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Physical Review Letters

Persistent currents in an interacting 1D disordered ring: Manifestations of the Mott-Hubbard transition

Michael Abraham, Richard Berkovits

Published Mar 8, 1993• 141 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.70.1509

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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.
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.
Using numerical exact diagonalization and analytical variational calculations, we examine the effect of an electronic two-band structure on the persistent current of an interacting disordered one-dimensional ring. Several different features in comparison to a single band model are encountered. Among them are a transition in the magnitude of current for a critical ratio of the hopping elements in the two bands, and a large increase in the rms value of the persistent current for certain values of interaction and disorder. Possible experimental implications are discussed.
A comparison between the persistent currents in a diagonal and an off-diagonal disordered one-dimensional (1D) interacting ring, using a numerical exact diagonalization method, reveals essential differences in behavior. While the diagonally disordered system exhibits some increase in the current as a function of electron-electron (e-e) interactions, the off-diagonally disordered system shows a consistent decrease. The different behavior of the two systems is explained by the different nature of the many-body eigenstates in both cases.
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.