[Smeagol-discuss] Understanding of some basic concepts

[Ivan Rungger]

Dear Xiaohong and Ian,

to the comments of Ian I add the following:
> 1. Although the scattering region is supposed to be neutral, the
> Poisson equation is solved  for the electrons, not for the whole
> charge ( the sum of the ionic charge and electronic charge). So the
> k=0 term will not be 0, but proportional to Q/V (namely, the average
> electron density). Q is the total electrons, not zero.
The trick is that in siesta the Poisson equation is solved for
delta_rho, where delta_rho is the deviation from the neutral charge. You
can look at the siesta code for this. So if the system is neutral the
integral of delta_rho over the unit cell is 0.
> 2. In my understanding, the scattering region is not necessarily
> neutral since it is an open system. The scattering region may be
> charged or discharged. So, if there is some extra charge in the
> scattering region, I think it might be reasonable. In fact, in a
> previous post (by Prof. Sanvito?) I find that, due to the self-energy
> from the leads, the Hamiltonian becomes non-hermitian now and the
> charge can not be exactly conserved.
The scattering region is not necessarily neutral because mathematically
the NEGF allows for finite charge. However from a physical point of view
a finite charge does not make sense. Just imagine the system would be
charged, then since we join it to metallic leads there would be a
compensating charge building up around the scattering region. The point
now is that until there is a screening charge in the metal you can not
join the leads, because the assumption of the system reaching bulk
properties is not yet fullfilled. So if you have a finite charge you
would have to make the scattering region larger, until the charge is
neutral. Then you can join the leads.

Finite charge calculations are surely possible, but a modification of
the basic concepts is needed.

Cheers,

 Ivan
>
> Sincerely,
> Xiaohong
>
>
>>> (4) In the solution of Poisson equation by FFT, to dispose the k = 0
>>> term does not affect  the physics, of course, because this term is
>>> just a constant. But what is the advantage of disposing this term,
>>> please? Just for saving computation time? If we keep this term, then
>>> the potential matching might not be a problem, especially for cases
>>> where we use different leads. Because now, we do not need to get the
>>> average in the lead for the potential matching in the scattering
>>> region. Of course, we still have to do some matching, but we should
>>> do the matching according to the Fermi levels in the three parts. We
>>> should align their Fermi levels to the same energy point and thus
>>> shift the hartree potentials of the three parts accordingly. How do
>>> you think about this, please?
>>>       
>> One of the main assumptions in smeagol is that the scattering region is
>> neutral, so that the k=0 term is 0 (small fluctuations of the excess
>> charge around 0 are OK in practice). If the system has a finite extra
>> charge then this term is not 0 and we have an incorrect potential with
>> the FFT. But there should always be enough leads slices inside the
>> scattering region to screen the potential before joining the leads, this
>> always results in a neutral scattering region. This is the case also for
>> different leads.
>>  
>> Cheers,
>>
>>  Ivan
>>   
>
>


-- 
=================================================
Ivan Rungger,

School of Physics,  
Trinity College Dublin,  
Dublin 2,  IRELAND  
Phone: +353-1-6088454  
Email: runggeri at tcd.ie

=================================================