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Magneto-transport in mesoscopic rings and cylinders: Effects of electron-electron interaction and spin-orbit coupling

We undertake an in-depth analysis of the magneto-transport properties in mesoscopic single-channel rings and multi-channel cylinders within a tight-binding formalism. The main focus of this review is to illustrate how the long standing anomalies between the calculated and measured current amplitudes carried by a small conducting ring upon the application of a magnetic flux $ϕ$ can be removed. We discuss two different cases. First, we examine the combined effect of second-neighbor hopping integral and Hubbard correlation on the enhancement of persistent current in presence of disorder. A significant change in current amplitude is observed compared to the traditional nearest-neighbor hopping model and the current amplitude becomes quite comparable to experimental realizations. In the other case we verify that in presence of spin-orbit interaction a considerable enhancement of persistent current amplitude takes place, and the current amplitude in a disordered ring becomes almost comparable to that of an ordered one. In addition to these, we also present the detailed band structures and some other related issues to get a complete picture of the phenomena at the microscopic level.