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 Experimental and Theoretical Physics Letters

One-dimensional strongly interacting electrons with a single impurity: Conductance reemergence

V. V. Afonin, Victor Yu. Petrov

Published May 1, 2015• 4 citations
Publisher

Abstract

We show that the conductance of a 1D channel with one point-like impurity critically depends on the asymptotic behavior of the e - e interaction at low momenta k (about the inverse length of the channel). The conductance reemerges (contrary to the case of a point-like repulsive potential) if the potential satisfies the condition V ( k = 0) = 0. For example, this happens if the bare e - e interaction is screened by the charges in the bulk. The relation of this phenomenon to the long-range order present in the Luttinger model is discussed. We consider spinless electrons but generalization is straightforward.

DOI
10.1134/s0021364015090027

Related papers

One-dimensional strongly interacting electrons with single impurity: conductance reemergence

V. V. Afonin, Victor Yu. Petrov

We show that conductance of 1D channel with one point-like impurity critically depends on asymptotic behavior of e-e interaction at small momenta k (about inverse length of a channel). Conductance reemerges (contrary to the case of point-like repulsive potential) if potential V(k=0)= 0. For example, this happens if the bare e-e interaction is screened by the charges in the bulk. The relation of this phenomena to the long-range order present in the Luttinger model is discussed.

arXiv:1406.2297•Jun 9, 2014•0 citations

On the Exact Solution for a Luttinger Liquid with Repulsion and a Single Point Impurity

V. V. Afonin, Victor Yu. Petrov

The expression for the conductance of a 1D channel, which has been obtained using the well-known exact solution, is analyzed. It is shown that in the case of strong electron—electron interaction, the slowest (linear in frequency) asymptotics of the conductance is determined by the behavior of electron—electron interaction in the region of transition from 1D to 3D motion realized near the impurity.

Журнал Экспериментальной и Теоретической Физики•Dec 15, 2023•0 citations

On the Exact Solution for a Luttinger Liquid with Repulsion and a Single Point Impurity

V. V. Afonin, Victor Yu. Petrov

Abstract The expression for the conductance of a 1D channel, which has been obtained using the well-known exact solution, is analyzed. It is shown that in the case of strong electron—electron interaction, the slowest (linear in frequency) asymptotics of the conductance is determined by the behavior of electron—electron interaction in the region of transition from 1D to 3D motion realized near the impurity.

Journal of Experimental and Theoretical Physics•Sep 1, 2023•1 citation

Resonant fractional conductance through a 1D Wigner chain

Rose Davies, Igor V. Lerner, I. V. Yurkevich

Abstract In recent experiments on conductance of one-dimensional (1D) channels in ultra-clean samples, a diverse set of plateaus were found at fractions of the quantum of conductance in zero magnetic field. We consider a discrete model of strongly interacting electrons in a clean 1D system where the current between weak tunneling contacts is carried by fractionally charged solutions. While in the spinless case conductance remains unaffected by the interaction, as is typical for the strongly interacting clean 1D systems, we demonstrate that in the spinful case the peak conductance takes fractional values that depend on the filling factor of the 1D channel.

arXiv:2307.07877•Communications Physics•Feb 28, 2024•3 citations

Resonant tunneling and low-energy impurity behavior in a resonant-level model

Vadim V. Ponomarenko

We study the effect of screening of an impurity charge by conduction electrons on resonant tunneling at arbitrary energy of the impurity level. We examine the exactly solvable model of the resonant level. We find the ground-state solutions of the model at all possible Coulomb interactions. The principle of equivalence between its universal behavior and the Kondo model is proved. However, the dependence of its scale invariant variable on the bare variables has different forms in two different regions of the parameter variations. This means that besides the well-known Kondo-like fixed point of the renormalization at weak Coulomb interaction a new stable point exists. The latter determines a singular low-energy behavior of the impurity. Based on the solution, the tunneling amplitude is calculated. It is shown that for a narrow gap or quasi-one-dimensional junction a severe renormalization of the one-electron half-width ${\mathrm{\ensuremath{\Gamma}}}_{0}$ occurs ${\mathrm{\ensuremath{\Gamma}}}_{\mathit{R}}$\ensuremath{\propto}${\mathrm{\ensuremath{\Gamma}}}_{0}$(${\mathrm{\ensuremath{\Gamma}}}_{0}$/D${)}^{\mathrm{\ensuremath{\alpha}}/(1\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\alpha}})}$. The comparison with perturbation results is discussed. Finally the conductance of the junction with randomly located impurities is calculated to clarify the crucial role of the non-Fermi-liquid behavior on the resonant tunneling under certain conditions.

Physical review. B, Condensed matter•Aug 15, 1993•30 citations

Interplay between electron-electron interactions and impurities in one-dimensional rings

弘之 森

The persistent current and charge stiffness of a one-dimensional Luttinger liquid on a ring threaded by a magnetic flux are calculated by Monte Carlo simulation. By changing the random impurity potential strength and the electron-electron interaction, we see a crossover behavior between weak- and strong-impurity limits. For weak-impurity potentials, interactions enhance impurity effects, that is, interactions decrease the current and the stiffness. On the other hand, interactions tend to screen impurities when the impurity potential is strong. Temperature dependence of the persistent current and the charge stiffness shows a peak at a characteristic temperature, consistent with a recent single-impurity study.

arXiv:cond-mat/9411068•Physical review. B, Condensed matter•May 15, 1995•11 citations
We show that the conductance of a 1D channel with one point-like impurity critically depends on the asymptotic behavior of the e - e interaction at low momenta k (about the inverse length of the channel). The conductance reemerges (contrary to the case of a point-like repulsive potential) if the potential satisfies the condition V ( k = 0) = 0. For example, this happens if the bare e - e interaction is screened by the charges in the bulk. The relation of this phenomenon to the long-range order present in the Luttinger model is discussed. We consider spinless electrons but generalization is straightforward.
Abstract In recent experiments on conductance of one-dimensional (1D) channels in ultra-clean samples, a diverse set of plateaus were found at fractions of the quantum of conductance in zero magnetic field. We consider a discrete model of strongly interacting electrons in a clean 1D system where the current between weak tunneling contacts is carried by fractionally charged solutions. While in the spinless case conductance remains unaffected by the interaction, as is typical for the strongly interacting clean 1D systems, we demonstrate that in the spinful case the peak conductance takes fractional values that depend on the filling factor of the 1D channel.
We study the effect of screening of an impurity charge by conduction electrons on resonant tunneling at arbitrary energy of the impurity level. We examine the exactly solvable model of the resonant level. We find the ground-state solutions of the model at all possible Coulomb interactions. The principle of equivalence between its universal behavior and the Kondo model is proved. However, the dependence of its scale invariant variable on the bare variables has different forms in two different regions of the parameter variations. This means that besides the well-known Kondo-like fixed point of the renormalization at weak Coulomb interaction a new stable point exists. The latter determines a singular low-energy behavior of the impurity. Based on the solution, the tunneling amplitude is calculated. It is shown that for a narrow gap or quasi-one-dimensional junction a severe renormalization of the one-electron half-width ${\mathrm{\ensuremath{\Gamma}}}_{0}$ occurs ${\mathrm{\ensuremath{\Gamma}}}_{\mathit{R}}$\ensuremath{\propto}${\mathrm{\ensuremath{\Gamma}}}_{0}$(${\mathrm{\ensuremath{\Gamma}}}_{0}$/D${)}^{\mathrm{\ensuremath{\alpha}}/(1\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\alpha}})}$. The comparison with perturbation results is discussed. Finally the conductance of the junction with randomly located impurities is calculated to clarify the crucial role of the non-Fermi-liquid behavior on the resonant tunneling under certain conditions.
The persistent current and charge stiffness of a one-dimensional Luttinger liquid on a ring threaded by a magnetic flux are calculated by Monte Carlo simulation. By changing the random impurity potential strength and the electron-electron interaction, we see a crossover behavior between weak- and strong-impurity limits. For weak-impurity potentials, interactions enhance impurity effects, that is, interactions decrease the current and the stiffness. On the other hand, interactions tend to screen impurities when the impurity potential is strong. Temperature dependence of the persistent current and the charge stiffness shows a peak at a characteristic temperature, consistent with a recent single-impurity study.