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Canadian Journal of Physics

Systematic study of persistent currents in small systems: geometry and interactions

Brad L Johnson, George Kirczenow

Published Jan 1, 1998• 1 citation
Publisher

Abstract

The persistent current is calculated via an exact numerical diagonalization technique for both one- and two-dimensional-model geometries, with an emphasis on the effects of interactions. We find that the interactions can enhance the persistent current for the case of strong diagonal disorder by screening the on-site disorder potential. The screening effect is demonstrated by showing that for a particular configuration of disorder the many-body ground-state, which, for strong disorder, in the absence of interactions will fully occupy only the lowest energy sites, becomes more homogeneous with increasing interaction strength. We also show that the persistent-current vs.flux curves take on the qualitative character of the noninteracting, no-disorder curves for the same structure and filling, which is consistent with the screening mechanism.PACS Nos. 71.10.+x,31.10.+z

DOI
10.1139/cjp-76-3-173

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The persistent current is calculated via an exact numerical diagonalization technique for both one- and two-dimensional-model geometries, with an emphasis on the effects of interactions. We find that the interactions can enhance the persistent current for the case of strong diagonal disorder by screening the on-site disorder potential. The screening effect is demonstrated by showing that for a particular configuration of disorder the many-body ground-state, which, for strong disorder, in the absence of interactions will fully occupy only the lowest energy sites, becomes more homogeneous with increasing interaction strength. We also show that the persistent-current vs.flux curves take on the qualitative character of the noninteracting, no-disorder curves for the same structure and filling, which is consistent with the screening mechanism.PACS Nos. 71.10.+x,31.10.+z
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 multichannel mesoscopic rings threaded by a magnetic flux are calculated using exact diagonalizations and self-consistent Hartree-Fock treatments of two-dimensional tori and cylinders of spinless interacting fermions. The validity of the Hartree-Fock approximation is controlled by a direct comparison with the exact results on small 4\ifmmode\times\else\texttimes\fi{}4 clusters. The existence of a crossover value for the disorder parameter Wc{\mathit{W}}_{\mathit{c}}Wc​ (depending on the electronic density and the system size) separating two different regimes is established. Decomposing the current I(\ensuremath{\varphi}) in terms of its fundamental harmonics, we find that, while the first harmonic is always enhanced by the interaction, the second harmonic is enhanced for WWc{\mathit{W}}_{\mathit{c}}Wc​ and strongly suppressed otherwise. This effect is stronger as we increase the disorder.
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.
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 have studied the effects of interactions on persistent currents in half-filled and quarter-filled Hubbard models with weak and intermediate strength disorder. Calculations are performed using a variational Gutzwiller ansatz that describes short-range correlations near the Mott transition. We apply an Aharonov-Bohm magnetic flux, which generates a persistent current that can be related to the Thouless conductance. The magnitude of the current depends on both the strength of the screened disorder potential and the strength of electron-electron correlations, and the Anderson localization length can be extracted from the scaling of the current with system size. At half-filling, the persistent current is reduced by strong correlations when the interaction strength is large. Surprisingly, we find that the disorder potential is strongly screened in the large interaction limit, so that the localization length grows with increasing interaction strength even as the magnitude of the current is suppressed. This supports earlier dynamical mean-field-theory predictions that the elastic scattering rate is suppressed near the Mott transition.
The persistent current is here studied in one-dimensional disordered rings that contain interacting electrons. We used the density matrix renormalization group algorithms in order to compute the stiffness, a measure that gives the magnitude of the persistent currents as a function of the boundary conditions for different sets of both interaction and disorder characteristics. In contrast to its noninteracting value, an increase in the stiffness parameter was observed for systems at and off half-filling for weak interactions and nonzero disorders. Within the strong interaction limit, the decrease in stiffness depends on the filling and an analytical approach is developed to recover the observed behaviors. This is required in order to understand its mechanisms. Finally, the study of the localization length confirms the enhancement of the persistent current for moderate interactions when disorders are present at half-filling. Our results reveal two different regimes, one for weak and one for strong interactions at and off half-filling.