sknano.generators.UnrolledSWNTGenerator.electronic_type

UnrolledSWNTGenerator.electronic_type

SWNT electronic type.

New in version 0.2.7.

The electronic type is determined as follows:

if $(2n + m)\,\mathrm{mod}\,3=0$, the nanotube is metallic.

if $(2n + m)\,\mathrm{mod}\,3=1$, the nanotube is semiconducting, type 1.

if $(2n + m)\,\mathrm{mod}\,3=2$, the nanotube is semiconducting, type 2.

The $x\,\mathrm{mod}\,y$ notation is mathematical shorthand for the modulo operation, which computes the remainder of the division of $x$ by $y$. So, for example, all armchair nanotubes must be metallic since the chiral indices satisfy: $2n + m = 2n + n = 3n$ and therefore $3n\,\mathrm{mod}\,3$ i.e. the remainder of the division of $3n/3=n$ is always zero.

Note

Mathematically, $(2n + m)\,\mathrm{mod}\,3$ is equivalent to $(n - m)\,\mathrm{mod}\,3$ when distinguishing between metallic and semiconducting. However, when distinguishing between semiconducting types, one must be careful to observe the following convention:

• Semiconducting, type 1 means:
  • $(2n + m)\,\mathrm{mod}\,3=1$
  • $(n - m)\,\mathrm{mod}\,3=2$
• Semiconducting, type 2 means:
  • $(2n + m)\,\mathrm{mod}\,3=2$
  • $(n - m)\,\mathrm{mod}\,3=1$