Dear Sayandip,
You have few mistakes in your code:
1) mount_vlead(syst,[L-1], 2). Here you have to provide a list of sites (an
interface) on which you want to attach a virtual lead.
Example: mount_vlead(syst,[lat(1),lat(5),lat(6)], 2)
2) inside the function "mount_vlead" you have to define
dim=len(vlead_interface)*norbs.
3) G12=kwant.greens_function(syst, energy=-1.8*1j,
in_leads=[L-1],out_leads=[L],\
check_hermiticity=False,params=par).data
Here, you have to provide the rank of the lead following the order you
attached them. 0 is the left lead, 1 is the right lead, 2 is the first
virtual lead, ....
Example:G12=kwant.greens_function(syst, energy=-1.8*1j,
in_leads=[2],out_leads=[3],\
check_hermiticity=False,params=par).data
You can check the previous post for more details [1]
I hope this helps,
Adel
[1]
https://www.mail-archive.com/[email protected]/msg01356.html
On Thu, Oct 21, 2021 at 7:20 PM Sayandip Dhara <[email protected]>
wrote:
> Hello,
> I am trying to extract Green's function between two arbitrary sites in a
> system. I have noticed from one of the previous threads that one way to do
> it is to attach virtual leads with zero self-energy on those specific
> sites. However, I am having trouble with the suggested function. It is
> telling me that whichever site I want to attach is not in the scattering
> region. The following is the code:
> import kwant
> from types import SimpleNamespace
> from copy import copy
> import tinyarray
> import numpy as np
> import csv
> import ipywidgets
> #import holoviews as hv
> #hv.extension('bokeh')
> from scipy import sparse
> from matplotlib import pyplot
> from scipy.optimize import minimize
> sigma_x = tinyarray.array([[0, 1], [1, 0]])
> sigma_y = tinyarray.array([[0, -1j], [1j, 0]])
> sigma_z = tinyarray.array([[1, 0], [0, -1]])
> sigma_0 = tinyarray.array([[1, 0], [0, 1]])
>
> tau_x = tinyarray.array([[0, 1], [1, 0]])
> tau_y = tinyarray.array([[0, -1j], [1j, 0]])
> tau_z = tinyarray.array([[1, 0], [0, -1]])
> tau_0 = tinyarray.array([[1, 0], [0, 1]])
>
> # mu=0.5,
> # t=-1.,delta=0.5,V_N=1.25, phi=0, L=3
>
> def make_system_ex3(L=10):
> lat = kwant.lattice.chain(norbs=2)
> syst = kwant.Builder()
>
> #### Define the scattering region. ####
> def onsite_sc(site,t,mu,delta):
> return (2.*t-mu )*tau_z + delta*tau_x
>
> def onsite_N(site,t,mu,V_N):
> return (2.*t-mu + V_N)*tau_z
>
> syst[(lat(x) for x in range(1, L))] = onsite_sc
>
> #superconducting onsite hamiltonian
>
> syst[lat(L)] = onsite_N #normal onsite hamiltonian
>
> syst[(lat(x) for x in range(L+1,2*L+1))] = onsite_sc #superconducting
> onsite hamiltonian
>
> def hop(site1,site2,t,phi):
> return -t*np.matmul(np.exp(1j*phi*tau_z),tau_z)
>
> syst[(lat(L-1), lat(L))] = hop
> for i in range(1,L-1):
> syst[(lat(i), lat(i+1))] = -t*tau_z
> for i in range(L,2*L):
> syst[(lat(i), lat(i+1))] = -t*tau_z
>
>
> #### Define the leads. ####
> sym_left = kwant.TranslationalSymmetry([-1])
> lead0 = kwant.Builder(sym_left)
> lead0[(lat(0))] = (2.*t-mu)*tau_z + delta*tau_x
> lead0[lat.neighbors()] = -t*tau_z
>
> sym_right = kwant.TranslationalSymmetry([1])
> lead1 = kwant.Builder(sym_right)
> lead1[(lat(2*L+1))] = (2.*t-mu)*tau_z + delta*tau_x
> lead1[lat.neighbors()] = -t*tau_z
>
> # #### Attach the leads and return the system. ####
> syst.attach_lead(lead0)
> syst.attach_lead(lead1)
>
>
> return syst,lat
>
> ----------------------------------------------------------------------------------------------------------------------------
> mu=1
> t=1.0
> delta=0.5
> V_N=1
> phi=0
> L=10
>
> par = dict(t=t,mu=mu,delta=delta,phi=phi,V_N=V_N)
>
> #
> syst,lat = make_system_ex3(L=10)
>
> def mount_vlead(sys, vlead_interface, norb):
> dim = norb
> 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)
>
>
> mount_vlead(syst,[L-1], 2) # number of orbitals =4. Here we mount lead
> number 2
> mount_vlead(syst,[L], 2) # number of orbitals =4. Here we mount lead
> number 3
>
> syst =syst.finalized()
>
> G12=kwant.greens_function(syst, energy=-1.8*1j,
> in_leads=[L-1],out_leads=[L],\
> check_hermiticity=False,params=par).data
> G21=kwant.greens_function(syst, energy=-1.8*1j,
> in_leads=[L],out_leads=[L-1],\
> check_hermiticity=False,params=par).data
>
>
> ----------------------------------------------------------------------------------------------------------------------------------
> The error message I am getting is
> " ValueError: Lead 2 is attached to a site that does not belong to the
> scattering region:
> 9"
> It would be great if you can suggest to me where I am going wrong.
> Thanks,
> Sayandip
>
--
Abbout Adel
