c = e = h = 1) flux-quantum periodicity. The current I$_{n}$ carried by n -th energy level hav- ing energy E$_{n}$ is obtained by taking the 1-st order derivative of E$_{n}$ with flux φ . Mathematically it can expressed as, At absolute zero temperature ( T = 0K), total cur- rent of a system, described with fixed number of electrons N$_{e}$ , will be obtained by taking the sum of I$_{n}$ = − ∂E$_{n}$ ∂φ (3) ( N$_{e}$ = 55) number of electrons, respectively. The solid and dotted curves correspond to the perfect ( W = 0) and disordered ( W = 1) rings, respec- tively. For the ordered ring, we set ϵ$_{i}$ = 0 for all i , while for the disordered case site energies ( ϵ$_{i}$ ) are chosen randomly from a “Box” distribution func- tion of width W = 1. From the results it is ob- served that, in impurity free rings current exhibits saw-tooth like variation as a function of φ provid- ing sharp transitions, associated with the crossing of energy levels, at φ = ± nφ 0 or ± nφ 0 / 2, depending on whether the ring contains even or odd number of electrons. On the other hand, this saw-tooth like behavior completely disappears as long as impuri- ties are introduced in the ring. This is due to the fact that, in presence of impurities all the degenera- cies move out, and accordingly, energy levels vary continuously with φ which provide continuous vari- ation of the current. Addition to this feature, it is also important to note that in disordered ring cur- rent amplitude gets reduced significantly compared to the ordered one. Such a behavior can be well un- derstood from the theory of Anderson localization, where we get more localization with the increase of disorder strength W [25]. Both for perfect and dirty rings, persistent current varies periodically with φ showing only φ 0 flux-quantum periodicity. GLYPH<Minus> 1.0 1.0 Φ GLYPH<Minus> 0.06 0.06 I GLYPH<LParen1> Φ GLYPH<RParen1> GLYPH<LParen1> b GLYPH<RParen1> GLYPH<Minus> 1.0 1.0 Φ GLYPH<Minus> 0.06 0.06 I GLYPH<LParen1> Φ GLYPH<RParen1> GLYPH<LParen1> a GLYPH<RParen1> 3 Persistent current in moe- bius strips Figure 3: Persistent current as a function of φ for or- dered (solid line) and disordered (dotted line) meso- scopic rings with N = 150 , where (a) N$_{e}$ = 50 and (b) N$_{e}$ = 55 . For the disordered case, we fix W = 1 . I ( φ ) = ∑ n I$_{n}$ ( φ ) (4) This section describes the behavior of persistent current in moebius strips. Persistent current in a moebius strip is highly sensitive on the intra- chain interaction strength and here we will focus our study in this particular aspect. The schematic view of a moebius strip, penetrated by a magnetic flux φ , is shown in Fig. 4. The vertical line connect- ing the atomic sites in upper and lower strands is called as ‘rung’. In presence of magnetic flux φ , the tight-binding Hamiltonian for a moebius strip with N rungs (i.e., 2 N atomic sites since in each strand individual contributions from the lowest N$_{e}$ energy levels. Thus, we can write the total current in the form, As representative examples, in Fig. 3 we show the variation of persistent current for a typical meso- scopic ring considering N = 150, where (a) and (b) represent the results for even ( N$_{e}$ = 50) and odd 4