Thanks Xavier. I now have a clearer picture. Regards, Shivang
On Thu, Jun 7, 2018 at 11:33 AM Xavier Waintal <xavier.wain...@cea.fr> wrote: > Hi Shivang, > > > Le 6 juin 2018 à 22:53, Shivang Agarwal <shivang.agar...@iitgn.ac.in> 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.default>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.default>.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.html#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
