Electronic properties of silicon nanotubes with distinct bond lengths

We analyze the band structure of a silicon nanotube with $s{p}^3$ bonds and variable bond lengths. This nanotube has many similarities with a carbon nanotube including a band gap at half-filling and conducting behavior which is dependent on structure. We derive a simple formula which predicts when the nanotube is metallic. We discuss our results in the context of a nanotube subject to small applied strains as this provides a means of distorting bond lengths in a predictable way and may be tested experimentally. The effects of strain on nanotube conductance have important implications for sensor technology.

Figure 1

(Color online) An irregular quadrilateral lattice with the two sublattices represented by circles and squares.

Figure 2

(Color online) A prismatic trapezoidal lattice.

Figure 3

The shaded area is where $p$ is real and the lines are where $p$ is an integer, i.e., where the SNT is metallic for the trapezoidal SNT with $n=0$, $m=12$ and (a) $\delta a=0.0001$, (b) $\delta a=0.2$.

Figure 4

The energy gap for the trapezoidal SNT with $n=0$, $m=12$, $\delta b=-0.25$, $\delta y=0$, and (a) $\delta a=0.0001$, (b) $\delta a=0.2$. The energy gap is measured in units of the proportionality constant $g$ which is defined by $t_l=g/{\sigma }_l^2$.