Dear Sumit,
The easiest way to calculate Green’s function on arbitrary set of sites in your system is to specify additional virtual lead with zero self energy with following builder class:
http://kwant-project.org/doc/1/reference/generated/kwant.builder.SelfEnergyLead#kwant.builder.SelfEnergyLead
Here is an example function, that can do it:
def mount_vlead(sys, vlead_interface, norb):
"""Mounts virtual lead to interfaces provided.
:sys: kwant.builder.Builder
An unfinalized system to mount leads
:vlead_interface: sequence of kwant.builder.Site
Interface of lead
:norb: integer
Number of orbitals in system hamiltonian.
"""
dim = len(vlead_interface)*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)
Then you can calculate Green’s gunction on interface of this lead. Basis in that case is specified on order of sites in vlead_interface.
If I remember correctly, calculation time in that case scales as n*N*log(N), where N is number of sites in system, n is number of sites to calculate Green’s function in.
With best regards,
Viacheslav Ostroukh
Instituut-Lorentz – Niels Bohrweg 2 – Room 259 – 2333 CA Leiden
ostroukh@ilorentz.org
slava@ostroukh.me
+31 6 444 968 12
+38 099 721 76 06
From: Sumit Ghosh
Sent: Tuesday, January 12, 2016 11:44
To: kwant-discuss@kwant-project.org
Subject: [Kwant] Green's function for each block
I am trying to calculate the Green's function for each layer/slice of a ribbon/wire. I can find the self energy and surface Green's function from which (in principle, I have not tried yet) it is possible find the Green's function for successive layer using RGF algorithm as discussed in this thread (http://thread.gmane.org/gmane.comp.science.kwant.user/647).
From the GreensFunction documentation, it looks like there is a way to specify the slice/block of the system and directly find the Green's function, but I don't find any example of that. Is there any way to do that ?
For example consider this graphene ribbon. I added a random impurity to break the translational symmetry so that I can distinguish each slice. I can find the Green's function for the sites which are connected to leads only. How do I calculate the Green's function for each slice?
Best,
Sumit
------------------------------------------------------
from __future__ import division
from math import sqrt
from matplotlib import pyplot
import kwant
import numpy as np
sin_30, cos_30 = (1 / 2, sqrt(3) / 2)
graphene = kwant.lattice.general([(1, 0), (sin_30, cos_30)],
[(0, 0), (0, 1 / sqrt(3))])
a, b = graphene.sublattices
L=3;W=3;
def box(pos): #scattering region
x, y = pos
return -L<x<L and -W<y<W
def lshape(pos): #lead
x,y = pos
return -W<y<W
def onsite(site):
return kwant.digest.uniform(repr(site))
hoppings = (((0, 0), a, b), ((0, 1), a, b), ((-1, 1), a, b))
def scater():
sys = kwant.Builder()
sys[graphene.shape(box, (0, 0))] = onsite
sys[[kwant.builder.HoppingKind(*hopping) for hopping in hoppings]] = -1
lead = kwant.Builder(kwant.TranslationalSymmetry(graphene.vec((-1, 0))))
lead[graphene.shape(lshape, (0, 0))] = 0
lead[[kwant.builder.HoppingKind(*hopping) for hopping in hoppings]] = -1
sys.attach_lead(lead)
sys.attach_lead(lead.reversed())
return sys
sys=scater()
#def family_colors(site):
# return 0 if site.family == a else 1
#kwant.plot(sys, site_color=family_colors, site_lw=0.1, colorbar=False)
sys = sys.finalized()
# Self energy
flead0 = sys.leads[0]
flead1 = sys.leads[1]
s_en = flead0.selfenergy(0.5)
#Green's function
g = kwant.greens_function(sys,0.5)
gg = g.submatrix(1,0)
--
Sumit Ghosh
Spintronics Theory Group
PSE Division
KAUST
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