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/9404072

Persistent Current of a One-Dimensional Wigner Crystal-Ring

Ilya V. Krive, Robert I Shekhter, S. M. Girvin, M. Jonson

Published Apr 22, 1994• 1 citation
arXivHTMLPDF

Abstract

We calculate the magnetic moment (`persistent current') in a strongly correlated electron system --- a Wigner crystal --- in a one-dimensional ballistic ring. The flux- and temperature dependence of the persistent current is shown to be essentially the same as for a system of non-interacting electrons. In contrast, by incorporating into the ring geometry a tunnel barrier, that pins the Wigner crystal, the current is suppressed and its temperature dependence is drastically changed. The competition between two temperature effects --- a reduced barrier height for macroscopic tunneling and a loss of quantum coherence --- results in a sharp peak in the temperature dependence, which for a rigid Wigner crystal appears at $T\sim 0.5\ \hbar s/L$, ($s$ is the sound velocity of the Wigner crystal, $L$ is the length of the ring).

DOI
10.48550/arxiv.cond-mat/9404072

Related papers

Persistent current and Wigner crystallization in a one dimensional quantum ring

Marc Siegmund, Markus Hofmann, Oleg Pankratov

We use Density Functional Theory to study interacting spinless electrons on a one-dimensional quantum ring in the density range where the system undergoes Wigner crystallization. The Wigner transition leads to a drastic ``collective'' electron localization due to the Wigner crystal pinning, provided a weak impurity potential is applied. To reveal this localization we examine a persistent current in a ring penetrated by a magnetic flux. Using the DFT-OEP method we calculated the current as a function of the interaction parameter r_S. We find that in the limit of vanishing impurity potential the persistent current stays constant up to a critical value of r_S^c=2.05 but shows a drastic exponential decay for larger r_S which reflects a formation of a pinned Wigner crystal. Above r_S^c the amplitude of the electron density oscillations exactly follows the (r_S-r_S^c)^{1/2} behaviour, confirming a second-order phase transition as expected in the mean-field-type OEP approximation.

arXiv:0711.2937•Nov 19, 2007•0 citations

Persistent currents in one-dimensional systems of strongly correlated electrons (review)

Andrei A. Zvyagin, Ilya V. Krive

Charge persistent currents in single-channel ballistic rings are investigated in various models of strongly correlated electrons (Wigner crystal, Luttinger liquid, Hubbard model, t–J model, and the fermion representation of the Heisenberg–Ising model). The primary objective of the survey is to compare the properties of Aharonov–Bohm oscillations for weakly and strongly correlated electrons and to formulate a set of persistent current characteristics that will unambiguously support the anomalous (departing from a Fermi liquid) behavior of one-dimensional electron systems. For this purpose the onset of the parity effect (dependence of the system response on whether the number of particles in the ring is odd or even) and various properties of the persistent current are analyzed in detail for model spinless fermions and real electrons. The influence of solitary impurities on the value and temperature dependence of the amplitude of the Aharanov–Bohm oscillations is also investigated. It is shown that the formation of a Wigner crystal (which is possible for weakly shielded Coulomb interaction) leads to a very pronounced anomalous (nonmonotonic) temperature dependence of the current in a nonideal ring. The properties of the charge current near the Mott metal–insulator transition are altered to the greatest degree by local types of electron–electron interaction.

Low Temperature Physics•Jul 1, 1995•11 citations

Correlation Effects in One-dimensional Electron Systems

P. Sandström

Theoretical studies suggest that an interacting one-dimensional electron system does not behave as a Fermi liquid. Instead, it is predicted to form a Luttinger liquid characterized e.g. by the absence of fermionic quasiparticles and interaction-dependent power-laws for transport quantities. So far, however, only a limited number of experiments have provided evidence for Luttinger liquid behavior. In this thesis we consider alternative methods to detect electronic correlations in one-dimensional electron systems based on our calculations of persistent currents and quantization of charge in ballistic single channel rings. The persistent current in an isolated impurity-free Luttinger liquid ring is found to be the same as for a system of non-interacting electrons. In contrast, a Luttinger liquid behavior is revealed if the ring is weakly connected to an electron reservoir and capacitively coupled to a gate electrode. The persistent current and the average charge in the ring are shown to change in a stepwise manner with the gate voltage at low temperatures. Both the step positions and the crossover temperatures are determined by the Luttinger liquid correlation parameter .alpha.(.alpha.c) which therefore can be measured. When a potential barrier is incorporated into the ring, the presence of strong interactions between electrons leads to a suppression of the persistent current and a change in its temperature dependence. A sharp maximum of the current is predicted to occur as a function of temperature. When two barriers are introduced into the ring, the possibility of resonant tunneling for the persistent current opens up. Two kinds of resonant behavior are discovered in the closed geometry: a current independent of the barrier transparency and a current analogous to the one with a single potential barrier. The persistent current in a ring containing a gas of fractionally charged excitations obeying fractional exclusion statistics is also studied. At finite temperatures, anomalous oscillations of the current are predicted as a manifestation of the statistics of the quasiparticles.

•Jan 1, 1998•0 citations

Possible bistability of the persistent current of two interacting electrons in a quantum ring

L. Wendler, Vladimir M. Fomin

We calculate the energy band structure and the persistent current of two interacting electrons in a quantum ring in the presence of a magnetic flux for a strongly correlated situation: a rotating Wigner molecule with internal vibrations. We discuss a possible bistability and hysteresis in the persistent current in dependence on the magnetic flux.

Physical review. B, Condensed matter•Jun 15, 1995•28 citations

Hartree-Fock Simulation of Persistent Current in Rings with Single Scatterer

R. Németh, Martin Moško

Using the self-consistent Hartree-Fock approximation for spinless electrons at zero temperature, we calculate the persistent current of the interacting electron gas in a one-dimensional ring containing a single δ barrier.Our results agree with correlated models like the Luttinger liquid model and lattice model with nearest-neighbor interaction.The persistent current is a sine-like function of magnetic flux.It decays with the ring length (L) faster than L -1 and eventually like L -α-1 , where α > 0 is universal.

Acta Physica Polonica A•Nov 1, 2005•1 citation

Spinless Hartree-Fock model of persistent current in rings with single scatterer: Comparison with correlated models

Radoslav Németh, Martin Moško

Using the self-consistent Hartree-Fock approximation for spinless electrons at zero temperature, we study the persistent current of the interacting electron gas in a one-dimensional continuous ring containing a single $δ$ barrier. We calculate the persistent current as a function of the ring circumference, magnetic flux threading the ring, barrier strength, etc. We compare our results with the results of correlated models like the Luttinger liquid model and the Hubbard model solved by means of the renormalization group. A good agreement is found. First, the persistent current decays with the increasing ring circumference ($L$) faster than $L^{-1}$ and eventually like $L^{-α-1}$, where $α>0$ depends only on the electron-electron interaction. Second, the persistent current is a sine-shaped function of magnetic flux. This sine-like dependence and in particular the universal power law $L^{-α-1}$ have sofar been believed to arise only in the correlated many-body models. Observation of these features within the Hartree-Fock model is a surprising result.

arXiv:cond-mat/0503146•Mar 7, 2005•0 citations
We calculate the magnetic moment (`persistent current') in a strongly correlated electron system --- a Wigner crystal --- in a one-dimensional ballistic ring. The flux- and temperature dependence of the persistent current is shown to be essentially the same as for a system of non-interacting electrons. In contrast, by incorporating into the ring geometry a tunnel barrier, that pins the Wigner crystal, the current is suppressed and its temperature dependence is drastically changed. The competition between two temperature effects --- a reduced barrier height for macroscopic tunneling and a loss of quantum coherence --- results in a sharp peak in the temperature dependence, which for a rigid Wigner crystal appears at T∼0.5 ℏs/LT\sim 0.5\ \hbar s/LT∼0.5 ℏs/L, (sss is the sound velocity of the Wigner crystal, LLL is the length of the ring).
We use Density Functional Theory to study interacting spinless electrons on a one-dimensional quantum ring in the density range where the system undergoes Wigner crystallization. The Wigner transition leads to a drastic ``collective'' electron localization due to the Wigner crystal pinning, provided a weak impurity potential is applied. To reveal this localization we examine a persistent current in a ring penetrated by a magnetic flux. Using the DFT-OEP method we calculated the current as a function of the interaction parameter r_S. We find that in the limit of vanishing impurity potential the persistent current stays constant up to a critical value of r_S^c=2.05 but shows a drastic exponential decay for larger r_S which reflects a formation of a pinned Wigner crystal. Above r_S^c the amplitude of the electron density oscillations exactly follows the (r_S-r_S^c)^{1/2} behaviour, confirming a second-order phase transition as expected in the mean-field-type OEP approximation.
Charge persistent currents in single-channel ballistic rings are investigated in various models of strongly correlated electrons (Wigner crystal, Luttinger liquid, Hubbard model, t–J model, and the fermion representation of the Heisenberg–Ising model). The primary objective of the survey is to compare the properties of Aharonov–Bohm oscillations for weakly and strongly correlated electrons and to formulate a set of persistent current characteristics that will unambiguously support the anomalous (departing from a Fermi liquid) behavior of one-dimensional electron systems. For this purpose the onset of the parity effect (dependence of the system response on whether the number of particles in the ring is odd or even) and various properties of the persistent current are analyzed in detail for model spinless fermions and real electrons. The influence of solitary impurities on the value and temperature dependence of the amplitude of the Aharanov–Bohm oscillations is also investigated. It is shown that the formation of a Wigner crystal (which is possible for weakly shielded Coulomb interaction) leads to a very pronounced anomalous (nonmonotonic) temperature dependence of the current in a nonideal ring. The properties of the charge current near the Mott metal–insulator transition are altered to the greatest degree by local types of electron–electron interaction.
Theoretical studies suggest that an interacting one-dimensional electron system does not behave as a Fermi liquid. Instead, it is predicted to form a Luttinger liquid characterized e.g. by the absence of fermionic quasiparticles and interaction-dependent power-laws for transport quantities. So far, however, only a limited number of experiments have provided evidence for Luttinger liquid behavior. In this thesis we consider alternative methods to detect electronic correlations in one-dimensional electron systems based on our calculations of persistent currents and quantization of charge in ballistic single channel rings. The persistent current in an isolated impurity-free Luttinger liquid ring is found to be the same as for a system of non-interacting electrons. In contrast, a Luttinger liquid behavior is revealed if the ring is weakly connected to an electron reservoir and capacitively coupled to a gate electrode. The persistent current and the average charge in the ring are shown to change in a stepwise manner with the gate voltage at low temperatures. Both the step positions and the crossover temperatures are determined by the Luttinger liquid correlation parameter .alpha.(.alpha.c) which therefore can be measured. When a potential barrier is incorporated into the ring, the presence of strong interactions between electrons leads to a suppression of the persistent current and a change in its temperature dependence. A sharp maximum of the current is predicted to occur as a function of temperature. When two barriers are introduced into the ring, the possibility of resonant tunneling for the persistent current opens up. Two kinds of resonant behavior are discovered in the closed geometry: a current independent of the barrier transparency and a current analogous to the one with a single potential barrier. The persistent current in a ring containing a gas of fractionally charged excitations obeying fractional exclusion statistics is also studied. At finite temperatures, anomalous oscillations of the current are predicted as a manifestation of the statistics of the quasiparticles.
Using the self-consistent Hartree-Fock approximation for spinless electrons at zero temperature, we calculate the persistent current of the interacting electron gas in a one-dimensional ring containing a single δ barrier.Our results agree with correlated models like the Luttinger liquid model and lattice model with nearest-neighbor interaction.The persistent current is a sine-like function of magnetic flux.It decays with the ring length (L) faster than L -1 and eventually like L -α-1 , where α > 0 is universal.
Using the self-consistent Hartree-Fock approximation for spinless electrons at zero temperature, we study the persistent current of the interacting electron gas in a one-dimensional continuous ring containing a single δδδ barrier. We calculate the persistent current as a function of the ring circumference, magnetic flux threading the ring, barrier strength, etc. We compare our results with the results of correlated models like the Luttinger liquid model and the Hubbard model solved by means of the renormalization group. A good agreement is found. First, the persistent current decays with the increasing ring circumference (LLL) faster than L−1L^{-1}L−1 and eventually like L−α−1L^{-α-1}L−α−1, where α>0α>0α>0 depends only on the electron-electron interaction. Second, the persistent current is a sine-shaped function of magnetic flux. This sine-like dependence and in particular the universal power law L−α−1L^{-α-1}L−α−1 have sofar been believed to arise only in the correlated many-body models. Observation of these features within the Hartree-Fock model is a surprising result.