GNR calculation

[jerry]

Dear,
 
    Recently, i have done some calculation for GNRs with armchair and zigzag shaped edges. The DFT results show that the aGNR is semiconducting or metallic which depends on its width, while zGNR is metallic. The results correspond to some other calculations quite well. However, some calculation show that both aGNR and zGNR are semiconducting (PRL 97, 216803 (2006)). Can someone help me explain this discrepancy?
 
Thanks a lot!
                                                                                                Jerry

[Anders Blom]

The simple answer is spin. If you include this degree of freedom, a gap opens up also for the zigzag edge ribbons. You can easily confirm this using ATK too, both with LDA and semi-empirical models.

[zh]

For zNGR, the non-spin polarized calculations will give a flat band at the Fermi level in the band structure or a very sharp peak at E_F  in the density of states. This suggest that the non-magnetic state is not stable. The spin-exchange splitting will occur to stabilize the system. So the spin-polarized calculations are needed to consider the magnetic states of the zigzag edges.

[Anders Blom]

Interestingly, the band is actually not absolutely flat, it has a small oscillation, and this adds up to a transmission of 4 in a very narrow interval, instead of 1 as it is for other energies around the Fermi level. But of course, with spin this disappears, and the gap opens up.

[jerry]

Thanks a lot!