Resonant cavities in metallic single-wall nanotubes: Green’s function calculations

We study the electronic transport of a metallic single-wall carbon nanotube sandwiched between two equal metallic single-wall nanotubes of different radii. We calculate the transmission function and the density of states using the Green’s function method. This cavity behaves as a resonant box with quasibound states producing resonances and antiresonances in transmission. This behavior is a consequence of the different band structures for nanotubes forming the cavity.

Figure 1

(Color online) Two different views of our structure $(6,6)∕4(9,9)∕(6,6)$. In the upper part, we see the relative positions of defects (a heptagonal and a pentagonal defect in each junction).

Figure 2

(a) $\Delta T\left(E\right)=T_{(9,9)}\left(E\right)-T_{(6,6)}\left(E\right)$ as a function of energy. (b) Transmission for the nanotube with a cavity $(6,6)∕4(9,9)∕(6,6)$. Regions where the number of channels is the same for both nanotubes (6,6) and (9,9) are shadowed. In these regions the transmission for $(6,6)∕4(9,9)∕(6,6)$ shows oscillations but it does not present any dip. For the interval of energy $0.91<\mid E\mid <1.33$ the transmission function clearly shows a depletion.

Figure 3

Transmission function (continuous line) and local density of states for the $(6,6)∕4(9,9)∕(6,6)$ nanotube. We show the LDOS inside the cavity (dashed line), whose peaks match with dips in transmission. The dotted line corresponds to the LDOS in the leads.

Figure 4

Participation number for a nanotube $(6,6)∕4(9,9)∕(6,6)$ formed with 1920 atoms, as a function of the energy. The horizontal dashed line corresponds to $P_n=600$. We can consider as quasibound states those under this line. The shadowed regions show the energy range for which $\Delta T=0$. In these regions we have no states with participation number lower than 600 as expected.

Figure 5

Transmission function of the $(6,6)∕4(9,9)∕(6,6)$ tube for energies lower than $-6.75\mathrm{eV}$. The vertical dotted lines show the energies for this range where we have a state with participation number lower than 600. The agreement with dips in transmission and quasibound states is quite good.

Figure 6

Occupation probability of three quasibound states for energies $E=-7.83$, $-7.46$, and $-6.92\mathrm{eV}$. These three states are shown in Fig. 5. The index $n$ labels each atom in the nanotube from left to right. As we can see, the probability function is almost extended over the central part of the nanotube, the cavity.

Figure 7

Transmission function as a function of the energy $(-0.91<E<0.91)$ for three cavities $(6,6)∕N(9,9)∕(6,6)$ with $N=2$ (continuous), 4 (dashed), and 8 (dotted). As $N$ increases the resonances in transmission are less pronounced.

Figure 8

Transmission function of $(9,9)∕4(6,6)∕(9,9)$, together with transmission functions of infinite pure (9, 9) and (6, 6). In the region $-0.91<E<0-91$ the situation is similar to the case of the cavity, with oscillations in transmission. For $0.91<\mid E\mid <1.33$ the transmission gets even higher than 2 (see horizontal dashed line in the lower part of the figure). There are no bound states for the rest of the energies.