Good Day!
From the Kwant paper, the raw outputs for the calculation of conductance are from the scattering matrix S_{mn}. Is there any code in Kwant that can extract the elements of this matrix (as in some text file)? Regards,James
james edward hernandez wrote:
From the Kwant paper, the raw outputs for the calculation of conductance are from the scattering matrix S_{mn}. Is there any code in Kwant that can extract the elements of this matrix (as in some text file)?
Hi James, did you check the documentation? If yes, I would be interested to know why you found it difficult to find the following: http://kwant-project.org/doc/1/reference/generated/kwant.solvers.common.SMat... Note that it is enough to send questions as yours to the mailing list only. There is no need to CC anyone from the core team. Christoph
Hello. For the last question, it turns out that I printed the submatrix incorrectly (Type Error). Another question, I would like to confirm whether my understanding on how the conductance is calculated is correct: 1. A (plane wave) wave function is generated 2. The wave function is acted by a (Discretized) Tight Binding Hamiltonian through the hamiltonian matrix3. The propagating modes are normalized (expectation value of current)4. The propagating modes can be treated as a sum of incoming, outgoing, and evanescent modes containing the scattering matrix5. Conductance (and Hall conductance) is directly calculated from the scattering matrix Are the Block matrices V_{L} and V_{S} diagonal matrices with nonzero elements = 1? Thanks and best regards,James On Saturday, April 2, 2016 3:09 PM, Christoph Groth <christoph.groth@cea.fr> wrote: james edward hernandez wrote:
From the Kwant paper, the raw outputs for the calculation of conductance are from the scattering matrix S_{mn}. Is there any code in Kwant that can extract the elements of this matrix (as in some text file)?
Hi James, did you check the documentation? If yes, I would be interested to know why you found it difficult to find the following: http://kwant-project.org/doc/1/reference/generated/kwant.solvers.common.SMat... Note that it is enough to send questions as yours to the mailing list only. There is no need to CC anyone from the core team. Christoph
Are the Block matrices V_{L} and V_{S} diagonal matrices with nonzero elements = 1? yes, assuming that you are talking about "simple" leads with a hopping
Hi James, For an understanding of how Kwant calculates scattering properties, I would recommend reading the Kwant paper: http://iopscience.iop.org/1367-2630/16/6/063065/article The basic idea can be summarized as follows: - calculate the modes of the leads by solving a small linear system defined on a lead unit cell (equation 6 in the Kwant paper) - use this mode decomposition to transform the Schrodinger equation defined on an infinite domain (eigenproblem) to a (large) linear system to be solved for the components of the wavefunction in the scattering region and the relevant components of the scattering matrix - solve this linear system to find the wavefunctions and scattering matrix coefficients parameter of 1. Hope that helps, Joe On 5 April 2016 at 14:57, james edward hernandez <kibwiw@yahoo.com.ph> wrote:
Hello. For the last question, it turns out that I printed the submatrix incorrectly (Type Error).
Another question, I would like to confirm whether my understanding on how the conductance is calculated is correct:
1. A (plane wave) wave function is generated 2. The wave function is acted by a (Discretized) Tight Binding Hamiltonian through the hamiltonian matrix 3. The propagating modes are normalized (expectation value of current) 4. The propagating modes can be treated as a sum of incoming, outgoing, and evanescent modes containing the scattering matrix 5. Conductance (and Hall conductance) is directly calculated from the scattering matrix
Are the Block matrices V_{L} and V_{S} diagonal matrices with nonzero elements = 1?
Thanks and best regards, James
On Saturday, April 2, 2016 3:09 PM, Christoph Groth < christoph.groth@cea.fr> wrote:
james edward hernandez wrote:
From the Kwant paper, the raw outputs for the calculation of conductance are from the scattering matrix S_{mn}. Is there any code in Kwant that can extract the elements of this matrix (as in some text file)?
Hi James, did you check the documentation? If yes, I would be interested to know why you found it difficult to find the following:
http://kwant-project.org/doc/1/reference/generated/kwant.solvers.common.SMat...
Note that it is enough to send questions as yours to the mailing list only. There is no need to CC anyone from the core team.
Christoph
Hi again, - calculate the modes of the leads by solving a small linear system defined
on a lead unit cell (equation 6 in the Kwant paper)
I was wrong about this step, it's actually a generalized eigenvalue problem that needs to be solved for the eigenvalue of the translation operator and the mode (the energy is an input). Joe
participants (3)
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Christoph Groth -
james edward hernandez -
Joseph Weston