Zigzag-Shaped Graphene Nanoribbons

​
ribbon type
Z60
Z120
A60
A120
ribbon parameters
ℓ
1
1
2
3
4
5
6
7
ℓ
2
1
2
3
4
5
6
7
w
2
3
4
5
6
7
unit cell
3D view
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23.
This Demonstration presents the atomic structure of superlattices based on graphene nanoribbons. All the structures have the same wiggly shape but different connections of edges.

Details

The unit cell of a zigzag-shaped graphene nanoribbon is described by these three lattice vectors of the honeycomb graphene lattice:
L
1
=
ℓ
1

ℓ
1
(red),
L
2
=
ℓ
2

ℓ
2
(blue) and
W
=w
w
(green),
where

ℓ
1
,

ℓ
2
and
w
are elementary lattice vectors and
ℓ
1
,
ℓ
2
and
w
are integers[1, 2].
The crystallographic orientation of the elementary vectors

ℓ
1
and

ℓ
2
defines the ribbon edges to be of type zigzag (
Z
) or armchair (
A
). The apex angle is the angle between vectors

ℓ
1
and

ℓ
2
. The edge type and the apex angle are used for classifying the wiggly structures. The snapshots present the four types of zigzag-shaped graphene nanoribbons.
Snapshot 1: zigzag edges with an apex angle of
°
60
(
Z60
)
Snapshot 2: zigzag edges with an apex angle of
°
120
(
Z120
)
Snapshot 3: armchair edges with an apex angle of
°
60
(
A60
)
Snapshot 4: armchair edges with an apex angle of
°
120
(
A120
)
The crystallographic orientation of the third elementary vector
w
determines the width ratio between the two fragments of the zigzag-shaped ribbon. The widths of fragments built on the vectors
L
1
,
W
and
L
2
,
W
are meant to be measured perpendicular to the vectors
L
1
and
L
2
. The width ratio is set to unity in this Demonstration, though a more generic case can also be considered[3].
The integers
ℓ
1
,
ℓ
2
and
w
specify the length and the width of the zigzag-shaped ribbon unit cell. The whole ribbon is obtained by repeated translation of the unit cell by
T
=
L
1
-
L
2
. In this Demonstration, only a few unit cells are shown for clarity.
A similar approach to the classification and atomic position generation can be applied to other two-dimensional crystalline structures, for example, silicene quantum dots[4].
The atomic coordinates generated in this Demonstration can be used for calculating physical properties of zigzag-shaped ribbons, for example, their electronic properties[1, 2]. The optical properties of these structures can be calculated as described for zigzag ribbons with straight edges[5].
Graphene nanoribbons very close in shape to those presented here have been produced by the self-assembling of subtly engineered organic molecular precursors[6].

References

[1] V. A. Saroka, K. G. Batrakov and L. A. Chernozatonskii, "Edge-Modified Zigzag-Shaped Graphene Nanoribbons: Structure and Electronic Properties," Physics of the Solid State, 56(10), 2014 pp. 2135–2145. doi:10.1134/S106378341410028X.
[2] V. A. Saroka, K. G. Batrakov, V. A. Demin and L. A. Chernozatonskii, "Band Gaps in Jagged and Straight Graphene Nanoribbons Tunable by an External Electric Field," Journal of Physics: Condensed Matter, 27(14), 2015 145305. doi:10.1088/0953-8984/27/14/145305.
[3] V. A. Saroka and K. G. Batrakov, "Zigzag-Shaped Superlattices on the Basis of Graphene Nanoribbons: Structure and Electronic Properties," Russian Physics Journal, 59(5), 2016 pp. 633–639. doi:10.1007/s11182-016-0816-6.
[4] H. Abdelsalam, M. H. Talaat, I. Lukyanchuk, M. E. Portnoi and V. A. Saroka, "Electro-absorption of Silicene and Bilayer Graphene Quantum Dots," Journal of Applied Physics, 120(1), 2016 014304. doi:10.1063/1.4955222.
[5] V. A. Saroka, M. V. Shuba and M. E. Portnoi, "Optical Selection Rules of Zigzag Graphene Nanoribbons," Physical Review B, 95(15), 2017 155438. doi:10.1103/PhysRevB.95.155438.
[6] F. Schulz, P. H. Jacobse, F. F. Canova, J. van der Lit, D. Z. Gao, A. van den Hoogenband, P. Han, R. J. M. Klein Gebbink, M.-E. Moret, P. M. Joensuu, I. Swart and P. Liljeroth, "Precursor Geometry Determines the Growth Mechanism in Graphene Nanoribbons," The Journal of Physical Chemistry C, 121(5), 2017 pp. 2896–2904. doi:10.1021/acs.jpcc.6b12428.

External Links

Carbon Nanotubes
Nanotube Builder

Permanent Citation

Vasil Saroka
​
​"Zigzag-Shaped Graphene Nanoribbons"​
​http://demonstrations.wolfram.com/ZigzagShapedGrapheneNanoribbons/​
​Wolfram Demonstrations Project​
​Published: August 3, 2017