Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/9504040

Low-temperature transport of correlated electrons

Reinhold Egger, Maura Sassetti, Weiss, U.

Published Apr 11, 1995• 2 citations
arXivHTMLPDF

Abstract

Transport properties of a single-channel Luttinger liquid impinging on a barrier have been studied for $g=1/2 - ε$, where $g$ is the dimensionless interaction constant and $|ε| \ll 1$. The relevant diagrams contributing to the conductance are identified and evaluated in all orders. Our approach represents a leading-log summation which is valid for sufficiently low temperature and small voltage. The asymptotic low-temperature corrections exhibit a turnover from the $T^{2/g-2}$ behavior to a universal $T^2$ law as the voltage is increased.

DOI
10.48550/arxiv.cond-mat/9504040

Related papers

Low-temperature nonequilibrium transport in a Luttinger liquid

Ulrich Weiß, Reinhold Egger, Maura Sassetti

The temperature-dependent nonlinear conductance for transport of a Luttinger liquid through a barrier is calculated in the nonperturbative regime for g=1/2-\ensuremath{\epsilon}, where g is the dimensionless interaction constant. To describe the low-energy behavior, we perform a leading-logarithmic summation of all diagrams contributing to the conductance which is valid for \ensuremath{\Vert}\ensuremath{\epsilon}\ensuremath{\Vert}\ensuremath{\ll}1. With increasing external voltage, the asymptotic low-temperature behavior displays a turnover from the ${\mathit{T}}^{2/\mathit{g}\mathrm{\ensuremath{-}}2}$ to a universal ${\mathit{T}}^{2}$ law.

arXiv:cond-mat/9509150•Physical review. B, Condensed matter•Dec 15, 1995•35 citations

Transport of interacting electrons through a potential barrier: Nonperturbative RG approach

D. N. Aristov, P. Wölfle

We calculate the linear response conductance of electrons in a Luttinger liquid with arbitrary interaction g 2 , and subject to a potential barrier of arbitrary strength, as a function of temperature. We first map the Hamiltonian in the basis of scattering states into an effective low-energy Hamiltonian in current algebra form. Analyzing the perturbation theory in the fermionic representation the diagrams contributing to the renormalization group (RG) β-function are identified. A universal part of the β-function is given by a ladder series and summed to all orders in g 2 . First non-universal corrections beyond the ladder series are discussed. The RG-equation for the temperature-dependent conductance is solved analytically. Our result agrees with known limiting cases.

arXiv:0709.1562•Europhysics Letters (EPL)•Mar 18, 2008•20 citations

Transport in a one-channel Luttinger liquid

C. L. Kane, Matthew P. A. Fisher

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.

Physical Review Letters•Feb 24, 1992•1,131 citations

Thermal Transport in a Luttinger Liquid

C. L. Kane, Matthew P. A. Fisher

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 $1/2<g<1$. For $g<1/2$ the Lorentz number diverges as $T\ensuremath{\rightarrow}0$. Possible relevance to thermal transport in conducting polymer systems is discussed.

arXiv:cond-mat/9509068•Physical Review Letters•Apr 22, 1996•194 citations

Transport in a Luttinger liquid with dissipation: Two impurities

Leiming Chen, Zoran Ristivojević, Thomas Nattermann

We consider theoretically the transport in a one-channel spinless Luttinger liquid with two strong impurities in the presence of dissipation. As a difference with respect to the dissipation free case, where the two impurities fully transmit electrons at resonance points, the dissipation prevents complete transmission in the present situation. A rich crossover diagram for the conductance as a function of applied voltage, temperature, dissipation strength, Luttinger liquid parameter $K$, and the deviation from the resonance condition is obtained. For weak dissipation and $1/2<K<1$, the conduction shows a nonmonotonic increase as a function of temperature or voltage. For strong dissipation the conduction increases monotonically but is exponentially small.

arXiv:0906.3995•Physical Review B•Nov 2, 2009•0 citations

From Tomonaga-Luttinger to Fermi liquid in transport through a tunneling barrier

Vadim V. Ponomarenko, Naoto Nagaosa

The finiteness of the length of a one-channel wire results in a crossover from Tomonaga-Luttinger to Fermi-liquid behavior with lowering energy scale. Under the condition that the voltage drop $(V)$ mostly occurs across a tunnel barrier inside the wire, we determined the coefficients of temperature and voltage expansion for low-energy conductance as a function of the interaction strength and the right and left traversal times. At higher voltage, the finite-length contribution exhibits oscillations related to both traversal times and becomes a slowly decaying correction to the scale-invariant ${V}^{1/g\ensuremath{-}1}$ dependence of the conductance.

arXiv:cond-mat/9709262•Physical review. B, Condensed matter•Nov 15, 1997•8 citations
Transport properties of a single-channel Luttinger liquid impinging on a barrier have been studied for g=1/2−εg=1/2 - εg=1/2−ε, where ggg is the dimensionless interaction constant and ∣ε∣≪1|ε| \ll 1∣ε∣≪1. The relevant diagrams contributing to the conductance are identified and evaluated in all orders. Our approach represents a leading-log summation which is valid for sufficiently low temperature and small voltage. The asymptotic low-temperature corrections exhibit a turnover from the T2/g−2T^{2/g-2}T2/g−2 behavior to a universal T2T^2T2 law as the voltage is increased.
The temperature-dependent nonlinear conductance for transport of a Luttinger liquid through a barrier is calculated in the nonperturbative regime for g=1/2-\ensuremath{\epsilon}, where g is the dimensionless interaction constant. To describe the low-energy behavior, we perform a leading-logarithmic summation of all diagrams contributing to the conductance which is valid for \ensuremath{\Vert}\ensuremath{\epsilon}\ensuremath{\Vert}\ensuremath{\ll}1. With increasing external voltage, the asymptotic low-temperature behavior displays a turnover from the ${\mathit{T}}^{2/\mathit{g}\mathrm{\ensuremath{-}}2}$ to a universal T2{\mathit{T}}^{2}T2 law.
We calculate the linear response conductance of electrons in a Luttinger liquid with arbitrary interaction g 2 , and subject to a potential barrier of arbitrary strength, as a function of temperature. We first map the Hamiltonian in the basis of scattering states into an effective low-energy Hamiltonian in current algebra form. Analyzing the perturbation theory in the fermionic representation the diagrams contributing to the renormalization group (RG) β-function are identified. A universal part of the β-function is given by a ladder series and summed to all orders in g 2 . First non-universal corrections beyond the ladder series are discussed. The RG-equation for the temperature-dependent conductance is solved analytically. Our result agrees with known limiting cases.
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.
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 L0{L}_{0}L0​ the Fermi liquid value---and the conductance 1/2<g<11/2<g<11/2<g<1. For g<1/2g<1/2g<1/2 the Lorentz number diverges as $T\ensuremath{\rightarrow}0$. Possible relevance to thermal transport in conducting polymer systems is discussed.
We consider theoretically the transport in a one-channel spinless Luttinger liquid with two strong impurities in the presence of dissipation. As a difference with respect to the dissipation free case, where the two impurities fully transmit electrons at resonance points, the dissipation prevents complete transmission in the present situation. A rich crossover diagram for the conductance as a function of applied voltage, temperature, dissipation strength, Luttinger liquid parameter KKK, and the deviation from the resonance condition is obtained. For weak dissipation and 1/2<K<11/2<K<11/2<K<1, the conduction shows a nonmonotonic increase as a function of temperature or voltage. For strong dissipation the conduction increases monotonically but is exponentially small.
The finiteness of the length of a one-channel wire results in a crossover from Tomonaga-Luttinger to Fermi-liquid behavior with lowering energy scale. Under the condition that the voltage drop (V)(V)(V) mostly occurs across a tunnel barrier inside the wire, we determined the coefficients of temperature and voltage expansion for low-energy conductance as a function of the interaction strength and the right and left traversal times. At higher voltage, the finite-length contribution exhibits oscillations related to both traversal times and becomes a slowly decaying correction to the scale-invariant ${V}^{1/g\ensuremath{-}1}$ dependence of the conductance.