Localized and conducting states in carbon nanotube superlattices

The electronic structure and quantum conductance of superlattices made of metallic carbon nanotubes are investigated. It is shown that minibands with the same origin as nonconductive states in metallic quantum dots [L. Chico and W. Jaskólski, Phys. Rev. B 69, 085406 (2004)] can have a nonzero conductance in superlattices. We also report on a peculiar behavior of some bound states in $(2n,0)∕(n,n)$ superlattices, which originate from dispersionless bands of $(2n,0)$ tubes, but localize exclusively in the neighboring $(n,n)$ sections. They are truly localized and do not yield any conductance.

Figure 1

Schematic representation of a part of $(12,0)∕(6,6)$ junction. Solid circles: (12,0) atoms, open circles: (6,6) atoms. $L_i$ marks the first and $L_f$ the last layer (horizontal) of atoms in (12,0) unit cell.

Figure 2

(a) and (b) Two wave functions $(k=0)$ belonging to the degenerate dispersionless band (at $E=t$) of (12,0) CN. The 48 atoms in the (12,0) unit cell are ordered along consecutive atomic layers marked as [1], [2], [3] and [4]. $\left[1\right]=L_i$ and $\left[4\right]=L_f$.

Figure 3

Energy bands for the $2(12,0)∕2(6,6)$ superlattice around $E_F$. The SL period is denoted by $d$. DL bands are indicated by arrows.

Figure 4

Density of states for several CNSL. $A$, $B$, $I$ and $X$ mark various types of quasilocalized and localized states.

Figure 5

$1(12,0)∕1(6,6)$ SL. Wave functions $(k=0)$ of two $A$-type states at $E=-2.66\mathrm{eV}$ (a) and at $E=1.1\mathrm{eV}$ (b). 72 nodes in the SL unit cell are ordered along consecutive atomic layers marked as [1],..,[6]. $\left[1\right]=L_i$ and $\left[4\right]=L_i$ of the (12,0) unit cell. Layers [5] and [6] belong to the (6,6) section.

Figure 6

Charge densities along atomic layers in the unit cell of the $6(12,0)∕4(6,6)$ SL for different kinds of discrete states. Vertical dashed lines mark the interface.

Figure 7

Local density of states at interfaces of $(12,0)∕4(6,6)∕(12,0)$ CNQD. From Ref. 11.

Figure 8

Conductance of superlattices shown in Fig. 4. No bands with width less than $10\mathrm{meV}$ are shown.