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Europhysics Letters (EPL)

Significant Interaction-Induced Enhancement of Persistent Currents in 2D Disordered Cylinders

Richard Berkovits, Y. Avishai

Published Feb 20, 1995• 34 citations
Publisher

Abstract

The persistent current of small disordered 2D cylinders is calculated by an exact numerical diagonalization of a tight-binding interacting model Hamiltonian. A significant enhancement in the ensemble-averaged persistent current amplitude occurs for a certain range of electron-electron interaction strength. For similar 1D and quasi-1D geometries no significant enhancement is observed. This current enhancement is due to the shift of the onset point of the Mott-Hubbard metal insulator transition. Our results may provide an explanation to a longstanding problem in mesoscopic physics, namely, the high values of persistent current measured in experiment.

DOI
10.1209/0295-5075/29/6/008

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The persistent current of small disordered 2D cylinders is calculated by an exact numerical diagonalization of a tight-binding interacting model Hamiltonian. A significant enhancement in the ensemble-averaged persistent current amplitude occurs for a certain range of electron-electron interaction strength. For similar 1D and quasi-1D geometries no significant enhancement is observed. This current enhancement is due to the shift of the onset point of the Mott-Hubbard metal insulator transition. Our results may provide an explanation to a longstanding problem in mesoscopic physics, namely, the high values of persistent current measured in experiment.
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 VF{\mathit{V}}_{\mathit{F}}VF​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.
Persistent currents in disordered mesoscopic rings threaded by a magnetic flux are calculated using exact diagonalization methods in the one-dimensional (1D) case and self-consistent Hartree-Fock treatments for two dimensional (2D) systems. For multichannel systems, a comparative study between models of spinless or spinfull (Hubbard) fermions has been done. First, it is shown that a purely one-dimensional model can not reproduce the correct order of magnitude of the observed currents. For 2D systems, going beyond first order pertubative calculations, we show that the second harmonic of the current is {\it strongly suppressed} in the case of spinless fermion models but {\it significantly enhanced} for the Hubbard model. This reduction (resp. increase) of the second harmonic is related to a strong increase (resp. reduction) of the spacial charge density fluctuations. Our work underlines the important role of the spin degrees of freedom in the persistent currents.
We investigate, by numerically calculating the charge stiffness, the effects of random diagonal disorder and electron-electron interaction on the nature of the ground state in the 2D Hubbard model through the finite-size exact diagonalization technique. By comparing with the corresponding 1D Hubbard model results and by using heuristic arguments we conclude that it is unlikely that there is a 2D metal-insulator quantum phase transition, although the effect of interaction in some range of parameters is to substantially enhance the noninteracting charge stiffness.
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.