparticles, the key parameter is the sizedependent fundamental band gap, i.e., the separation between the top of the valence band (HOMO) and the bottom of the conduction band (LUMO), which sensitively changes with quantum confinement, i.e., size. 2 Here, we present a novel case for armchair single-walled carbon nanotubes (SWCNTs), suspended in aqueous medium, for which the origin of their color depends on the interband excitonic resonance even though the individual particles are gapless, i.e., metallic. Armchair nanotubes enjoy a rather special status among the SWCNT family. The structure of each member, or species, of the family is uniquely specified by a pair of integers, (n,m), resulting in different species possessing different diameters, chiral angles, and electronic types (semiconducting or metallic). 3 Armchair SWCNTs are characterized by the simple relation n = m, i.e., (n,n), and they are known to be the only truly gapless species with excellent electrical properties, exhibiting ballistic conduction even at room temperature. 4 At the same time, their one-dimensional characteristics combined with their linear band dispersions have attracted much fundamental interest for exploring many-body phenomena. 5 However, systematic studies of macroscopic ensembles of armchair nanotubes have been impossible due to the coexistence of different (n,m) species of nanotubes in asgrown samples.Recent years have seen impressive progress in post-growth separation of SWCNTs using a variety of methods. One of the most successful methods has been density gradient ultracentrifugation (DGU), 6-10 which can sort out different species of SWCNTs in bulk quantities according to their diameters, chiralities, and electronic types, enabling studies of (n,m)-dependent properties using standard macroscopic characterization measurements. In a recent report, 10 we provided unambiguous evidence of bulk enrichment of armchair nanotubes through DGU by utilizing wavelength-dependen...

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“…The problems that arise are specially interesting in one-dimensional (1D) devices such as quantum wires and carbon nanotubes. In these cases the effect of electron-electron (e-e) interactions is crucial, leading to the so called Luttinger liquid (LL) behavior 2 , characterized by correlation functions which decay with interaction-dependent exponents 3 and a power law in the tunneling I − V characteristic curve 4 .…”

Section: Introductionmentioning

confidence: 99%

Electron-spin motion: a new tool to study ferromagnetic films and surfaces

Dey

Weber²

2011

J. Phys.: Condens. Matter

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We analyze the behavior of the four-terminal resistance, relative to the two-terminal resistance of an interacting quantum wire with an impurity, taking into account the invasiveness of the voltage probes. We consider a one-dimensional Luttinger model of spinless fermions for the wire. We treat the coupling to the voltage probes perturbatively, within the framework of non-equilibrium Green function techniques. Our investigation unveils the combined effect of impurities, electron-electron interactions and invasiveness of the probes on the possible occurrence of negative resistance.

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Luttinger-liquid behaviour in carbon nanotubes

Cited by 1,507 publications

References 22 publications

Microwave Transport in Metallic Single-Walled Carbon Nanotubes

Microwave Transport in Metallic Single-Walled Carbon Nanotubes

Unique Origin of Colors of Armchair Carbon Nanotubes

Electron-spin motion: a new tool to study ferromagnetic films and surfaces

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