sknano.structures.compute_electronic_type¶

sknano.structures.compute_electronic_type(*Ch)[source][source]

Compute nanotube 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:

• $$(2n + m)\,\mathrm{mod}\,3=2$$
• $$(n - m)\,\mathrm{mod}\,3=1$$
Parameters: *Ch : {tuple or ints} Either a 2-tuple of ints or 2 integers giving the chiral indices of the nanotube chiral vector $$\mathbf{C}_h = n\mathbf{a}_1 + m\mathbf{a}_2 = (n, m)$$. str