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arXiv:cond-mat/0310055 · Physical review. B, Condensed matter

Persistent currents in small, imperfect Hubbard rings

Pekka Koskinen, M. Manninen

Published Nov 4, 2003• 13 citations
arXivHTMLPDF

Abstract

We have done a study with small, imperfect Hubbard rings with exact diagonalization. The results for few-electron rings show that the imperfection, whether localized or not, nearly always decreases, but can also increase the persistent current, depending on the character of the imperfection and the on-site interaction. The calculations are generally in agreement with more specialized studies. In most cases the electron spin plays an important role.

DOI
10.1103/physrevb.68.195304

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We have done a study with small, imperfect Hubbard rings with exact diagonalization. The results for few-electron rings show that the imperfection, whether localized or not, nearly always decreases, but can also increase the persistent current, depending on the character of the imperfection and the on-site interaction. The calculations are generally in agreement with more specialized studies. In most cases the electron spin plays an important role.
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.
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.
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.
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 and spin-charge separation are studied in a one-dimensional (1D) Hubbard ring with side sites connected to the even sites of the ring. At half filling, the persistent current is always paramagnetic and has a period of flux quantum. Away from half filling, as the onsite repulsion UUU increases, the sign of the current may oscillate depending on the total number of electrons Ne{N}_{e}Ne​ and the hopping ttt between the ring site and the side site. For small hopping ttt, the number of electrons ${N}_{e}^{\ensuremath{'}}$ in the ring sites plays an important role in determining the sign of the current. In contrast to the 1D Hubbard model, a weak or a moderate UUU can strongly enhance the persistent current while the hopping ttt always suppresses the current. The study on the transmittance of the ring with two connected leads indicates that in the large UUU and small ttt case, the transmittance varies with a period $1∕{N}_{e}^{\ensuremath{'}}$ of a flux quantum, demonstrating a spin-charge separation in this system.