Abstract
We have computed persistent currents in a disordered mesoscopic ring in the presence of small electron-electron interactions, treated in first-order perturbation theory. We have investigated both a contact (Hubbard) and a nearest-neighbor interaction in one dimension and three dimensions (3D). Our results show that a repulsive Hubbard interaction produces a paramagnetic contribution to the average current (whatever the dimension) and increases the value of the typical current. On the other hand, a nearest-neighbor repulsive interaction results in a diamagnetic contribution in 1D and a paramagnetic one in 3D, and tends to decrease the value of the typical current in any dimension. Our study is based on numerical simulations on the Anderson model where the disorder is treated exactly. The numerical results could be justified analytically in the limit of very weak disorder. We have also investigated the influence of the amount of disorder and of the statistical (canonical or grand canonical) ensemble.
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