About the transmission spectrum of zigzag graphene nanoribbon under bias

[chp]

Hi:

     I performed some test calculations on zigzag graphene nanoribbon. The transmission spectrum, density of states (DOS), and projected density of states (PDOS) of the nanoribbon without bias can give a reasonable result. However, the transmission spectrum obtained under bias has an energy gap, conflicting with the corresponding results of DOS and PDOS (please see the attached picture, which gives the examples of zero bias and at the bias voltage of 0.5V, respectively). I cannot understand it. I doubt if I set any inappropriately parameter (please see the attached file). 

Thanks in advance.

[Anders Blom]

The electrode is too short, which you can see already from the zero-bias results, which are in fact not reasonable. Since the system is perfectly periodic, you should expect a step-like transmission spectrum with integer values of T(E). The fact that this is not the case indicates "scattering", caused by a mismatch between the electrode Fermi level and that of the device calculation.

You should at least double the electrode. See http://quantumwise.com/publications/tutorials/mini-tutorials/99 for more details.

[nori]

However, the transmission spectrum obtained under bias has an energy gap,

The reason why such a result is obtained is written in Phys. Rev. Lett. 100, 206802(2008).

[chp]

Thank you very much !

[chp]

However, I also want to know why the energy gap in the transmission spectrum under bias cannot coincide with the corresponding results of DOS and PDOS, where a high peak lies in the energy range.

[nori]

The gap around Fermi level is due to a forbidden tunneling derived from the symmetry of the wave function.
So the Bloch states are still present around Fermi level but are reflected almost perfectly.

If you analyze transmission eigenstates around Fermi level, you will realize the above thing clearly

[chp]

Thanks a lot !