Physical review. B, Condensed matter

Thermopower of an infinite Luttinger liquid

Igor Romanovsky, Ilya V. Krive, Eduard N. Bogachek, Uzi Landman

Published Feb 1, 2002• 17 citations

Abstract

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.

DOI: 10.1103/physrevb.65.075115

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Physical review. B, Condensed matter

Thermopower of an infinite Luttinger liquid

Igor Romanovsky, Ilya V. Krive, Eduard N. Bogachek, Uzi Landman

Published Feb 1, 2002• 17 citations

Publisher

Abstract

{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.

DOI: 10.1103/physrevb.65.075115

Related papers

Interaction enhanced thermopower in a Luttinger liquid

Ilya V. Krive, Eduard N. Bogachek, Andrew G. Scherbakov +1 more

The thermopower ${S}_{L}(T)$ of a finite Luttinger liquid (LL) wire containing an impurity and connected to leads of noninteracting electrons is calculated. It is shown that at low temperatures ${k}_{B}T\ensuremath{\ll}{\ensuremath{\Delta}}_{L}\ensuremath{\simeq}\ensuremath{\Elzxh}{\mathbf{v}}_{F}/gL$ (L is the length of the wire, ${\mathbf{v}}_{F}$ is the Fermi velocity of the electrons, and g is the correlation parameter of the LL), ${S}_{L}(T)$ is described by a Mott-type formula. However, at higher temperatures, that is, when ${\ensuremath{\Delta}}_{L}<~{k}_{B}T\ensuremath{\ll}{\ensuremath{\varepsilon}}_{F},$ the expression for ${S}_{L}(T)$ contains an interaction-dependent factor. For strong interelectron interaction, the enhancement of the thermopower is large and it is much more pronounced for spinless electrons.The thermopower ${S}_{L}(T)$ of a finite Luttinger liquid (LL) wire containing an impurity and connected to leads of noninteracting electrons is calculated. It is shown that at low temperatures ${k}_{B}T\ensuremath{\ll}{\ensuremath{\Delta}}_{L}\ensuremath{\simeq}\ensuremath{\Elzxh}{\mathbf{v}}_{F}/gL$ (L is the length of the wire, ${\mathbf{v}}_{F}$ is the Fermi velocity of the electrons, and g is the correlation parameter of the LL), ${S}_{L}(T)$ is described by a Mott-type formula. However, at higher temperatures, that is, when ${\ensuremath{\Delta}}_{L}<~{k}_{B}T\ensuremath{\ll}{\ensuremath{\varepsilon}}_{F},$ the expression for ${S}_{L}(T)$ contains an interaction-dependent factor. For strong interelectron interaction, the enhancement of the thermopower is large and it is much more pronounced for spinless electrons.

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

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{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.

The thermopower

{S}_{L}(T)

of a finite Luttinger liquid (LL) wire containing an impurity and connected to leads of noninteracting electrons is calculated. It is shown that at low temperatures ${k}_{B}T\ensuremath{\ll}{\ensuremath{\Delta}}_{L}\ensuremath{\simeq}\ensuremath{\Elzxh}{\mathbf{v}}_{F}/gL$ (L is the length of the wire,

{\mathbf{v}}_{F}

is the Fermi velocity of the electrons, and g is the correlation parameter of the LL),

{S}_{L}(T)

is described by a Mott-type formula. However, at higher temperatures, that is, when ${\ensuremath{\Delta}}_{L}<~{k}_{B}T\ensuremath{\ll}{\ensuremath{\varepsilon}}_{F},$ the expression for

{S}_{L}(T)

contains an interaction-dependent factor. For strong interelectron interaction, the enhancement of the thermopower is large and it is much more pronounced for spinless electrons.

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.

{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.

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

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.