[Smeagol-discuss] Understanding of some basic concepts

[lan haiping]

Dear XIAOHONG:

A basic sense, the scattering region calculation is performed under
periodic cell, which of course prevents any  extra charge situations.

On Tue, Apr 1, 2008 at 5:59 AM, XIAOHONG ZHENG <exhzheng at gmail.com> wrote:

> 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
> >
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-- 
Hai-Ping Lan
Department of Electronics ,
Peking University , Bejing, 100871
lanhaiping at gmail.com, hplan at pku.edu.cn
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