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arXiv:cond-mat/9701026 · Physical review. B, Condensed matter

Interaction-induced enhancement and oscillations of the persistent current

Charles Allen Stafford, D. F. Wang

Published Aug 15, 1997• 6 citations
arXivHTMLPDF

Abstract

The persistent current $I$ in integrable models of multichannel rings with both short- and long-ranged interactions is investigated. $I$ is found to oscillate in sign and increase in magnitude with increasing interaction strength due to interaction-induced correlations in the currents contributed by different channels. For sufficiently strong interactions, the contributions of all channels are found to add constructively, leading to a giant enhancement of $I.$ Numerical results confirm that this parity-locking effect is robust with respect to intersubband scattering.

DOI
10.1103/physrevb.56.r4383

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Orbital magnetism in an integrable model of a multichannel ring with long-ranged electron-electron interactions is investigated. In a noninteracting multichannel system, the response to an external magnetic flux is the sum of many diamagnetic and paramagnetic contributions, but we find that for sufficiently strong correlations, the contributions of all channels add constructively, leading to a parity (diamagnetic or paramagnetic) which depends only on the total number of electrons. Numerical results confirm that this parity-locking effect is robust with respect to subband mixing due to disorder. The free energy F(φ) of a metallic ring threaded by an Aharonov-Bohm flux (¯hc/e)φ is a periodic function of φ, with period 2π [1]. The system is said to be diamagnetic if F is minimal for φ = 0, and paramagnetic if F is minimal for φ = π (1/2 flux quantum). A purely one-dimensional (1D) ring with N spinless electrons is diamagnetic if N is even and paramagnetic if N is odd, independent
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.
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 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.