Dear Sayandip,
The Green's function you obtain is a submatrix of the total retarded
Green's function. I mean by this that you obtain the Green's function
matrix between the two sites that are at L and L-1 as you wrote your code.
I suppose here that the fictitious lead you added on sites L and L-1 are
ranked 2 and 3
I hope this helps,
Adel
On Tue, Nov 9, 2021 at 7:21 PM Sayandip Dhara <sayan...@knights.ucf.edu>
wrote:
> Hi Abbout,
> Thanks for pointing out the mistakes that I was making. Now, I want to
> implement a formula like the one mentioned in the thread before to
> calculate the equilibrium dc current for a Josephson junction:
> I = 2*(KbT/hbar)/sum_{w_p} [trace(H21*G^R_{12}) - trace(H12*G^R_{21})
> where w_p are the Matsubara frequencies.
> I wrote the following to get the green's functions:
> _______________________________________________________________
> def mount_vlead(sys, vlead_interface, norb):
> dim = norb*len(vlead_interface)
> print(dim)
> zero_array = np.zeros((dim, dim), dtype=float)
> def selfenergy_func(energy, args=()):
> return zero_array
>
> vlead = kwant.builder.SelfEnergyLead(selfenergy_func,
> vlead_interface,())
> sys.leads.append(vlead)
>
>
> lead2 = mount_vlead(syst,[lat(L-1)], 2)
> lead3 = mount_vlead(syst,[lat(L)], 2)
>
> syst =syst.finalized()
>
> G12=kwant.greens_function(syst, energy=-1.8*1j,
> in_leads=[2],out_leads=[3],\
> check_hermiticity=False,params=par).data
> G21=kwant.greens_function(syst, energy=-1.8*1j,
> in_leads=[3],out_leads=[2],\
> check_hermiticity=False,params=par).data
>
>
> H12=syst.hamiltonian_submatrix(to_sites=[L-1], from_sites=[L],params=par)
> H21=syst.hamiltonian_submatrix(to_sites=[L], from_sites=[L-1],params=par)
> So my question is now, that if the Green's functions that I am using above
> are truly the retarded Green's function of the system?
> Thanks,
> Sayandip
>
--
Abbout Adel
