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Luttinger parameter

About: Luttinger parameter is a research topic. Over the lifetime, 153 publications have been published within this topic receiving 10025 citations.


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01 Jan 2004
TL;DR: In this paper, the Sine-Gordon F.1. Peculiarities of d = 1 2. Bosonization 3. Luttinger liquids 4. Refinements 5. Microscopic methods 6. Spin 1/2 chains 7. Interacting fermions on a lattice 8. Coupled fermionic chains 9. Disordered systems 10. Boundaries and isolated impurities 11.
Abstract: 1. Peculiarities of d=1 2. Bosonization 3. Luttinger liquids 4. Refinements 5. Microscopic methods 6. Spin 1/2 chains 7. Interacting fermions on a lattice 8. Coupled fermionic chains 9. Disordered systems 10. Boundaries and isolated impurities 11. Significant others A. Basics of many body B. Not so important fine technical points C. Correlation functions D. Bosonization directory E. Sine-Gordon F. Numerical solution

3,131 citations

Journal ArticleDOI
TL;DR: The explicitly soluble Luttinger model is used as a basis for the description of the general interacting Fermi gas in one dimension, which will be called "LUTtinger liquid theory" as mentioned in this paper.
Abstract: The explicitly soluble Luttinger model is used as a basis for the description of the general interacting Fermi gas in one dimension, which will be called 'Luttinger liquid theory', by analogy with Fermi liquid theory. The excitation spectrum of the Luttinger model is described by density-wave, charge and current excitations; its spectral properties determine a characteristic parameter that controls the correlation function exponents. These relations are shown to survive in non-soluble generalisations of the model with a non-linear fermion dispersion. It is proposed that this low-energy structure is universal to a wide class of 1D systems with conducting or fluid properties, including spin chains.

1,451 citations

Journal ArticleDOI
18 Feb 1999-Nature
TL;DR: In this article, the authors present measurements of the conductance of single-walled carbon nanotubes (SWNTs) as a function of temperature and voltage that agree with predictions for tunnelling into a Luttinger liquid.
Abstract: Electron transport in conductors is usually well described by Fermi-liquid theory, which assumes that the energy states of the electrons near the Fermi level EF are not qualitatively altered by Coulomb interactions. In one-dimensional systems, however, even weak Coulomb interactions cause strong perturbations. The resulting system, known as a Luttinger liquid, is predicted to be distinctly different from its two- and three-dimensional counterparts1. For example, tunnelling into a Luttinger liquid at energies near the Fermi level is predicted to be strongly suppressed, unlike in two- and three-dimensional metals. Experiments on one-dimensional semiconductor wires2, 2,3 have been interpreted by using Luttinger-liquid theory, but an unequivocal verification of the theoretical predictions has not yet been obtained. Similarly, the edge excitations seen in fractional quantum Hall conductors are consistent with Luttinger-liquid behaviour4, 5, but recent experiments failed to confirm the predicted relationship between the electrical properties of the bulk state and those of the edge states6. Electrically conducting single-walled carbon nanotubes (SWNTs) represent quantum wires7,8,9,10 that may exhibit Luttinger-liquid behaviour11, 12. Here we present measurements of the conductance of bundles (‘ropes’) of SWNTs as a function of temperature and voltage that agree with predictions for tunnelling into a Luttinger liquid. In particular, we find that the conductance and differential conductance scale as power laws with respect to temperature and bias voltage, respectively, and that the functional forms and the exponents are in good agreement with theoretical predictions.

1,251 citations

Journal ArticleDOI
TL;DR: In this article, the conductance of individual ropes of carbon nanotubes (SWNTs) as a function of temperature and bias voltage was measured and the power-law functional forms and the inferred exponents were in good agreement with theoretical predictions for tunneling into a Luttinger liquid.
Abstract: An interacting one-dimensional (1D) electron system is predicted to behave very differently than its higher-dimensional counterparts. Coulomb interactions strongly modify the properties away from those of a Fermi liquid, resulting in a Luttinger liquid (LL) characterized by a power-law vanishing of the density of states at the Fermi level. Experiments on one-dimensional semiconductor wires and fractional quantum Hall conductors have been interpreted using this picture, but questions remain about the connection between theory and experiment. Recently, single-walled carbon nanotubes (SWNTs) have emerged as a new type of 1D conductor that may exhibit LL behavior. Here we present measurements of the conductance of individual ropes of such SWNTs as a function of temperature and voltage. Power law behavior as a function of temperature or bias voltage is observed: G~ T^a and dI/dV ~ V^a. Both the power-law functional forms and the inferred exponents are in good agreement with theoretical predictions for tunneling into a LL.

1,059 citations

Journal ArticleDOI
TL;DR: In this paper, a universal description of low-energy properties of one-dimensional quantum fluids, based on a harmonic theory of long-wavelength density fluctuations with use of renormalized parameters, is outlined.
Abstract: A universal description of the low-energy properties of one-dimensional quantum fluids, based on a harmonic theory of long-wavelength density fluctuations with use of renormalized parameters, is outlined. The structure of long-distance correlations of a spinless fluid is obtained, showing the essential similarity of one-dimensional Bose and Fermi fluids. The results are illustrated by application to the one-dimensional Bose fluid with $\ensuremath{\delta}$-function interaction.

834 citations

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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20218
202011
20198
20186
201714
20168