correlation in the present model is a major chal- lenge to us. The presence of electron-phonon inter- action in Aharonov-Bohm interferometers provides phase shifts of the conducting electrons and due to this dephasing process electron transport through an AB interferometer becomes highly sensitive to the AB flux φ with the increase of electron-phonon coupling strength [53]. In the present work, we have addressed our results considering the site energies of all the atomic sites of the interferometer are identi- cal i.e., we have treated the ordered system. But in real case, the presence of impurities will affect the electronic structure and hence the transport proper- ties. The effect of the temperature has already been pointed out earlier, and, it has been examined that the presented results will not change significantly even at finite temperature, since the broadening of the energy levels of the interferometer due to its coupling to the electrodes will be much larger than that of the thermal broadening [46]. At the end, we would like to mention that we need further study in such systems by incorporating all these effects. The importance of this article is mainly con- cerned with (i) the simplicity of the geometry and (ii) the smallness of the size, and our exact analy- sis may be utilized to study electron transport in Aharonov-Bohm geometries. References [1] J. Chen, M. A. Reed, A. M. Rawlett, J. M. Tour, Science 286 (1999) 1550. [2] P. Ball, Nature (London) 404 (2000) 918. [3] Y. Imry, Introduction to Mesoscopic Physics , Oxford University Press, Oxford (2002). [4] Y. Imry, R. Landauer, Rev. Mod. Phys. 71 (1999) S306. [5] Y. Gefen, arXiv:cond-mat/0207440v1. [6] Y. Aharonov, D. Bohm, Phys. Rev. 115 (1959) 485. 10 [7] K.-W. Chen, C.-R. Chang, J. Appl. Phys. 103 (2008) 07B708. [8] Y. Han, W. Gong, H. Wu, G. Wei, Physica B 404 (2009) 2001. [9] Z.-B. He, Y.-J. Xiong, Phys. Lett. A 349 (2006) 276. [10] S. Welack, S. Mukamel, Y. Yan, Eur. Phys. Lett. 85 (2009) 57008. [11] D. Rohrlich, O. Zarchin, M. Heiblum, D. Ma- halu, V. Umansky, Phys. Rev. Lett. 98 (2007) 096803. [12] A. Aviram, M. Ratner, Chem. Phys. Lett. 29 (1974) 277. [13] A. W. Holleitner, R. H. Blick, A. K. H¨ uttel, K. Eberl, J. P. Kotthaus, Science 297 (2002) 70. [14] K. Kobayashi, H. Aikawa, S. Katsumoto, Y. Iye, Phys. Rev. Lett. 88 (2002) 256806. [15] K. Kobayashi, H. Aikawa, A. Sano, S. Kat- sumoto, Y. Iye, Phys. Rev. B 70 (2004) 035319. [16] Y. Ji, M. Heiblum, H. Shtrikman, Phys. Rev. Lett. 88 (2002) 076601. [17] A. Yacoby, M. Heiblum, D. Mahalu, H. Shtrik- man, Phys. Rev. Lett. 74 (1995) 4047. [18] J. Chen, M. A. Reed, A. M. Rawlett, J. M. Tour, Science 286 (1999) 1550. [19] M. A. Reed, C. Zhou, C. J. Muller, T. P. Bur- gin, J. M. Tour, Science 278 (1997) 252. [20] P. A. Orellana, M. L. Ladron de Guevara, M. Pacheco, A. Latge, Phys. Rev. B 68 (2003) 195321. [21] P. A. Orellana, F. Dominguez-Adame, I. Gomez, M. L. Ladron de Guevara, Phys. Rev. B 67 (2003) 085321. [22] A. Nitzan, Annu. Rev. Phys. Chem. 52 (2001) 681.