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

Physical review. B, Condensed matter

Conductivity of an interacting two-channel Tomonaga-Luttinger model

T. Kimura, Kazuhiko Kuroki, Hideo Aoki, Mikio Eto

Published Jun 15, 1994• 8 citations
Publisher

Abstract

Conductivity of a coupled two-channel dirty Tomonaga-Luttinger model is calculated from the Mori formalism. We find that the conductivity becomes enhanced as the interchannel interaction is turned on even when the interaction is repulsive. This effect is opposite to those from the 2${\mathit{K}}_{\mathit{F}}$ charge-fluctuation coupling in systems with the channel separation 1/${\mathit{k}}_{\mathit{F}}$, and is considered to come from the suppressed charge-density-wave fluctuations.

DOI
10.1103/physrevb.49.16852

Related papers

Kondo effect in a Tomonaga-Luttinger liquid

Akira Furusaki, Naoto Nagaosa

The Kondo effect in a repulsively interacting electron system (Tomonaga-Luttinger liquid) is studied. By using the poor man's scaling method it is shown that the Kondo coupling in this model flows to the strong-coupling regime not only for the antiferromagnetic but also for the ferromagnetic case. The ground state is governed by stable strong-coupling fixed points where the impurity spin is completely screened; the fixed-point Hamiltonian consists of two semi-infinite Tomonaga-Luttinger liquids and a spin singlet. Specific heat, susceptibility, and conductance are calculated for low temperatures.

Physical Review Letters•Feb 7, 1994•204 citations

Conductance renormalization and conductivity of a multisubband Tomonaga-Luttinger model

T. Kimura

We studied the conductance renormalization and conductivity of multisubband Tomonaga-Luttinger models with intersubband interactions. We found that, as in single-band systems, the conductance of a multisubband system with an arbitrary number of subbands is not renormalized due to interaction between electrons. We derived a formula for the conductivity in multisubband models. We applied it to a simplified case and found that intersubband interaction enhances the conductivity, which is contrary to the intrasubband repulsive interaction, and that the conductivity is further enhanced for a larger number of subbands.

arXiv:cond-mat/0109116•Physical review. B, Condensed matter•Nov 15, 2001•1 citation

DC Josephson Effect in a Tomonaga–Luttinger Liquid

Yositake Takane

The dc Josephson effect in a one-dimensional Tomonaga-Luttinger (TL) liquid is studied on the basis of two bosonized models. We first consider a TL liquid sandwiched between two superconductors with a strong barrier at each interface. Both the interfaces are assumed to be perfect if the barrier potential is absent. We next consider a TL liquid with open boundaries, weakly coupled with two superconductors. Without putting strong barriers, we instead assume that the coupling at each interface is described by a tunnel junction. We calculate the Josephson current in each model, and find that the two models yield same results. The Josephson current is suppressed by repulsive electron-electron interactions. It is shown that the suppression is characterized by only the correlation exponent for the charge degrees of freedom. This result is inconsistent with a previously reported result, where the spin degrees of freedom also affects the suppression. The reason of this inconsistency is discussed.

arXiv:cond-mat/0411638•Journal of the Physical Society of Japan•Feb 15, 2002•4 citations

Berezinskii-Kosterlitz-Thouless transition in disordered multichannel Luttinger liquids

Max Jones, Igor V. Lerner, I. V. Yurkevich

We study the phase transition between conducting and insulating states taking place in disordered multichannel Luttinger liquids with interchannel interactions. We derive renormalization-group equations which are perturbative in disorder but nonperturbative in interaction. In the vicinity of the simultaneous phase transition in all channels, these equations become a set of coupled Berezinskii-Kosterlitz-Thouless equations, which we analyze within two models: an array of identical wires and a two-channel model with distinct channels. We show that a competition between disorder and interaction results in a variety of phases, expected to be observable at intermediate temperatures where the interaction and disorder are relevant but weak hybridization and the charge-density-wave interaction may be ignored.

arXiv:1709.07380•Physical review. B./Physical review. B•Nov 27, 2017•7 citations

Generation of spin-polarized currents in Zeeman-split Tomonaga-Luttinger models

T. Kimura, Kazuhiko Kuroki, Hideo Aoki

In a magnetic field an interacting electron gas in one dimension may be described as a Tomonaga-Luttinger model comprising two components with different Fermi velocities due to the Zeeman splitting. This destroys the spin-charge separation, and even the quantities such as the density-density correlation involve the spins. Specifically, we have shown that the ratio of the up-spin and down-spin conductivities in a dirty system diverges at low temperatures like an inverse power of the temperature, resulting in a spin-polarized current. In finite, clean systems the conductance becomes different for up and down spins as another manifestation of the electron-electron interaction. \textcopyright{} 1996 The American Physical Society.

arXiv:cond-mat/9510125•Physical review. B, Condensed matter•Apr 15, 1996•42 citations

Tomonaga-Luttinger liquid physics in electronic quantum circuits

S. Jézouin, Mathias Albert, François D. Parmentier +5 more

In one-dimensional conductors, Coulomb interactions result in correlated electronic systems called Tomonaga-Luttinger liquids (TLL). The TLL physics also applies to other many-body phenomena, providing complementary viewpoints while benefiting from the powerful TLL framework. One such phenomenon is the low-energy conductance suppression of a quantum coherent conductor embedded in a dissipative circuit, an effect called dynamical Coulomb blockade. Here we investigate the basic class of mesoscopic circuits constituted by a short single-channel quantum conductor in series with a resistance R. Remarkably, such circuits can be mapped on a TLL of interaction parameter 1/(1+Re^2/h), with an impurity. From this mapping, generalized to realistic dissipative circuits, a scaling law for the suppressed conductance is derived at R=h/e^2, and small deviations computed for R \neq h/e^2. We find that the scaling law is obeyed by our data for arbitrary quantum channels, emulated by a Ga(Al)As quantum point contact, and by the recent data of Mebrahtu et al. [Nature 488, 61 (2012)] obtained using a carbon nanotube. This demonstrates a highly tunable test-bed for TLL physics, and consolidates a recently proposed phenomenological expression for the conductance of a quantum channel in a linear circuit.

•Jan 17, 2013•0 citations
Conductivity of a coupled two-channel dirty Tomonaga-Luttinger model is calculated from the Mori formalism. We find that the conductivity becomes enhanced as the interchannel interaction is turned on even when the interaction is repulsive. This effect is opposite to those from the 2KF{\mathit{K}}_{\mathit{F}}KF​ charge-fluctuation coupling in systems with the channel separation 1/kF{\mathit{k}}_{\mathit{F}}kF​, and is considered to come from the suppressed charge-density-wave fluctuations.
The Kondo effect in a repulsively interacting electron system (Tomonaga-Luttinger liquid) is studied. By using the poor man's scaling method it is shown that the Kondo coupling in this model flows to the strong-coupling regime not only for the antiferromagnetic but also for the ferromagnetic case. The ground state is governed by stable strong-coupling fixed points where the impurity spin is completely screened; the fixed-point Hamiltonian consists of two semi-infinite Tomonaga-Luttinger liquids and a spin singlet. Specific heat, susceptibility, and conductance are calculated for low temperatures.
We studied the conductance renormalization and conductivity of multisubband Tomonaga-Luttinger models with intersubband interactions. We found that, as in single-band systems, the conductance of a multisubband system with an arbitrary number of subbands is not renormalized due to interaction between electrons. We derived a formula for the conductivity in multisubband models. We applied it to a simplified case and found that intersubband interaction enhances the conductivity, which is contrary to the intrasubband repulsive interaction, and that the conductivity is further enhanced for a larger number of subbands.
The dc Josephson effect in a one-dimensional Tomonaga-Luttinger (TL) liquid is studied on the basis of two bosonized models. We first consider a TL liquid sandwiched between two superconductors with a strong barrier at each interface. Both the interfaces are assumed to be perfect if the barrier potential is absent. We next consider a TL liquid with open boundaries, weakly coupled with two superconductors. Without putting strong barriers, we instead assume that the coupling at each interface is described by a tunnel junction. We calculate the Josephson current in each model, and find that the two models yield same results. The Josephson current is suppressed by repulsive electron-electron interactions. It is shown that the suppression is characterized by only the correlation exponent for the charge degrees of freedom. This result is inconsistent with a previously reported result, where the spin degrees of freedom also affects the suppression. The reason of this inconsistency is discussed.
We study the phase transition between conducting and insulating states taking place in disordered multichannel Luttinger liquids with interchannel interactions. We derive renormalization-group equations which are perturbative in disorder but nonperturbative in interaction. In the vicinity of the simultaneous phase transition in all channels, these equations become a set of coupled Berezinskii-Kosterlitz-Thouless equations, which we analyze within two models: an array of identical wires and a two-channel model with distinct channels. We show that a competition between disorder and interaction results in a variety of phases, expected to be observable at intermediate temperatures where the interaction and disorder are relevant but weak hybridization and the charge-density-wave interaction may be ignored.
In a magnetic field an interacting electron gas in one dimension may be described as a Tomonaga-Luttinger model comprising two components with different Fermi velocities due to the Zeeman splitting. This destroys the spin-charge separation, and even the quantities such as the density-density correlation involve the spins. Specifically, we have shown that the ratio of the up-spin and down-spin conductivities in a dirty system diverges at low temperatures like an inverse power of the temperature, resulting in a spin-polarized current. In finite, clean systems the conductance becomes different for up and down spins as another manifestation of the electron-electron interaction. \textcopyright{} 1996 The American Physical Society.
In one-dimensional conductors, Coulomb interactions result in correlated electronic systems called Tomonaga-Luttinger liquids (TLL). The TLL physics also applies to other many-body phenomena, providing complementary viewpoints while benefiting from the powerful TLL framework. One such phenomenon is the low-energy conductance suppression of a quantum coherent conductor embedded in a dissipative circuit, an effect called dynamical Coulomb blockade. Here we investigate the basic class of mesoscopic circuits constituted by a short single-channel quantum conductor in series with a resistance R. Remarkably, such circuits can be mapped on a TLL of interaction parameter 1/(1+Re^2/h), with an impurity. From this mapping, generalized to realistic dissipative circuits, a scaling law for the suppressed conductance is derived at R=h/e^2, and small deviations computed for R \neq h/e^2. We find that the scaling law is obeyed by our data for arbitrary quantum channels, emulated by a Ga(Al)As quantum point contact, and by the recent data of Mebrahtu et al. [Nature 488, 61 (2012)] obtained using a carbon nanotube. This demonstrates a highly tunable test-bed for TLL physics, and consolidates a recently proposed phenomenological expression for the conductance of a quantum channel in a linear circuit.