Table 1 The number of equivalent but different orientations of a 2D material on a substrate based on the interplay between their symmetries.

From: The epitaxy of 2D materials growth

G2D

C6V

C4V

C3V

C2V

GSub

C6V

C4V

C3V

C2V

C6V

C4V

C3V

C2V

C6V

C4V

C3V

C2V

C6V

C4V

C3V

C2V

G2D@Sub

C6V

C2V

C3V

C2V

C2V

C4V

CV

C2V

C3V

CV

C3V

CV

C2V

C2V

CV

C2V

∣Gsub∣

12

8

6

4

12

8

6

4

12

8

6

4

12

8

6

4

∣G2D@sub∣

12

4

6

4

4

8

2

4

6

2

6

2

4

4

2

4

N1

1

2

1

1

3

1

3

1

2

4

1

2

3

2

3

1

  1. Here, GSub, G2D and G2D@Sub are symmetry groups of the substrate, the 2D material and the 2D material–substrate system, ∣Gsub∣ and ∣G2D@sub∣ are the orders of GSub and G2D@Sub; and N1 = ∣Gsub∣/∣G2D@sub∣ is the number of equivalent but different directions of the 2D material on the substrate.
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