Phonon transmission in Kwant
Dear Kwant developers, I wonder whether it is possible to calculate phonon transmission via NEGF formalism in Kwant. For example within the force constant model, is it possible to construct the dynamical matrix and calculate phonon self energies via surface Green's functions? Or do you recommend any other way to implement the phonon transmission in Kwant? Best, Ran
Dear Ran,
If you are talking about the transmission of electrons in the presence of
Phonons, you can express the Green's function in a self consistent way in a
certain approximation.
I suggest for you the following reference:
A. Cresti, G. Grosso, and G. Pastori Parravicini, J. Phys.: Condens. Matter
18, 10059 (2005).
I hope this helps
Adel
On Thu, Jul 9, 2020 at 2:22 PM Ran Mutc
Dear Kwant developers,
I wonder whether it is possible to calculate phonon transmission via NEGF formalism in Kwant.
For example within the force constant model, is it possible to construct the dynamical matrix and calculate phonon self energies via surface Green's functions?
Or do you recommend any other way to implement the phonon transmission in Kwant?
Best, Ran
 Abbout Adel
Dear Adel, For clarity, let me explain what I'd like to perform, via this paper: https://arxiv.org/pdf/0802.2761.pdf What I'd like to calculate is the transmission of phonons, e.g. please see right subfigure of Fig. 1 in the paper. My plan is to calculate the Caroli formula (Eq. 57) in which the self energies and Green's functions are of phonons. For example, rather than calculating the electron Green's function as G=[EIHsigma_L(E)sigma_R(E)]^1 I need to calculate the phonon Green's function as G=[w^2*IKsigma_L(w)sigma_R(w)]^1. Here K is the dynamical matrix, please see Eq. (2) in the paper above. I guess I'd need the surface Green's functions to calculate the self energies. My question is whether doing all these is possible in Kwant or not? I tried to search the maillist but couldn't encounter with anyone done that. So I thought maybe it is not doable at all and wanted to ask. Would it be possible to calculate the transmission of phonons in Kwant by this way or any other? Best, Ran
Dear Ran;
Up to my knowledge the the transmission of phonons are done by solving the
vibrational dynamics of the system where generally equations of motion are
written using the harmonic approximation.
In this case the dominant parameters are the bonding strength constant
between the two atomic sites.
However, in Kwant we use the discretized Schrodinger equation where the
dominant parameters are the onsite energy and hopping.
So it appears to me that those approaches are some how not similar in terms
of constants to provide to kwant and equations.
Finaly the kwant developer might have clear answer to you.
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Le ven. 10 juil. 2020 à 20:35, Ran Mutc
Dear Adel,
For clarity, let me explain what I'd like to perform, via this paper: https://arxiv.org/pdf/0802.2761.pdf
What I'd like to calculate is the transmission of phonons, e.g. please see right subfigure of Fig. 1 in the paper. My plan is to calculate the Caroli formula (Eq. 57) in which the self energies and Green's functions are of phonons.
For example, rather than calculating the electron Green's function as G=[EIHsigma_L(E)sigma_R(E)]^1 I need to calculate the phonon Green's function as G=[w^2*IKsigma_L(w)sigma_R(w)]^1. Here K is the dynamical matrix, please see Eq. (2) in the paper above. I guess I'd need the surface Green's functions to calculate the self energies.
My question is whether doing all these is possible in Kwant or not? I tried to search the maillist but couldn't encounter with anyone done that. So I thought maybe it is not doable at all and wanted to ask.
Would it be possible to calculate the transmission of phonons in Kwant by this way or any other?
Best, Ran
Dear Ran,
To my understanding, you can not do that: Kwant solves the Schrodinger
equation on a lattice whereas your paper studies a lattice wave equation
which is different since it is quadratic in the time derivative.
I hope this helps,
Adel
On Fri, Jul 10, 2020 at 9:35 PM Ran Mutc
Dear Adel,
For clarity, let me explain what I'd like to perform, via this paper: https://arxiv.org/pdf/0802.2761.pdf
What I'd like to calculate is the transmission of phonons, e.g. please see right subfigure of Fig. 1 in the paper. My plan is to calculate the Caroli formula (Eq. 57) in which the self energies and Green's functions are of phonons.
For example, rather than calculating the electron Green's function as G=[EIHsigma_L(E)sigma_R(E)]^1 I need to calculate the phonon Green's function as G=[w^2*IKsigma_L(w)sigma_R(w)]^1. Here K is the dynamical matrix, please see Eq. (2) in the paper above. I guess I'd need the surface Green's functions to calculate the self energies.
My question is whether doing all these is possible in Kwant or not? I tried to search the maillist but couldn't encounter with anyone done that. So I thought maybe it is not doable at all and wanted to ask.
Would it be possible to calculate the transmission of phonons in Kwant by this way or any other?
Best, Ran
 Abbout Adel
Hi Ran, the problem you described seems to be more adapted to tkwant or its extension tkwantOperator which computes energy and heat transport. So, you may give it a try. Regards, Ousmane
participants (4)

Abbout Adel

Adel Belayadi

ousmane.ly＠kaust.edu.sa

Ran Mutc