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Charles L. Kane - One of the best experts on this subject based on the ideXlab platform.
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Sliding Luttinger Liquid phases
Physical Review B, 2001Co-Authors: Ranjan Mukhopadhyay, Charles L. Kane, Tom C. LubenskyAbstract:We study systems of coupled spin-gapped and gapless Luttinger Liquids. First, we establish the existence of a sliding Luttinger Liquid phase for a system of weakly coupled parallel quantum wires, with and without disorder. It is shown that the coupling can stabilize a Luttinger Liquid phase in the presence of disorder. We then extend our analysis to a system of crossed Luttinger Liquids and establish the stability of a non-FermiLiquid state: the crossed sliding Luttinger Liquid phase. In this phase the system exhibits a finite-temperature, long-wavelength, isotropic electric conductivity that diverges as a power law in temperature T as T!0. This two-dimensional system has many properties of a true isotropic Luttinger Liquid, though at zero temperature it becomes anisotropic. An extension of this model to a three-dimensional stack exhibits a much higher in-plane conductivity than the conductivity in a perpendicular direction.
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Crossed sliding Luttinger Liquid phase
Physical Review B, 2001Co-Authors: Ranjan Mukhopadhyay, Charles L. Kane, Tom C. LubenskyAbstract:We study a system of crossed spin-gapped and gapless Luttinger Liquids. We establish the existence of a stable non-Fermi Liquid state with a finite-temperature,long-wavelength, isotropic electric conductivity that diverges as a power law in temperature $T$ as $T\to 0$. This two-dimensional system has many properties characteristic of a true isotropic Luttinger Liquid, though at zero temperature it becomes anisotropic. This model can easily be extended to three dimensions.
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Thermal transport in a Luttinger Liquid.
Physical Review Letters, 1996Co-Authors: Charles L. Kane, Matthew P. A. FisherAbstract:We study thermal transport in a one-dimensional (1D) interacting electron gas, employing the Luttinger Liquid model. Both thermal conductance and thermopower are analyzed for a pure 1D gas and with impurities. The universal ratio of electrical to thermal conductance in a Fermi Liquid---the Wiedemann-Franz law---is modified, whereas the thermopower is still linear in temperature. For a single impurity the Lorentz number is given by $L(T\ensuremath{\rightarrow}0){\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3L}_{0}/({2g+g}^{2})$---with ${L}_{0}$ the Fermi Liquid value---and the conductance $1/2lgl1$. For $gl1/2$ the Lorentz number diverges as $T\ensuremath{\rightarrow}0$. Possible relevance to thermal transport in conducting polymer systems is discussed.
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Transport in a one-channel Luttinger Liquid.
Physical review letters, 1992Co-Authors: Charles L. Kane, Matthew P. A. FisherAbstract:We study theoretically the transport of a one-channel Luttinger Liquid through a weak link. For repulsive electron interactions, the electrons are completely reflected by even the smallest scatterer, leading to a truly insulating weak link, in striking contrast to that for noninteracting electrons. At finite temperature (T) the conductance is nonzero, and is predicted to vanish as a power of T. At T=0 power-law current-voltage characteristics are predicted. For attractive interactions, a Luttinger Liquid is argued to be perfectly transmitted through even the largest of barriers. The role of Fermi-Liquid leads is also explored.
Gregory A. Fiete - One of the best experts on this subject based on the ideXlab platform.
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Colloquium: The spin-incoherent Luttinger Liquid
Reviews of Modern Physics, 2007Co-Authors: Gregory A. FieteAbstract:In contrast to the well-known Fermi-Liquid theory of three dimensions, interacting one-dimensional and quasi-one-dimensional systems of fermions are described at low energy by an effective theory known as Luttinger Liquid theory. This theory is expressed in terms of collective many-body excitations that show exotic behavior such as spin-charge separation. Luttinger Liquid theory is commonly applied on the premise that “low energy” describes both the spin and charge sectors. However, when the interactions in the system are very strong, as they typically are at low particle densities, the ratio of spin to charge energy may become exponentially small. It is then possible at very low temperatures for the single-spin excitation energy to be low compared to the characteristic single excitation charge energy, but still high compared to the characteristic spin energy. This energy window of near ground-state charge degrees of freedom but highly thermally excited spin degrees of freedom is called a spin-incoherent Luttinger Liquid. The spin-incoherent Luttinger Liquid exhibits a higher degree of universality than the Luttinger Liquid and its properties are qualitatively distinct. In this Colloquium some recent theoretical developments in the field are detailed and experimental indications of such a regime in gated semiconductor quantum wires are described.
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Transport in a spin-incoherent Luttinger Liquid
Physical Review B, 2005Co-Authors: Gregory A. Fiete, Karyn Le Hur, Leon BalentsAbstract:We theoretically investigate transport in a spin-incoherent one-dimensional electron system, which may be realized in quantum wires at low-electron density and finite temperature. Both the pure and disordered cases are considered, both in finite wires and in the thermodynamic limit. The effect of Fermi-Liquid leads attached to the finite-length system is also addressed. In the infinite system, we find a phase diagram identical to that obtained for a spinless Luttinger Liquid, provided we make the identification $g=2{g}_{c}$, where $g$ is the interaction parameter in a spinless Luttinger Liquid and ${g}_{c}$ is the interaction parameter of the charge sector of a Luttinger-Liquid theory for electrons with spin. For a finite-length wire attached to Fermi-Liquid leads, the transport depends on the details of the disorder in the wire. A simple picture for the crossover from the spin-incoherent regime to the spin-coherent regime as the temperature is varied is also discussed, as well as some physical implications.
Leon Balents - One of the best experts on this subject based on the ideXlab platform.
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Transport in a spin-incoherent Luttinger Liquid
Physical Review B, 2005Co-Authors: Gregory A. Fiete, Karyn Le Hur, Leon BalentsAbstract:We theoretically investigate transport in a spin-incoherent one-dimensional electron system, which may be realized in quantum wires at low-electron density and finite temperature. Both the pure and disordered cases are considered, both in finite wires and in the thermodynamic limit. The effect of Fermi-Liquid leads attached to the finite-length system is also addressed. In the infinite system, we find a phase diagram identical to that obtained for a spinless Luttinger Liquid, provided we make the identification $g=2{g}_{c}$, where $g$ is the interaction parameter in a spinless Luttinger Liquid and ${g}_{c}$ is the interaction parameter of the charge sector of a Luttinger-Liquid theory for electrons with spin. For a finite-length wire attached to Fermi-Liquid leads, the transport depends on the details of the disorder in the wire. A simple picture for the crossover from the spin-incoherent regime to the spin-coherent regime as the temperature is varied is also discussed, as well as some physical implications.
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Spin pumping and magnetization dynamics in ferromagnet-Luttinger Liquid junctions
Physical Review B, 2004Co-Authors: Cristina Bena, Leon BalentsAbstract:We study spin transport between a ferromagnet with time-dependent magnetization and a conducting carbon nanotube or quantum wire, modeled as a Luttinger Liquid. The precession of the magnetization vector of the ferromagnet due for instance to an outside applied magnetic field causes spin pumping into an adjacent conductor. Conversely, the spin injection causes increased magnetization damping in the ferromagnet. We find that, if the conductor adjacent to the ferromagnet is a Luttinger Liquid, spin pumping/damping is suppressed by interactions, and the suppression has clear Luttinger Liquid power law temperature dependence. We apply our result to a few particular setups. First we study the effective Landau-Lifshitz-Gilbert (LLG) coupled equations for the magnetization vectors of the two ferromagnets in a FM-LL-FM junction. Also, we compute the Gilbert damping for a FM-LL and a FM-LL-metal junction.
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Luttinger-Liquid behaviour in carbon nanotubes
Nature, 1999Co-Authors: Marc Bockrath, David Cobden, Andrew G. Rinzler, Richard E. Smalley, Leon Balents, Paul L. MceuenAbstract: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.
Matthew P. A. Fisher - One of the best experts on this subject based on the ideXlab platform.
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Thermal transport in a Luttinger Liquid.
Physical Review Letters, 1996Co-Authors: Charles L. Kane, Matthew P. A. FisherAbstract:We study thermal transport in a one-dimensional (1D) interacting electron gas, employing the Luttinger Liquid model. Both thermal conductance and thermopower are analyzed for a pure 1D gas and with impurities. The universal ratio of electrical to thermal conductance in a Fermi Liquid---the Wiedemann-Franz law---is modified, whereas the thermopower is still linear in temperature. For a single impurity the Lorentz number is given by $L(T\ensuremath{\rightarrow}0){\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3L}_{0}/({2g+g}^{2})$---with ${L}_{0}$ the Fermi Liquid value---and the conductance $1/2lgl1$. For $gl1/2$ the Lorentz number diverges as $T\ensuremath{\rightarrow}0$. Possible relevance to thermal transport in conducting polymer systems is discussed.
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Transport in a one-channel Luttinger Liquid.
Physical review letters, 1992Co-Authors: Charles L. Kane, Matthew P. A. FisherAbstract:We study theoretically the transport of a one-channel Luttinger Liquid through a weak link. For repulsive electron interactions, the electrons are completely reflected by even the smallest scatterer, leading to a truly insulating weak link, in striking contrast to that for noninteracting electrons. At finite temperature (T) the conductance is nonzero, and is predicted to vanish as a power of T. At T=0 power-law current-voltage characteristics are predicted. For attractive interactions, a Luttinger Liquid is argued to be perfectly transmitted through even the largest of barriers. The role of Fermi-Liquid leads is also explored.
D N Aristov - One of the best experts on this subject based on the ideXlab platform.
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conductance scaling of junctions of Luttinger Liquid wires out of equilibrium
Physical Review B, 2018Co-Authors: D N Aristov, P WolfleAbstract:We develop the renormalization group theory of the conductances of $N$-lead junctions of spinless Luttinger-Liquid wires as functions of bias voltages applied to $N$ independent Fermi-Liquid reservoirs. Based on the perturbative results up to second order in the interaction we demonstrate that the conductances obey scaling. The corresponding renormalization group $\ensuremath{\beta}$ functions are derived up to second order.
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tunneling into a Luttinger Liquid revisited
Physical Review Letters, 2010Co-Authors: I. V. Gornyi, D. G. Polyakov, D N Aristov, A P Dmitriev, Yu V Kachorovskii, P WolfleAbstract:We study how electron-electron interactions renormalize tunneling into a Luttinger Liquid beyond the lowest order of perturbation in the tunneling amplitude. We find that the conventional fixed point has a finite basin of attraction only in the point contact model, but a finite size of the contact makes it generically unstable to the tunneling-induced breakup of the Liquid into two independent parts. In the course of renormalization to the nonperturbative-in-tunneling fixed point, the tunneling conductance may show a nonmonotonic behavior with temperature or bias voltage.
