It works for me.
But there is a series of things you need to consider.
- If there is gate under the entire system, such that the system is uniform in all space, then for the semi-emperical models then all atoms are identical, and hence the gate can not introduce any transfer of charge, and as a result it has no effect on the electrostatic and therefore for the semi-emperical models it has no effect, no matter the gate voltage size or anything.
- Furthermore the solution to the Poisson equation when there is metallic gate in the entire bottom area, is the normal solution plus a constant (namely the gate potential), and therefore all matrix elements get equally scaled with the same constant, giving the exact same eigensystem and therefore the exact same bandstructure, and therefore there is no effect of the gate.
- Finally, one should consider what is the desired effect of a gate. Without much loss of generality it can be assumed that the effect of the gate can be divided into two parts. One comes from the interaction between the atoms in configuration and the atoms in the gate, the other is the effect of the electric field emitted from the gate. The metallic regions is only a model for the last. This model is good when the distance between the gate and the system is
longer (like in your experiement) or the interaction between the system and the gate is weak. Given this model gate, the effect we are searching for, is a shift of the eigenvalues and their related quantities. But this shift in these eigenvalues is in absolute energy, and therefore the eigenvalues and the transmission spectrum is unchanged relative to the fermi level. Therefore there is no effect of the gate for the Transmission Spectrum in this kind of system, and which is expected behavior for perfect graphene.
If you want to model the resistance in the paper, you will have to make a system that is closer to the experiment. As I see it there is two routes that would be a excellent starting point:
- Calculate the resistance between a graphene to graphene junction where the one part is gated and the other is not. This will show the effect of the energy levels that have been shifted.
- Alternative calculate the resistance between a electrode surface (gold?) and graphene, and check that the effect of a gate of graphene gives the same behavior as the experiments
Moderator edit: Fixed spelling mistake in subject
