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

Journal of Physics Condensed Matter

Ballistic thermoelectric transport in a Luttinger liquid

Yu. V. Ivanov

Published Jun 1, 2010• 4 citations
Publisher

Abstract

The Seebeck and Peltier coefficients of a homogeneous Luttinger liquid are calculated in the ballistic regime. Nonlinearity of the electron spectrum is taken into account. It is shown that, in the framework of the defined approximations, the thermoelectric power of a Luttinger liquid is equal to zero, in agreement with the exponentially small thermopower of a one-dimensional degenerate Fermi gas. The Peltier coefficient is controlled by a nonequilibrium state of the system. It is finite and renormalized by the interaction in the case of a convective flow of a Luttinger liquid. The zero modes of bosonic excitations and the dispersion-induced contribution to the electric current operator are taken into account in calculations.

DOI
10.1088/0953-8984/22/24/245602

Related papers

Interacting Tomonaga-Lüttinger liquid with impurity for interaction constant $K = 1/2$: Thermopower investigation, entropy variation and heat capacity densities associated with thermoelectric particle transport

Abdellah Touati, Redoune Zamoum, Farhi Houssam Eddine

We investigate thermoelectric and thermodynamic properties of a Tomonaga-Luttinger liquid with interaction parameter $K=1/2$ in the presence of a localized impurity. Using bosonization and refermionization, we derive an exact expression for the thermopower in the nonlinear regime and obtain the corresponding Seebeck coefficient in linear response. At low temperature, the Seebeck coefficient follows a Mott-like relation governed by the energy dependence of the transmission coefficient and is found to be closely related to the entropy per particle. This connection allows us to derive using Kelvin formula the thermopower contribution to the entropy density variation and the charge-carriers contribution to the heat capacity density. Both quantities exhibit Mott-like behavior in the low-temperature regime. We apply our results to a fractional quantum Hall quantum point contact and to a one-channel quantum conductor coupled to an Ohmic environment. Our results demonstrate the close connection between thermoelectric transport and thermodynamic properties in interacting one-dimensional quantum systems.

arXiv:2609.11810•Sep 10, 2026•0 citations

Thermopower of an infinite Luttinger liquid

Igor Romanovsky, Ilya V. Krive, Eduard N. Bogachek +1 more

The thermopower of a Luttinger liquid (LL), originating from the energy dispersion of electrons at the Fermi level and/or from the backscattering of electrons by impurities, is analytically evaluated. It is shown that in both cases the thermopower is described by a corresponding Fermi-liquid formula renormalized by an interaction-dependent factor. For an infinite LL the renormalization coefficients decrease with an increase of the electron-electron interaction. In a realistic situation, when a LL wire is connected to leads of noninteracting electrons, the dispersion-induced thermopower in the limit of strong repulsive interaction is strongly suppressed, ${S}_{W}^{(d)}\ensuremath{\sim}{g}^{2}{S}_{0}^{(d)}\ensuremath{\ll}{S}_{0}^{(d)}$ (here ${S}_{0}^{(d)}$ is the corresponding Fermi-liquid value for the thermopower and $g\ensuremath{\ll}1$ is the LL correlation parameter), while the impurity-induced thermopower ${S}_{W}^{(i)}\ensuremath{\sim}{S}_{0}^{(i)}/g$ is enhanced by the interelectron interaction.

Physical review. B, Condensed matter•Feb 1, 2002•17 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

Thermopower of a Luttinger-liquid-based Two-channel Charge Kondo Circuit: Nonperturbative Solution

Anton V. Parafilo, T. K. T. Nguyen

Recently, the influence of electron-electron interactions on the thermoelectric transport in a two-channel charge Kondo circuit has been studied in [Phys. Rev. B 105, L121405 (2022)]. In this paper, we revisit the Luttinger-liquid-based model and discuss in details the limit where the spin field is noninteracting (\(g_\sigma = 1\)) and the interaction in the charge sector is repulsive (\(0< g_\rho \leq 1\)). The thermoelectric transport coefficients are computed nonperturbatively with respect to the reflection amplitude at the quantum point contact. At low temperatures the thermopower shows the non-Fermi liquid behavior in the vicinity of the Coulomb peaks. We also demonstrate that repulsive interaction results in the enhancement of the thermoelectrical power.

Communications in Physics•Feb 21, 2023•5 citations

Electrical and Thermal Transport in Inhomogeneous Luttinger Liquids

Wade DeGottardi, К. А. Матвеев

We study the transport properties of long quantum wires by generalizing the Luttinger liquid approach to allow for the finite lifetime of the bosonic excitations. Our theory accounts for long-range disorder and strong electron interactions, both of which are common features of experiments with quantum wires. We obtain the electrical and thermal resistances and thermoelectric properties of such quantum wires and find a strong deviation from perfect conductance quantization. We cast our results in terms of the thermal conductivity and bulk viscosity of the electron liquid and give the temperature scale above which the transport can be described by classical hydrodynamics.

arXiv:1412.0693•Physical Review Letters•Jun 12, 2015•17 citations

KINETIC PROCESSES IN FERMI-LUTTINGER LIQUIDS

A. Levchenko, T. MICKLITZ

In this work we discuss extensions of the pioneering analysis by Dzyaloshinski ǐ and Larkin [Sov.Phys.JETP 38, 202 (1974)] of correlation functions for one-dimensional Fermi systems, focusing on the effects of quasiparticle relaxation enabled by a nonlinear dispersion.Throughout the work we employ both, the weakly interacting Fermi gas picture and nonlinear Luttinger liquid theory to describe attenuation of excitations and explore the fermion-boson duality between both approaches.Special attention is devoted to the role of spin-exchange processes, effects of interaction screening, and integrability.Thermalization rates for electron-and hole-like quasiparticles, as well as the decay rate of collective plasmon excitations and the momentum space mobility of spin excitations are calculated for various temperature regimes.The phenomenon of spin-charge drag is considered and the corresponding momentum transfer rate is determined.We further discuss how momentum relaxation due to several competing mechanisms, viz.triple electron collisions, electron-phonon scattering, and long-range inhomogeneities affect transport properties, and highlight energy transfer facilitated by plasmons from the perspective of the inhomogeneous Luttinger liquid model.Finally, we derive the full matrix of thermoelectric coefficients at the quantum critical point of the first conductance plateau transition, and address magnetoconductance in ballistic semiconductor nanowires with strong Rashba spin-orbit coupling.

Журнал Экспериментальной и Теоретической Физики•Jan 1, 2021•1 citation
The Seebeck and Peltier coefficients of a homogeneous Luttinger liquid are calculated in the ballistic regime. Nonlinearity of the electron spectrum is taken into account. It is shown that, in the framework of the defined approximations, the thermoelectric power of a Luttinger liquid is equal to zero, in agreement with the exponentially small thermopower of a one-dimensional degenerate Fermi gas. The Peltier coefficient is controlled by a nonequilibrium state of the system. It is finite and renormalized by the interaction in the case of a convective flow of a Luttinger liquid. The zero modes of bosonic excitations and the dispersion-induced contribution to the electric current operator are taken into account in calculations.
Interacting Tomonaga-Lüttinger liquid with impurity for interaction constant K=1/2K = 1/2K=1/2: Thermopower investigation, entropy variation and heat capacity densities associated with thermoelectric particle transport
We investigate thermoelectric and thermodynamic properties of a Tomonaga-Luttinger liquid with interaction parameter K=1/2K=1/2K=1/2 in the presence of a localized impurity. Using bosonization and refermionization, we derive an exact expression for the thermopower in the nonlinear regime and obtain the corresponding Seebeck coefficient in linear response. At low temperature, the Seebeck coefficient follows a Mott-like relation governed by the energy dependence of the transmission coefficient and is found to be closely related to the entropy per particle. This connection allows us to derive using Kelvin formula the thermopower contribution to the entropy density variation and the charge-carriers contribution to the heat capacity density. Both quantities exhibit Mott-like behavior in the low-temperature regime. We apply our results to a fractional quantum Hall quantum point contact and to a one-channel quantum conductor coupled to an Ohmic environment. Our results demonstrate the close connection between thermoelectric transport and thermodynamic properties in interacting one-dimensional quantum systems.
The thermopower of a Luttinger liquid (LL), originating from the energy dispersion of electrons at the Fermi level and/or from the backscattering of electrons by impurities, is analytically evaluated. It is shown that in both cases the thermopower is described by a corresponding Fermi-liquid formula renormalized by an interaction-dependent factor. For an infinite LL the renormalization coefficients decrease with an increase of the electron-electron interaction. In a realistic situation, when a LL wire is connected to leads of noninteracting electrons, the dispersion-induced thermopower in the limit of strong repulsive interaction is strongly suppressed, ${S}_{W}^{(d)}\ensuremath{\sim}{g}^{2}{S}_{0}^{(d)}\ensuremath{\ll}{S}_{0}^{(d)}$ (here S0(d){S}_{0}^{(d)}S0(d)​ is the corresponding Fermi-liquid value for the thermopower and $g\ensuremath{\ll}1$ is the LL correlation parameter), while the impurity-induced thermopower ${S}_{W}^{(i)}\ensuremath{\sim}{S}_{0}^{(i)}/g$ is enhanced by the interelectron interaction.
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.
Recently, the influence of electron-electron interactions on the thermoelectric transport in a two-channel charge Kondo circuit has been studied in [Phys. Rev. B 105, L121405 (2022)]. In this paper, we revisit the Luttinger-liquid-based model and discuss in details the limit where the spin field is noninteracting (gσ=1g_\sigma = 1gσ​=1) and the interaction in the charge sector is repulsive (0<gρ≤10< g_\rho \leq 10<gρ​≤1). The thermoelectric transport coefficients are computed nonperturbatively with respect to the reflection amplitude at the quantum point contact. At low temperatures the thermopower shows the non-Fermi liquid behavior in the vicinity of the Coulomb peaks. We also demonstrate that repulsive interaction results in the enhancement of the thermoelectrical power.
We study the transport properties of long quantum wires by generalizing the Luttinger liquid approach to allow for the finite lifetime of the bosonic excitations. Our theory accounts for long-range disorder and strong electron interactions, both of which are common features of experiments with quantum wires. We obtain the electrical and thermal resistances and thermoelectric properties of such quantum wires and find a strong deviation from perfect conductance quantization. We cast our results in terms of the thermal conductivity and bulk viscosity of the electron liquid and give the temperature scale above which the transport can be described by classical hydrodynamics.
In this work we discuss extensions of the pioneering analysis by Dzyaloshinski ǐ and Larkin [Sov.Phys.JETP 38, 202 (1974)] of correlation functions for one-dimensional Fermi systems, focusing on the effects of quasiparticle relaxation enabled by a nonlinear dispersion.Throughout the work we employ both, the weakly interacting Fermi gas picture and nonlinear Luttinger liquid theory to describe attenuation of excitations and explore the fermion-boson duality between both approaches.Special attention is devoted to the role of spin-exchange processes, effects of interaction screening, and integrability.Thermalization rates for electron-and hole-like quasiparticles, as well as the decay rate of collective plasmon excitations and the momentum space mobility of spin excitations are calculated for various temperature regimes.The phenomenon of spin-charge drag is considered and the corresponding momentum transfer rate is determined.We further discuss how momentum relaxation due to several competing mechanisms, viz.triple electron collisions, electron-phonon scattering, and long-range inhomogeneities affect transport properties, and highlight energy transfer facilitated by plasmons from the perspective of the inhomogeneous Luttinger liquid model.Finally, we derive the full matrix of thermoelectric coefficients at the quantum critical point of the first conductance plateau transition, and address magnetoconductance in ballistic semiconductor nanowires with strong Rashba spin-orbit coupling.