[Smeagol-discuss] Understanding of some basic concepts

[XIAOHONG ZHENG]

Dear Ivan,

Thank you very much for your help. I still have some doubts about your 
answers.

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.

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.

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
>