Thanks Xavier. I now have a clearer picture.
Regards,
Shivang
On Thu, Jun 7, 2018 at 11:33 AM Xavier Waintal
Hi Shivang,
Le 6 juin 2018 à 22:53, Shivang Agarwal
a écrit : Hello authors,
I am trying to perform an eigenchannel analysis of a graphene nanoribbon. For that I will be using the formula : *T(E) = ГL(E)½ GC†(E) ГR(E) GC(E) ГL(E)½ * where *ГL(E)* is the coupling matrix between the left lead and the conductor, *GC(E)* is the greens function matrix of the conductor (system) and '†' is the dagger operator. The equation is from the following paper: https://journals.aps.org/prb/pdf/10.1103/PhysRevB.73.075429
(1) Now as far as I know, Kwant allows us to calculate transmission as a number T(E). What I need for my code is 't' where Trace(t*†*t) = T(E). Could somebody let me know how can I get the desired quantity 't'?. But I don't know how I can get the coupling matrix *ГL(E) between the left (or right) lead and the conductor*
The scattering matrix is actually the basic object that Kwant calculate directly. You can access it through
kwant.solvers.default https://kwant-project.org/doc/1/reference/kwant.solvers#module-kwant.solvers...s.smatrix( …)
The smatrix between two different leads is your transmission matrix t. For the same lead it is the reflexion matrix r.
see: https://kwant-project.org/doc/1/reference/kwant.solvers
You could also calculate the Green function and the Gamma matrix that you mention, but I see no point in doing it.
That would be kwant.solvers.default https://kwant-project.org/doc/1/reference/kwant.solvers#module-kwant.solvers....greens_function() for G(E) And kwant.physic https://kwant-project.org/doc/1/reference/kwant.physics#module-kwant.physics s.selfenergy https://kwant-project.org/doc/1/reference/generated/kwant.physics.selfenergy...() for the lead self energy S(E) with Gamma(E) = i [ S(E) - S(E)^dagger]
Best regards, Xavier
(2) Also, we know that t = *ГL(E)½ GC(E) ГR(E)½ .But I don't know how I can get the coupling matrix ГL(E) between the left (or right) lead and the conductor. Is it possible to get too?*
*PS - My aim is to find the wavefunctions inside the nanoribbon (which Kwant can do very conveniently) and also their phases! I have found the wavefunctions but am unable to find their phases. If there's any other way to find it that would also be extremely helpful.*
*Any help would be greatly appreciated.*
*Thanks and Regards,* *Shivang Agarwal* -- *Shivang Agarwal* Junior Undergraduate Discipline of Electrical Engineering IIT Gandhinagar
Contact: +91-9869321451
-- *Shivang Agarwal* Junior Undergraduate Discipline of Electrical Engineering IIT Gandhinagar Contact: +91-9869321451