[Smeagol-discuss] Understanding of some basic concepts

[XIAOHONG ZHENG]

Hello, Dear All,

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?

1.  About the matching of the Hartree potential.
HartreeLeadsLeft (Physical):
Position in space in the left-hand side lead where the Hartree potential 
of the scattering region should match that of the bulk.
Default value: 0.0 Ang

HartreeLeadsRight (Physical):
Position in space of the right-hand side lead where the Hartree 
potential in the scattering region should match that of the bulk.
Default value: 0.0 Ang

(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.

(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?

(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?

(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?

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.

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?  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.

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?

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?

I am sorry to put so many questions here. Any reply or comments are very 
welcome. Thanks a lot.

Sincerely,
Xiaohong