Why are zigzag graphene nanoribbons metallic?

[anahita]

Hi.
Why Zigzag graphene nanoribbons is metallics??

 

[jedishrfu]

This may have your answer:

https://en.wikipedia.org/wiki/Graphene_nanoribbons

They state that it depends on several factors:

Electronic structure
...

Calculations based on tight binding theory predict that zigzag GNRs are always metallic[contradictory] while armchairs can be either metallic or semiconducting, depending on their width. However, density functional theory (DFT) calculations show that armchair nanoribbons are semiconducting with an energy gap scaling with the inverse of the GNR width.[18] Experiments verified that energy gaps increase with decreasing GNR width.[19] Graphene nanoribbons with controlled edge orientation have been fabricated by scanning tunneling microscope (STM) lithography.[20] Energy gaps up to 0.5 eV in a 2.5 nm wide armchair ribbon were reported.

Zigzag nanoribbons are semiconducting[contradictory] and present spin polarized edges. ...