Electronic Properties of Armchair Carbon Nanotubes: Bosonization Approach

Yoshioka, Hideo; Odintsov, A. A.

doi:10.1103/physrevlett.82.374

Cited by 90 publications

(111 citation statements)

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“…A compelling correlated state of one-dimensional systems is the Luttinger liquid (LL) state. There is now abundant evidence from both theoretical [3,4,5,6,7] and experimental [8,9,10,11] side that the low energy properties of CNTs with a single shell, the single-wall carbon nanotubes (SWCNTs) can be described with the LL state. As a result, SWCNTs are regarded as a model system of the LL state, which could be exploited to further test the theories and novel experimental methods.…”

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confidence: 99%

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Electron Spin Resonance Signal of Luttinger Liquids and Single-Wall Carbon Nanotubes

et al. 2008

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A comprehensive theory of electron spin resonance (ESR) for a Luttinger liquid (LL) state of correlated metals is presented. The ESR measurables such as the signal intensity and the line-width are calculated in the framework of Luttinger liquid theory with broken spin rotational symmetry as a function of magnetic field and temperature. We obtain a significant temperature dependent homogeneous line-broadening which is related to the spin symmetry breaking and the electronelectron interaction. The result crosses over smoothly to the ESR of itinerant electrons in the non-interacting limit. These findings explain the absence of the long-sought ESR signal of itinerant electrons in single-wall carbon nanotubes when considering realistic experimental conditions. PACS numbers: 73.63.Fg, The experimental and theoretical studies of strong correlation effects are in the forefront of condensed matter research. Low-dimensional carbonaceous systems, fullerenes, carbon nanotubes (CNTs), and graphene exhibit a rich variety of such phenomena including superconductivity in alkali doped fullerenes [1], quantized transport in SWCNTs, and massless Dirac quasi-particles showing a half integer quantum Hall-effect in graphene even at room temperature [2]. A compelling correlated state of one-dimensional systems is the Luttinger liquid (LL) state. There is now abundant evidence from both theoretical [3,4,5,6,7] and experimental [8,9,10,11] side that the low energy properties of CNTs with a single shell, the single-wall carbon nanotubes (SWCNTs) can be described with the LL state. As a result, SWCNTs are regarded as a model system of the LL state, which could be exploited to further test the theories and novel experimental methods.Electron spin resonance (ESR) is a well established and powerful method to characterize correlated states of itinerant electrons. It helped to resolve e.g. the singlet nature of superconductivity in elemental metals [12], the magnetically ordered spin-density state in lowdimensional organic metals [13] and in alkali doped fullerides [14]. In three-dimensional metals, the ESR signal intensity is proportional to the Pauli spin-susceptibility, the ESR line-width and g-factor are determined by the mixing of spin up and down states due to spin-orbit (SO) coupling in the conduction band. These ESR measurables are affected when correlations are present and thus their study holds information about the nature of the correlated state.This motivated a decade long quest to find the ESR signal of itinerant electrons in SWCNTs and to characterize its properties in the framework of the expected correlations [15,16,17]. Detection of ESR in SWCNTs is also vital for applications as it enables to determine the spinlattice relaxation time, T 1 , which determines the usability for spintronics [18]. However, to our knowledge no conclusive evidence for this observation has been reported. An often cited argument for this anomalous absence of the ESR signal is the large heterogeneity of the system, the lack of crystallinity, and the pr...

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“…The DOS was ob-tained with a Green's function approach from the band structure that was calculated with a large k-point sampling. We considered the (9,9), (15,6), (10,10), (18,0), and (11,11) SWCNTs in order of increasing diameter. Here (n, m) denotes the lattice vectors on the graphene basis along which a cut-out stripe is folded up to represent a SWCNT [31].…”

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Electron Spin Resonance Signal of Luttinger Liquids and Single-Wall Carbon Nanotubes

et al. 2008

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“…These parallel closely to the investigation of coupled Luttinger liquid chains. Their effect can be summarized as follows: at half filling, umklapp scattering generates a finite charge (Mott) gap in both the symmetric and antisymmetric charge sector, while spin backscattering leads to the opening of a spin gap in the spin sectors 3,4,5 . This is analogous to the spin ladder magnon excitations 14 found in the strong antiferromagnetic coupling limit.…”

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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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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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“…9 From a theoretical point of view, it is well-known that the Luttinger liquid regime may break down in the carbon nanotubes, due to a variety of low-temperature instabilities. [10][11][12][13][14][15] When the effective phonon-mediated interactions are taken into account, it can be shown that the superconducting correlations may grow large upon suitable screening of the Coulomb interaction in the nanotubes. 16,17 This has raised the hopes that such correlations could be amplified by considering nanotube geometries with enhanced electron-phonon couplings.…”

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Coulomb screening and electronic instabilities of small-diameter (5,0) nanotubes

González

Perfetto

2005

Phys. Rev. B

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We investigate the instabilities that may lead to the breakdown of the Luttinger liquid in the small-diameter ͑5,0͒ nanotubes, paying attention to the competition between the effective interaction mediated by phonon exchange and the Coulomb interaction. We use bosonization methods to achieve an exact treatment of the Coulomb interaction at small momentum transfer, and apply next renormalization group methods to analyze the low-energy behavior of the electron system. This allows us to discern the growth of several response functions for charge-density-wave modulations and for superconducting instabilities with different order parameters. We show that, in the case of single nanotubes exposed to screening by external gates, the Luttinger liquid is unstable against the onset of a strong-coupling phase with very large charge-density-wave correlations. The temperature of crossover to the new phase depends crucially on the dielectric constant of the environment, ranging from T c ϳ 10 −4 K ͑at Ϸ 1͒ up to a value T c ϳ 10 2 K ͑reached from Ϸ 10͒. The physical picture is however different when we consider the case of a large array of nanotubes, in which there is a three-dimensional screening of the Coulomb interaction over distances much larger than the intertube separation. The electronic instability is then triggered by the divergence of one of the charge stiffnesses in the Luttinger liquid, implying a divergent compressibility and the appearance of a regime of phase separation into spatial regions with excess and defect of electron density.

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Electronic Properties of Armchair Carbon Nanotubes: Bosonization Approach

Cited by 90 publications

References 20 publications

Electron Spin Resonance Signal of Luttinger Liquids and Single-Wall Carbon Nanotubes

Electron Spin Resonance Signal of Luttinger Liquids and Single-Wall Carbon Nanotubes

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

Coulomb screening and electronic instabilities of small-diameter (5,0) nanotubes

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