GLYPH<Minus> 12 GLYPH<Minus> 8 GLYPH<Minus> 4 0 4 8 12 V 0 GLYPH<Minus> 12 12 GLYPH<Minus> 6 GLYPH<LParen1> b GLYPH<RParen1> 6 I GLYPH<Minus> 12 GLYPH<Minus> 8 GLYPH<Minus> 4 0 4 8 12 V 0 GLYPH<Minus> .4 .4 GLYPH<Minus> .2 GLYPH<LParen1> a GLYPH<RParen1> .2 I the transmission function T . With the increase of the bias voltage V , the electrochemical potentials on the electrodes are shifted gradually, and finally cross one of the quantized energy levels of the inter- ferometer. Accordingly, a current channel is opened up which provides a jump in the I - V characteristic Figure 4: (Color online). I - V characteristics of the interferometer with four atomic sites ( N = 4) for a fixed value of φ$_{1}$ = 0 . 2, where the red, blue and black curves correspond to φ$_{2}$ = 0, 0 . 1 and 0 . 4, re- spectively. (a) Weak-coupling limit and (b) strong- coupling limit. curve. The most important feature observed from the I - V curves for this weak-coupling limit is that, the non-zero value of the current appears beyond a finite bias voltage, the so-called threshold voltage V$_{th}$ . This is quite analogous to the semiconducting nature of a material. Most interestingly, the results predict that the threshold bias voltage of electron conduction can be controlled very nicely by tuning the AB flux φ$_{2}$ . The situation becomes much dif- ferent for the strong-coupling case. The results are given in Fig. 4(b). In this limit, the current varies 7 Now, we draw our attention on the variation of the typical current amplitude with anyone of these two fluxes, when the other one is fixed. To explore it, in Fig. 5, we show the variation of the typical cur- rent amplitude ( I$_{typ}$ ) with φ$_{2}$ , considering φ$_{1}$ as a constant, where (a) and (b) correspond to φ$_{1}$ = 0 and 0 . 3, respectively. The black and red lines rep- resent the results for the weak- and strong-coupling limits, respectively. The typical current amplitudes are calculated for the fixed bias voltage V = 1 . 02. Both for these two limiting cases, the typical current amplitude varies periodically with φ$_{2}$ , exhibiting φ$_{0}$ flux-quantum periodicity, as expected. Similar fea- ture is also observed for the I$_{typ}$ vs φ$_{1}$ curves, when φ$_{2}$ becomes constant. Here it is also important to 3.1.4 Typical current amplitude I$_{typ}$ as a function of φ$_{2}$ almost continuously with the applied bias voltage and achieves much larger amplitude than the weak- coupling case. The reason is that, in the limit of strong-coupling all the energy levels get broadened which provide larger current in the integration pro- cedure of the transmission function T . Thus by tun- ing the strength of the interferometer-to-electrode coupling, we can achieve very large, even an order of magnitude, current amplitude from the very low one for the same bias voltage V , which provides an important signature in designing nanoelectronic de- vices. In contrary to the weak-coupling limit, here the electron starts to conduct as long as the bias voltage is given i.e., V$_{th}$ → 0, which reveals the metallic nature. Thus it can be emphasized that the interferometer-to-electrode coupling is a key pa- rameter which controls the electron transport in a meaningful way. Additionally, the existence of the semiconducting or the metallic behavior of the in- terferometer also significantly depends on the AB fluxes φ$_{1}$ and φ$_{2}$ . The nature of all these I - V curves, presented in Fig. 4, will be exactly similar if we plot the results for the different values of φ$_{1}$ , keeping φ$_{2}$ as a constant.