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Journal of Physics Condensed Matter

Persistent currents in 1D rings and the metal-insulator transition under strong long-range Coulomb repulsion

Richard Berkovits, V Frelikher, I. V. Yurkevich, A. A. Slutskin

Published Apr 4, 1994• 0 citations

Abstract

A perturbative approach for large (in comparison with electron overlap and onsite disorder) long-range Coulomb interaction is developed for a 1D ring model. The explicit expression for low-lying energy levels has been obtained. It is shown that in the case of strong repulsive long-range interaction persistent current does not depend exclusively on the filling factor nu =p/q but is extremely sensitive to its denominator q. It also depends on the common factor M of electrons and sites number. In the absence of a common factor (M=1) there exists only one quasiparticle that experiences no strong Coulomb interaction, thus moving freely with bare electron overlap, which provides an unexpectedly large persistent current. For the case of an arbitrary M and a large enough q a system of M weakly interacting quasiparticles has been introduced, which undergoes a metal-insulator transition at unusually small overlap even for a filling factor close to one half. Suppression of the persistent current by disorder is taken into account. Comparison of analytically obtained expressions with the results of numerical calculations shows a reasonable agreement.

DOI: 10.1088/0953-8984/6/14/011

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A perturbative approach for large (in comparison with electron overlap and onsite disorder) long-range Coulomb interaction is developed for a 1D ring model. The explicit expression for low-lying energy levels has been obtained. It is shown that in the case of strong repulsive long-range interaction persistent current does not depend exclusively on the filling factor nu =p/q but is extremely sensitive to its denominator q. It also depends on the common factor M of electrons and sites number. In the absence of a common factor (M=1) there exists only one quasiparticle that experiences no strong Coulomb interaction, thus moving freely with bare electron overlap, which provides an unexpectedly large persistent current. For the case of an arbitrary M and a large enough q a system of M weakly interacting quasiparticles has been introduced, which undergoes a metal-insulator transition at unusually small overlap even for a filling factor close to one half. Suppression of the persistent current by disorder is taken into account. Comparison of analytically obtained expressions with the results of numerical calculations shows a reasonable agreement.

Persistent current is a small but perpetual electric current that flows in metallic rings in the absence of any applied source. We compute the persistent currents of one-dimensional disordered metallic rings of interacting electrons in the presence of impurity on lattices up to 8-sites at half-filling and also away from half-filling using the Lanczos algorithm. For the case of half-filling, we observe that both interaction and disorder suppress the amplitude of the persistent currents by localizing the electrons. However, in the presence of disorder and away from half-filling, the Coulomb interaction is observed to enhance the persistent current. Furthermore, in the half-filled case, there is a transition from metal to insulator as U is increased significantly. In addition, shifting away from half-filling, the system is observed to remain in the metallic state irrespective of the value of the Coulomb repulsion (U). The observations are quite in agreement with the results from other techniques.

We present an exact calculation of the persistent current in interacting disordered 1D rings. This system exhibits a variety of interesting behaviors depending on the disorder and the strength of electron-electron interactions. We find that even for the disordered case the current at high values of interactions is strongly suppressed due to the Mott-Hubbard metal-insulator transition. We observe that no dramatic increase of the averaged current or its rms value as a result of interactions is possible for these systems.

We present an exact calculation of the persistent current of electrons with Hubbard interactions in disordered one-dimensional rings. Numerical simulations show that the currents exhibit an interesting dependence on the configuration and strength W of disorder, and the value of the Hubbard interaction U. Our numerical simulations show that disorder and interaction both can monotonically suppress the amplitude of the current. The interaction can sometimes enhance the current of a disordered ring depending on its configuration and degree of disorder, even though smaller than the corresponding ideal-ring value

{\mathit{V}}_{\mathit{F}}

e/L. We have also studied the effect of negative U, and shown that it can influence the current as the positive U does. Based on the eigenvalue theory of a matrix, we give a simple explanation of the effects of disorder and interaction on currents. The main results are consistent with the numerical results for the case of long-range Coulomb interactions.

The role of repulsive on-site and nearest-neighbor Coulomb interactions in disordered half-filled Aharanov-Bohm rings is studied by world-line quantum Monte Carlo simulations. The diverse dependence of the equilibrium persistent current on the couplings is found to relate systematically to the magnetic phase of the model: the maximum charge stiffness (or the persistent current) coexists with the phase-transition line between the dominant charge-density-wave state and the dominant spin-density-wave state. The stiffness vanishes with an increasing departure from the transition line. Thus in the disordered rings the Coulomb interactions can enhance the charge stiffness over the noninteracting limit in such a way as to drive the system toward the phase-transition regime. \textcopyright{} 1996 The American Physical Society.

In this paper, we study persistent charge and spin currents in the ground state of the one-dimensional mesoscopic Hubbard ring with repulsive interaction based on its Bethe-ansatz solution. We find that the persistent charge current is suppressed by the on-site Coulomb interaction more significantly at half-filling than away from half-filling. As the system size increases the charge current decays exponentially as I ∼ L −1 e − L /ξ in the half-filling case and decays in a power law away from the half-filling case. We also find that the persistent spin current is suppressed by the on-site Coulomb interaction, and it decays algebraically as the system size increases both at half-filling and away from half-filling.