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arXiv:cond-mat/9605202

Enhancement of Persistent Current on Multichannel Ring

Feodor V. Kusmartsev

Published Jun 1, 1996• 0 citations
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Abstract

We describe a "train" effect which may exist in small metallic and semiconductor rings and might be associated with the long-standing problem of the persistent current enhancement. The current is associated with the cooperative motion of N electrons constituing the N-electron "train". The train arises via an excitation or a backflow of spin waves or of interchannel charge density sound modes. The impurities and defects have a little effect on the "train" current. The reason is that the "train" current is associated with a small momentum transfer, which is much smaller than the momentum transfer of the free electron current equal to 2 pi/L. For an illustration of the "train" effect we have calculated the persistent current in the framework of the Bethe ansatz solutions for Hubbard model. The fractional M/N periodicities of the persistent current serve as an indication of the electron "train"

DOI
10.48550/arxiv.cond-mat/9605202

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We describe a "train" effect which may exist in small metallic and semiconductor rings and might be associated with the long-standing problem of the persistent current enhancement. The current is associated with the cooperative motion of N electrons constituing the N-electron "train". The train arises via an excitation or a backflow of spin waves or of interchannel charge density sound modes. The impurities and defects have a little effect on the "train" current. The reason is that the "train" current is associated with a small momentum transfer, which is much smaller than the momentum transfer of the free electron current equal to 2 pi/L. For an illustration of the "train" effect we have calculated the persistent current in the framework of the Bethe ansatz solutions for Hubbard model. The fractional M/N periodicities of the persistent current serve as an indication of the electron "train"
We study the effect of strong electron-electron interactions on the persistent current in a multichannel ring with the aid of Bosonization and the Bethe ansatz equation discussed by Sutherland and Tsvelik. The interaction acts differently on a single and multichannel ring. If, in the first case, the current is suppressed, then in the second case the current may be enhanced. With the interaction the current is proportional to square of the number of channels. The maximum effect corresponds to medium values of the interaction, where U∼VFU\sim V_FU∼VF​. The new phenomenon of the fractional p/q- Aharonov-Bohm effect appears for interacting electrons on the multichannel ring.
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.
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.
The effect of spin-orbit interaction on persistent currents in mesoscopic Hubbard rings threaded by an Aharonov-Bohm flux is investigated, with attention focused on orbital magnetism. The nonperturbative treatment of the spin-orbit interaction developed by Meir et al. is combined with the Bethe ansatz solution in order to deal with this problem exactly. We find that the interplay of spin-orbit interaction and electron-electron interaction plays a crucial role, bringing about some remarkable effects on orbital magnetism.
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 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.