lines in Figs. 3(a) and (b). All these features are equally valid irrespective of disorder strength and disordered configurations. Thus, in brief we can say that for one-channel rings described with fixed number of electrons, sign of low-field currents can be precisely determined. 

At the end, we focus on the behavior of low-field magnetic response in moebius geometries. For these systems, sign of low-field currents strongly depends on the strength of intra-chain interaction ( v$_{⊥}$ ). For v$_{⊥}$ = 0, a moebius strip becomes a single channel ring, and therefore, sign of low-field currents can be mentioned exactly according to the above prescrip- tion. On the other hand for the case where v$_{⊥}$ is finite, sign of low-field currents cannot be predicted accurately as it strongly depends on the number of electrons and specific realization of disordered con- figuration in the strips. 

## 5 Concluding remarks 

To summarize, we have studied the behavior of persistent current and low-field magnetic suscepti- bility in strictly one-channel mesoscopic rings and moebius strips penetrated by magnetic flux φ . A tight-binding framework is given to describe the system, where all calculations are done numerically to study the magnetic response. In perfect rings current shows saw-tooth like variation as a func- tion of φ , while it varies continuously in disordered rings. Both for perfect and disordered rings cur- rent varies periodically with φ exhibiting φ 0 flux- quantum periodicity. In moebius strips a uncon- ventional φ 0 / 2 periodic nature of persistent current is observed for the particular case when v$_{bot}$ = 0. While, current gets back its φ 0 periodicity when electrons are able to hop along the transverse direc- tion i.e., v$_{⊥}$ ̸ = 0. In the study of low-field magnetic response we have seen that for one-channel meso- scopic rings described with constant number of elec- trons, sign of low-field currents can be mentioned precisely. While, for moebius strips with v$_{⊥}$ ̸ = 0, 

sign of low-field currents cannot be predicted ex- actly as it depends on the number of electrons as well as disordered configurations. Our exact analy- sis can provide some physical insight to study mag- netic response in mesoscopic loop geometries. 

## References 

[1] N. Byers and C. N. Yang, Phys. Rev. Lett. 7 , 46 (1961). 

[2] M. B¨ uttiker, Y. Imry, and R. Landauer, Phys. Lett. 96A , 365 (1983). 

[3] H. F. Cheung, Y. Gefen, E. K. Riedel, and W. H. Shih, Phys. Rev. B 37 , 6050 (1988). 

[4] H. F. Cheung and E. K. Riedel, Phys. Rev. Lett. 62 , 587 (1989). 

[5] G. Montambaux, H. Bouchiat, D. Sigeti, and R. Friesner, Phys. Rev. B 42 , 7647 (1990). 

[6] B. L. Altshuler, Y. Gefen, and Y. Imry, Phys. Rev. Lett. 66 , 88 (1991). 

[7] F. von Oppen and E. K. Riedel, Phys. Rev. Lett. 66 , 84 (1991). 

[8] A. Schmid, Phys. Rev. Lett. 66 , 80 (1991). 

[9] V. Ambegaokar and U. Eckern, Phys. Rev. Lett. 65 , 381 (1990). 

[10] G. Bouzerar, D. Poilblanc, and G. Montam- baux, Phys. Rev. B 49 , 8258 (1994). 

[11] T. Giamarchi and B. S. Shastry, Phys. Rev. B 51 , 10915 (1995). 

[12] N. Yu and M. Fowler, Phys. Rev. B 45 , 11795 (1992). 

[13] I. O. Kulik, Physica B 284 , 1880 (2000). 

[14] K. Yakubo, Y. Avishai, and D. Cohen, Phys. Rev. B 67 , 125319 (2003). 

