2 4 6 8 10 12 14 16 N 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Δ E GLYPH<Minus> 2 GLYPH<Minus> 1 0 1 2 E 0.0 1.0 GLYPH<LParen1> b GLYPH<RParen1> 2.0 g GLYPH<LParen1> E GLYPH<RParen1> GLYPH<Minus> 2 GLYPH<Minus> 1 0 1 2 E 0.0 1.0 GLYPH<LParen1> a GLYPH<RParen1> 2.0 g GLYPH<LParen1> E GLYPH<RParen1> Figure 4: (Color online). Variation of the central energy gap δE as a function of the width N for some lattice ribbons with fixed lengths M . The red and blue curves correspond to M = 2 and 4 respectively. Figure 3: (Color online). Conductance g as a func- tion of the energy E for some lattice ribbons with fixed length M = 4 and varying widths where (a) N = 5 and (b) N = 10. since the relation g = 2 T follows from the Lan- dauer conductance formula, Eq. 1, with e = h = 1. Now the reduction of the transmission probability ( T < 1) for some particular energies can be ex- plained by considering the quantum interference ef- fects of the electronic waves passing through the different arms of the ribbon. The interpretation is as follow. During the motion of the electrons from manifests itself the electronic structure of the rib- bon. Due to the large number of energy levels, associated with the size of the ribbons, the reso- nant peaks almost overlap with each other and form quasi-continuous spectra in the g - E characteristics. The most significant feature observed from the spec- tra, given in Fig. 2, is that a central energy gap ( δE ) appears across the energy E = 0. With the increase of the length of the ribbon some more reso- nant peaks appear around E = 0, and accordingly, the gap decreases which is clearly observed from Figs. 2(a) and (b). Thus for a fixed width, the cen- tral gap can be controlled by tuning the length of the ribbon. In the same fashion, to characterize the depen- dence of the electron transport on the widths of the ribbons for a fixed length, in Fig. 3 we plot the re- sults for some typical lattice ribbons considering the length M = 4. The spectra shown in Figs. 3(a) and (b) correspond to the ribbons with widths N = 5 and 10 respectively. Quite similar to the above case, here also a gap appears across E = 0 and it de- creases with the increase of the width of the ribbon though the reduction is much small. Thus from the results described in Figs. 2 and 3 we can empha- size that the width of the central energy gap always decreases with the increase of the size (length and width) of the ribbon. the source to drain through the lattice ribbon, the electron waves propagating along the different pos- sible pathways can get a phase shift among them- selves, according to the result of quantum interfer- ence. Therefore, the probability amplitude of get- ting an electron across the ribbon either becomes strengthened or weakened. This causes the trans- mittance cancellations and provides anti-resonances in the conductance spectrum. Thus it can be em- phasized that the electron transmission is strongly affected by the quantum interference effects, and hence the ribbon to electrode interface structure. Now all these resonant peaks are associated with the energy eigenvalues of the ribbon, and accord- ingly, we can say that the conductance spectrum To illustrate the dependence of the gap δE with other system sizes, in Fig. 4, we display the varia- tion of δE as a function of the width N for some typical lattice ribbons with fixed lengths. The red and blue curves correspond to the lengths M = 2 and 4 respectively. Quite interestingly we see that, 5