MPSH in quasi-1D homogeneous systems?

[beark]

MPSH in a molecular device model has clear physically meanings. One can use it to see how the molecular orbitals changes due to the applied bias voltage.
But in a  homogeneous system, such as quasi-1D nanotubes and graphene ribbons, I don't know how to distinguish the surface layers and the real middle part, because they are the same!
Also I wonder what is the physical meaning of MPSH in such a system? Can we still use MPSH to analysis the middle part?
For example, if I introduce a vacancy in the central region, can I still calculate MPSH? How does it means? If so, how to choose the related layers? All central region?

[Nordland]

MPSH gives most insight value in molecular device, however there is still somewhat information to be gained in other systems.
The MPSH states is calculated, simply by finding the eigenstates of that hamiltonian, that determines the green function for the device, and therefore we studying a perfect system, where there should be no scattering, the MPSH states should resemble the bloch states of the electrodes perfectly or else an artifical scattering has be introduced. Therefore you can use this to determine if the system obeys the assumption that the algorithm needs.

If you introduce a defect in a carbon nanotube - perhaps removing a single atom - then you can use the MPSH to give a hint on what is the mechanics behind the altered transmission,
is due to perhaps a small modification of the eigenstates in the vicinity of the defect or perhaps it is a total collaspe of the entire wave function for the entire wire near the defect.

For Al-wire in the official manual tutorial, I think, you can use the MPSH to see that the defect makes the wave function collapse for certain k-points/modes, however for others it is merely a minor disturbance to the bloch state.

[beark]

Thank you, Nordland. Do you mean that I may calculate MPSH of the whole central region to see if it obeys the assumption that the algorithm needs? For example, if it introduces an artifical scattering state, then we can't use MPSH for analysis?
If the coupling is too strong, MPSH can't be applied in such a system. The peaks in the transmission bias windows doesn't have a corresponding MPSH state, How to descrbe the the physical meaning of the peak?  I am not quite sure of the meaning of the eigenstates of the transmission eigenchannels, how to relate it to the central region?
I have some results below. And the peaks in the MPSH and the transmission spectrum doesn't have obvious relation. Does it means the peaks in the MPSH are just fake, and means nothing?

[Anders Blom]

For a perfect periodic system, the MPSH is meaningless. For the concept to make any sense there has to be a clearly defined "molecular" part to "project" on.

However, as soon as you introduce a defect or e.g. add an atom/molecule to the outside of a nanotube, etc, then you have precisely such a part, and also your projection atoms are quite obvious. In case of a single added atom, you may want to include the neighboring atoms too to account for the modified bonding between these.

It is also relevant to compare not just the transmission but also the surface density of states to the MPSH spectrum. If there at some energy is an MPSH level but no peak in the DOS, then the level is anyway not actively participating in the transmission (a peak in the DOS corresponds to some kind of localized level, which typically deteriorates the transmission), since it is not coupled to the leads.

What is the system corresponding to the results you posted? There seems to be a corresponding peak at -0.25 in both, but not at +0.25 eV, but that could just mean that the first peak is related to some localized molecular level and the other is due to some feature in the band structure.

If you have a single vacancy, I would select the atoms that previously used to be bound to that atom as the part to project on.

[Anders Blom]

Oh, one more thing. You can also compute the 3D real-space molecular orbital of each MPSH eigenstate. Then you will immediately see where in space it is localized. If there is a peak in the MPSH, and a dip in the transmission, and it sits right at the vacancy, then you can be quite sure that this is a localized molecular level due to the impurity, which destroys the transmission at this energy.

[beark]

Thanks. Excuse me, I don't know how to calculate surface density of states. Would there be some tutorial?
In the first post, I just take vacancy for example. The system in my post is a perfect nanoribbon in which central region have different spin from the electrode. The peaks in the transmission spectrum should be due to the mismatch of the wavefunction between the central region and electrode. The MPSH is calculated from the whole central region. When I increase the bias voltage, the peak in the transmission spetrum moves, but the MPSH level seems don't have corresponding changes . So I think there is no obvious relation between the transmission and MPSH. And I wonder if there is some other method could descrbe the move of the transmisson peak if MPSH is not applicable?
below are results of higher bias voltage of the same system:

[Nordland]

If the transmission spectrum you post is from a perfect 1d system, then you have too short electrode! since the transmission will always be step like if the system is perfect.

[Anders Blom]

If you have a constrained spin configuration, where the central region does not match the electrodes, then of course this constitutes a scattering barrier. But the system is not particularly physical...

To compute the surface density of states is just as easy as to calculate the transmission function, just use the function calculateDensityOfStates() (also available if you set up the calculation in VNL).

[beark]

Thank you, all!
I just use it as a model system to see the effect of wavefunction mismatching. 

Oh, I didn't know the DOS in two-probe systems means "surface density of states".
What does "surface" here means? Because it includes the DOS of the electrode?

[Anders Blom]

Ok, have fun with that

Yes, this is not a bulk DOS, as you would obtain for a periodic structure. Instead, it is computed from the Green's function, and thus also takes into account the open boundary conditions in the transport direction.