[Smeagol-discuss] Understanding of some basic concepts

[Ivan Rungger]

Dear Xiaohong,
> I am a new user of smeagol.  I have read the User's Guide very 
> carefully. However, I find several questions that I am very confused 
> with or I do not understand well. Could you help me to understand them, 
> please?
>   
You can also have a look at the history in the mailing list, there are a
few mails where users have asked similar questions to yours.
> 1.  About the matching of the Hartree potential.
>
> (1) Does "Position in space in the left-hand side lead" here means the 
> point in the left lead part that is included in the scattering region? 
> If what I understand is right,  then the leftmost point in the 
> scattering region should match the left bulk. So the defaut value 0.0 
> Ang for HartreeLeadsLeft is OK. And the rightmost point of the 
> scattering region should match the right bulk. And the default value for 
> HartreeLeadsRight should not be 0.0 Ang, but should be the length of the 
> scattering region along the transport direction.
>   
The values you write (0 for left and length of unit cell for right
matching) are the ones that I suggest to use. However it is not
compulsory, you can also use different values. They should however
always be close to the left and right side of the scattering region.
> (2) HartreeLeadsBottom: this is determined by getting the average value 
> of the Hartree potential in the leads over a plane perpendicular to the 
> transport direction. From the manual, it seems that we can use different 
> leads ( with different material, sizes, etc.?). If we use different 
> leads, then there should be two such parameters to match the left lead 
> and right lead respectively. But why there is only one here?
>   
At the moment different leads can not be used, exactly because of this
problem that it is assumed that there is only one Fermi energy. However
the code can do different leads, but a few modifications are needed. I
think Alex has written a small script for this, but I think it is still
to be tested.
> (3) In the lead, the Hartree potential is solved by FFT. How is the 
> Hartree potential in the scattering region solved? Still by FFT or 
> multigrid method in real space?
>   
FFT.
> (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.
> By the way, one small point about Pot.exe. In the latest version of 
> Potential_f90.f I downloaded several days ago, I think there is a minor 
> bug. Line 289
> do l=2,mesh(3)
> should be changed to
> do l=1,mesh(3)
>
> Otherwise, we can not get the first point so that we can not get the 
> correct HartreeLeadsBottom.
>   
This is correct (by coincidence I sent the updated Potential_f90.f file
in a mail to the mailing list last week).
> 2. About NSlices:
>
> NSlices (Integer):
> Number of slices of the bulk Hamiltonian substituted into the left- and 
> right-hand side part
> of scattering region. The Hamiltonian of these slices is not 
> recalculated self-consistently
> and these “buffer” layers help the convergence, in particular when the 
> two leads are different.
> Default value: 1
>
> The default value is 1. In what condition shall we use 2 or bigger? Can 
> we use 0?
Usually we use 1. I have never used 2 or larger, 0 can be used (but even
here one leads unit cell has to be included on each side of the
scattering region).
> Do you think that the most important role of inserting some 
> slices of the bulk Hamiltonian into the scattering region is to make the 
> calculation of self-energy easier? Because if we include one lead 
> supercell in the scattering region, then the self-energy is only 
> determined by the Hamiltonian of this included part and it is fixed in 
> SCF steps for different biases. So the self-energy needs to be 
> calculated for only once and can be stored in disk or memory and used 
> for all other biases. Then, in the calculation of the transmission of 
> other biases, what needs to be updated is only the Green functions of 
> the scattering region.
>   
What you write is right. This is a thing that certainly should be done
for future releases.
> 3. About the kpoints calculation:
>
> Smeagol can give the contribution from each K point, this is very nice. 
> Do the  K points here mean the kpoints in the lead calculation or those 
> in the scattering region? How is the weight for each K point determined 
> when we  calculate the total transmission by integrating over the 
> k-points? In a previous post of this discussion forum, it was said that 
> the total transmission should be divided by the number of K points, does 
> it mean that each k point contributes equal, please?
>   
The k-points used and the corresponding weights are the ones given in
the .KP file for the scattering region, they are determined in a siesta
routine.
> 4. About the choice of the K points in the leads and the scattering region:
>
> If I use 8x8 k points in the x-y plane in the lead calculation, does it 
> mean that I also should use 8x8 for the x-y plane in the scattering 
> region, please?
>   
For the selfconsistent calculation of the scattering region the same
number of k-points should be used along x and y for both leads and
scattering region, and many k-points should be used along z in the
leads. This helps convergence. To calculate the transmission coefficient
for a given selfconsistent solution usually we use many more k-points in
the scattering region, but we still use the same leads files (calculated
with fewer k-points).

Cheers,

 Ivan
> I am sorry to put so many questions here. Any reply or comments are very 
> welcome. Thanks a lot.
>
> Sincerely,
> Xiaohong
>
>
>
>
>
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-- 
=================================================
Ivan Rungger,

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

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