Correlated transport and non-Fermi-liquid behavior in single-wall carbon nanotubes

Egger, Reinhold; Gogolin, Alexander O.

doi:10.1007/s100510050315

Cited by 195 publications

(236 citation statements)

References 61 publications

(149 reference statements)

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“…A compelling correlated state of one-dimensional systems is the Tomonaga-Luttinger liquid (TLL) state. The TLL state has been suggested to describe the low energy properties of CNTs with a single shell, the single-wall carbon nanotubes 2,3,4,5,6 . Transport 7 and photoemission studies 8,9 provided evidence for the existence of the TLL state in SWCNTs.…”

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confidence: 99%

Spin Gap and Luttinger Liquid Description of the NMR Relaxation in Carbon Nanotubes

et al. 2007

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Recent NMR experiments by Singer et al. [Singer et al. Phys. Rev. Lett. 95, 236403 (2005).] showed a deviation from Fermi-liquid behavior in carbon nanotubes with an energy gap evident at low temperatures. Here, a comprehensive theory for the magnetic field and temperature dependent NMR 13 C spin-lattice relaxation is given in the framework of the Tomonaga-Luttinger liquid. The low temperature properties are governed by a gapped relaxation due to a spin gap (∼ 30 K), which crosses over smoothly to the Luttinger liquid behaviour with increasing temperature.PACS numbers: 71.10. Pm,71.20.Tx, Low dimensional carbonaceous systems, fullerenes, carbon nanotubes (CNTs), and graphene display a rich variety of exotic states and strongly correlated phenomena. These include superconductivity in alkali doped fullerenes 1 , quantized transport in singlewall carbon nanotubes (SWCNTs), and massless Dirac quasi-particles showing a halve integer quantum Halleffect in graphene even at room temperature. A compelling correlated state of one-dimensional systems is the Tomonaga-Luttinger liquid (TLL) state. The TLL state has been suggested to describe the low energy properties of CNTs with a single shell, the single-wall carbon nanotubes 2,3,4,5,6 . Transport 7 and photoemission studies 8,9 provided evidence for the existence of the TLL state in SWCNTs. In these studies, power-law behavior of temperature and bias dependent conductivity and a power-law Fermi edge was observed, respectively.Nuclear magnetic resonance (NMR) is a powerful method to characterize correlated states of materials as it is sensitive to the density of states near the Fermi edge. For a material with a Fermi-liquid state, the temperature dependent spin-lattice relaxation time, T 1 follows the so-called Korringa temperature dependence for which 1/T 1 T is constant. Recently, 13 C enriched SWCNTs were grown inside carbon nanotubes from 13 C enriched fullerenes 10 . This allowed a high precision measurement of T 1 in small diameter SWCNTs by Singer et al. 11 . A tentative fit of the experiments with a gapped Fermi liquid type density of states (DOS) indicated overall agreement but obvious discrepancies in detail. When the magnetic field and temperature dependent data for T 1 were fitted with this phenomenological model a gap at the Fermi surface with 2∆ ≃ 40 K opened already above room temperature, i.e. its T c is larger than 300 K. This strongly violates the 2∆/k B T > 3.52 relation, thus simple mean field theories are not applicable 12 . Also, the phenomenological description can not account for the strong overshoot of 1/T 1 T when T approaches the gap.Here, we analyze the NMR results in the framework of the Luttinger liquid and Luther-Emery liquid pictures (interacting one-dimensional electrons without and with a gap, respectively). At high temperatures, the former dominates, while the latter accounts for the dominance of a spin gap at low temperatures. We show that the temperature and magnetic field dependent T 1 of 13 C can be explained in the TLL scenario wit...

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Spin Gap and Luttinger Liquid Description of the NMR Relaxation in Carbon Nanotubes

et al. 2007

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“…(3.23) in Ref. 5 . Further studies are needed to clarify the effects of defect on the electronic correlation in a TLL state for SWCNTs, which may open up a new method for manipulating nanotube properties.…”

Section: Resultsmentioning

confidence: 95%

“…The strength of the effective electron-electron interactions is characterized by the charge Luttinger parameter (hereinafter referred to as Luttinger parameter), which ranges from 0 (very strong interactions) to 1 (no interactions, i.e., Fermi liquids) for repulsive interactions. [3][4][5] The theoretical estimate of the Luttinger parameter for an isolated SWCNT is approximately 0.2.…”

Section: Introductionmentioning

confidence: 99%

Intertube effects on one-dimensional correlated state of metallic single-wall carbon nanotubes probed by C13 NMR

et al. 2017

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The electronic states in isolated single-wall carbon nanotubes (SWCNTs) have been considered as an ideal realization of a Tomonaga-Luttinger liquid (TLL). However, it remains unclear whether one-dimensional correlated states are realized under local environmental effects such as the formation of a bundle structure. Intertube effects originating from other adjacent SWCNTs within a bundle may drastically alter the one-dimensional correlated state. In order to test the validity of the TLL model in bundled SWCNTs, low-energy spin excitation is investigated by nuclear magnetic resonance (NMR). The NMR relaxation rate in bundled mixtures of metallic and semiconducting SWCNTs shows a power-law temperature dependence with a theoretically predicted exponent. This demonstrates that a TLL state with the same strength as that for effective Coulomb interactions is realized in a bundled sample, as in isolated SWCNTs. In bundled metallic SWCNTs, we found a power-law temperature dependence of the relaxation rate, but the magnitude of the relaxation rate is one order of magnitude smaller than that predicted by theory. Furthermore, we found an almost doubled magnitude of the Luttinger parameter. These results indicate suppressed spin excitations with reduced Coulomb interactions in bundled metallic SWCNTs, which are attributable to intertube interactions originating from adjacent metallic SWCNTs within a bundle. Our findings give direct evidence that bundling reduces the effective Coulomb interactions via intertube interactions within bundled metallic SWCNTs.

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“…Following Ref. 10, the electron field Ψ rασ (x, t) in the nanotube, describing the electron moving along the direction r = ±1, from the mode α = ±1 with a spin σ = ±1, can be written in terms of the bosonic field ϕ rασ (x, t) as…”

Section: Model Hamiltonianmentioning

confidence: 99%

Electron injection in a nanotube with leads: Finite-frequency noise correlations and anomalous charges

Lebedev

Crépieux²,

Martin³

2005

Phys. Rev. B

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The non-equilibrium transport properties of a carbon nanotube which is connected to Fermi liquid leads, where electrons are injected in the bulk, are computed. A previous work which considered an infinite nanotube showed that the zero frequency noise correlations, measured at opposite ends of the nanotube, could be used to extract the anomalous charges of the chiral excitations which propagate in the nanotube. Here, the presence of the leads have the effect that such-noise crosscorrelations vanish at zero frequency. Nevertheless, information concerning the anomalous charges can be recovered when considering the spectral density of noise correlations at finite frequencies, which is computed perturbatively in the tunneling amplitude. The spectrum of the noise crosscorrelations is shown to depend crucially on the ratio of the time of flight of quasiparticles traveling in the nanotube to the "voltage" time which defines the width of the quasiparticle wave-packets injected when an electron tunnels. Potential applications toward the measurement of such anomalous charges in non-chiral Luttinger liquids (nanotubes or semiconductor quantum wires) are discussed.

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Correlated transport and non-Fermi-liquid behavior in single-wall carbon nanotubes

Cited by 195 publications

References 61 publications

Spin Gap and Luttinger Liquid Description of the NMR Relaxation in Carbon Nanotubes

Spin Gap and Luttinger Liquid Description of the NMR Relaxation in Carbon Nanotubes

Intertube effects on one-dimensional correlated state of metallic single-wall carbon nanotubes probed by C13 NMR

Electron injection in a nanotube with leads: Finite-frequency noise correlations and anomalous charges

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