Effective Low-Energy Theory for Correlated Carbon Nanotubes

Egger, Reinhold; Gogolin, Alexander O.

doi:10.1103/physrevlett.79.5082

Cited by 543 publications

(702 citation statements)

References 16 publications

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“…In the case of single nanotubes, the dominant contribution to the forward-scattering couplings in ͑7͒ comes from the strong Coulomb potential in ͑2͒, with some infrared cutoff which is dictated in general by the longitudinal size of the nanotube. 11 This leads to values of the charge stiffnesses that are typically smaller than 1 and in agreement with the experimental observations of Luttinger liquid behavior in the carbon nanotubes. 2,3 For energy scales much lower than E c , however, the rest of the interaction channels neglected in the above analysis may become as important as the forwardscattering channels.…”

Section: ͑15͒supporting

confidence: 71%

“…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.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: ͑15͒supporting

confidence: 71%

Section: Introductionmentioning

confidence: 99%

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

González

Perfetto

2005

Phys. Rev. B

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“…However, carbon nanotubes are known to be described in terms of a four-channel LL 6,7,20 . The four channels are responsible for the charge-flavour (φ c− ), total spin (φ s− ), spin-flavour (φ s+ ) and total charge (φ c+ ) excitations.…”

Section: Field Emission From Luttinger Liquids and Swntsmentioning

confidence: 99%

“…One of the most important of these is the universality class of 1D correlated electrons or the so-called Luttinger liquids (LLs), which are e.g. realised in single-wall carbon nanotubes (SWNTs), as has been shown both theoretically and experimentally 6,7,8,9 .…”

Section: Introductionmentioning

confidence: 99%

On the visibility of electron–electron interaction effects in field emission spectra

Schmidt

Komnik

2005

Solid State Communications

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One of the most convenient methods to obtain information about the energy distribution function of electrons in conducting materials is the measurement of the energy resolved current j(ω) in field emission (FE) experiments. Its high energy tail j>(ω) (above the Fermi edge) contains invaluable information about the nature of the electron-electron interactions inside the emitter. Thus far, j>(ω) has been calculated to second order in the tunnelling probability, and it turns out to be divergent toward the Fermi edge for a wide variety of emitters. The extraction of the correlation properties from real experiments can potentially be obscured by the eventually more divergent contributions of higher orders as well as by thermal smearing around EF . We present an analysis of both factors and make predictions for the energy window where only the second order tunnelling events dominate the behaviour of j>(ω). We apply our results to the FE from Luttinger liquids and single-wall carbon nanotubes.

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“…We expect that our results-with the appropriate changes [2] in the equations relating scaling exponents to the LL parameter K-directly carry over to the case of spin-1/2 electrons if the two-particle interaction is long-ranged (unscreened) in real space (that is, if the g 1,⊥ term of the g-ology classification [4] can be neglected) and spin-rotationally invariant. This is generally assumed to be the case in single wall carbon nanotubes [5]. For semiconductor heterostructures the range of the interaction can strongly depend on the ... ... Figure 1.…”

Section: Introductionmentioning

confidence: 99%

Coupling-geometry-induced temperature scales in the conductance of Luttinger liquid wires

Wächter

Meden

Schönhammer

2009

J. Phys.: Condens. Matter

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Abstract. We study electronic transport through a one-dimensional, finite-length quantum wire of correlated electrons (Luttinger liquid) coupled at arbitrary position via tunnel barriers to two semi-infinite, one-dimensional as well as stripe-like (twodimensional) leads, thereby bringing theory closer towards systems resembling setups realized in experiments. In particular, we compute the temperature dependence of the linear conductance G of a system without bulk impurities. The appearance of new temperature scales introduced by the lengths of overhanging parts of the leads and the wire implies a G(T ) which is much more complex than the power-law behavior described so far for end-coupled wires. Depending on the precise setup the wide temperature regime of power-law scaling found in the end-coupled case is broken up in up to five fairly narrow regimes interrupted by extended crossover regions. Our results can be used to optimize the experimental setups designed for a verification of Luttinger liquid power-law scaling.

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Effective Low-Energy Theory for Correlated Carbon Nanotubes

Cited by 543 publications

References 16 publications

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

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

On the visibility of electron–electron interaction effects in field emission spectra

Coupling-geometry-induced temperature scales in the conductance of Luttinger liquid wires

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