Dear Patrik,
Your program has some mistakes:
1) When you define a site, you need to use its coordinates, so no need to
multiply by the lattice constant
ie sys[lat(0,0,11)]=3 and not sys[lat(0,0,11*a]=3
2) You should not use the loop "for" when you define the lead. This means
that you added more than one site to your cell. Just define one site.
3) No need to add 2 extra sites to your system in order to attach the
leads. one site is sufficient. This is not a mistake but it makes your
program simpler.
4) You are using a 1D lead and your energies are starting from 0. So, in
order to have a conducting mode, you need to change the potential from 4t
to 2t.
5) Avoid energy 0 (the bottom of the band) when you calculate the
scattering matrix otherwise you will get an error ValueError: Input a
needs to be a square matrix.
start from 0.0001 for example.
Now I want to make a comment on your problem. In kwant, the hamiltonian is
a graph. The position of the sites in your case are not important. only the
onsite potentials and the hoppings are relevent. In your case, you can put
all the sites in a line and this will change nothing since you do not have
a field which depend on space. Your geometry is not relevent. So, if you do
not intend to put an electric field or magnetic field which will add a
space dependence to your hoppings, your problem boils down to 1D uniform
chain and you will get conductance equal to 1 for all the energies (check
the program below.)
Here is your program with the corrections:
I hope this helps.
Adel
-----------------------------------------------------------------------------------------------
import matplotlib.pyplot as plt from mpl_toolkits.mplot3d import Axes3D
from scipy.spatial import * from matplotlib import rcParams from numpy
import * from numpy.linalg import * import pickle import sys import os
import string import heapq import kwant import tinyarray
#pb.pltutils.use_style() from matplotlib import pyplot cl_1dl3=True if
cl_1dl3: a = 0.34 t = 1.0 N = 31 class
Amorphous(kwant.builder.SimpleSiteFamily): def normalize_tag(self, tag):
return tinyarray.array(tag, float) def pos(self, tag): return tag atoms =
Amorphous() syst = kwant.Builder() #coordinates of a chiral chain imported
manually sites=atoms(0.0, 0.0, 0.0), atoms(-0.1336881039, 0.4114496766,
0.3400000000), atoms(-0.4836881039, 0.6657395614, 0.6800000000),
atoms(-0.9163118961, 0.6657395614, 1.0200000000), atoms(-1.2663118961,
0.4114496766, 1.3600000000), atoms(-1.4000000000, 0.0000000000,
1.7000000000), atoms(-1.2663118961, -0.4114496766, 2.0400000000),
atoms(-0.9163118961, -0.6657395614, 2.3800000000), atoms(-0.4836881039,
-0.6657395614, 2.7200000000), atoms(-0.1336881039, -0.4114496766,
3.0600000000), atoms(0.0000000000, -0.0000000000, 3.4000000000),
atoms(-0.1336881039, 0.4114496766, 3.7400000000), atoms(-0.4836881039,
0.6657395614, 4.0800000000), atoms(-0.9163118961, 0.6657395614,
4.4200000000), atoms(-1.2663118961, 0.4114496766, 4.7600000000),
atoms(-1.4000000000, 0.0000000000, 5.1000000000), atoms(-1.2663118961,
-0.4114496766, 5.4400000000), atoms(-0.9163118961, -0.6657395614,
5.7800000000), atoms(-0.4836881039, -0.6657395614, 6.1200000000),
atoms(-0.1336881039, -0.4114496766, 6.4600000000), atoms(0.0000000000,
-0.0000000000, 6.8000000000), atoms(-0.1336881039, 0.4114496766,
7.1400000000), atoms(-0.4836881039, 0.6657395614, 7.4800000000),
atoms(-0.9163118961, 0.6657395614, 7.8200000000), atoms(-1.2663118961,
0.4114496766, 8.1600000000), atoms(-1.4000000000, 0.0000000000,
8.5000000000), atoms(-1.2663118961, -0.4114496766, 8.8400000000),
atoms(-0.9163118961, -0.6657395614, 9.1800000000), atoms(-0.4836881039,
-0.6657395614, 9.5200000000), atoms(-0.1336881039, -0.4114496766,
9.8600000000), atoms(0.0, 0.0, 10.2) #adding the onsite and hopping to the
system for i in range(N): syst[sites[i]] = 2 * t if i > 0: syst[sites[i],
sites[i-1]] = -t #syst[sites[N-1], sites[0]] = -t kwant.plot(syst) # If we
want to attach to vertical 1D chains to the system # we first add a slice
of the down lead to the scattering region lat=kwant.lattice.cubic(a)
syst[lat(0, 0, -1)] = 2 * t # now we add the hopping to the chiral chain
syst[sites[0], lat(0, 0, -1)] = -t # fWe make a regular down lead and
attach it to the system dn_lead =
kwant.Builder(kwant.TranslationalSymmetry((0, 0, -a))) #for i in range(2):
dn_lead[lat(0, 0, -2)] = 2 * t dn_lead[lat.neighbors()] = -t
syst.attach_lead(dn_lead) syst[lat(0, 0, N)] = 2 * t syst[lat(0, 0, N),
sites[N-1]] = -t # finally we make a regular lead and attach it to the top
up_lead = kwant.Builder(kwant.TranslationalSymmetry((0, 0, a))) #for i in
range(N, N+2): up_lead[lat(0, 0, 11)] = 2 * t up_lead[lat.neighbors()] = -t
syst.attach_lead(up_lead) kwant.plot(syst) trans=True if trans: syst =
syst.finalized() energies = [] data = [] for ie in range(1,100): energy =
ie * 0.01 smatrix = kwant.smatrix(syst, energy=energy)
energies.append(energy) data.append(smatrix.transmission(1, 0))
pyplot.figure() pyplot.plot(energies, data) pyplot.ylim([0,1.2])
pyplot.xlabel("energy [t]") pyplot.ylabel("conductance [e^2/h]")
pyplot.show()
On Fri, Jul 7, 2017 at 6:01 PM, Patrik Arvoy <arv...@gmail.com> wrote:
>
> Hi Anton,
>
> Thank you for the reply!
> I used your suggestion to attach two 1D leads along the z axis to a chiral
> 1D chain.
>
> I inserted my code in the following and added comments to each part.
>
> I have two questions:
> 1- I successfully add a 1D chain to the lower part of the chiral system but
> when I try to add a 1D chain as the upper lead to the top of the system,
> it is automatically added
> somewhere in the middle, which is not clear to me why.
>
> 2- How can I avoid zero conductance?
>
> Thanks in advance
> Patrik
>
>
> ----------------------------------------------------------
> import matplotlib.pyplot as plt
> from mpl_toolkits.mplot3d import Axes3D
> from scipy.spatial import *
> from matplotlib import rcParams
> from numpy import *
> from numpy.linalg import *
> import pickle
> import sys
> import os
> import string
> import heapq
> import kwant
> import tinyarray
> pb.pltutils.use_style()
>
>
>
> cl_1dl3=True
> if cl_1dl3:
> a = 0.34
> t = 1.0
> N = 31
>
>
> class Amorphous(kwant.builder.SimpleSiteFamily):
> def normalize_tag(self, tag):
> return tinyarray.array(tag, float)
>
> def pos(self, tag):
> return tag
>
>
> atoms = Amorphous()
> syst = kwant.Builder()
> #coordinates of a chiral chain imported manually
> sites=atoms(0.0, 0.0, 0.0), atoms(-0.1336881039, 0.4114496766,
> 0.3400000000), atoms(-0.4836881039, 0.6657395614, 0.6800000000),
> atoms(-0.9163118961, 0.6657395614, 1.0200000000), atoms(-1.2663118961,
> 0.4114496766, 1.3600000000), atoms(-1.4000000000, 0.0000000000,
> 1.7000000000), atoms(-1.2663118961, -0.4114496766, 2.0400000000),
> atoms(-0.9163118961, -0.6657395614, 2.3800000000), atoms(-0.4836881039,
> -0.6657395614, 2.7200000000), atoms(-0.1336881039, -0.4114496766,
> 3.0600000000), atoms(0.0000000000, -0.0000000000, 3.4000000000),
> atoms(-0.1336881039, 0.4114496766, 3.7400000000), atoms(-0.4836881039,
> 0.6657395614, 4.0800000000), atoms(-0.9163118961, 0.6657395614,
> 4.4200000000), atoms(-1.2663118961, 0.4114496766, 4.7600000000),
> atoms(-1.4000000000, 0.0000000000, 5.1000000000), atoms(-1.2663118961,
> -0.4114496766, 5.4400000000), atoms(-0.9163118961, -0.6657395614,
> 5.7800000000), atoms(-0.4836881039, -0.6657395614, 6.1200000000),
> atoms(-0.1336881039, -0.4114496766, 6.4600000000), atoms(0.0000000000,
> -0.0000000000, 6.8000000000), atoms(-0.1336881039, 0.4114496766,
> 7.1400000000), atoms(-0.4836881039, 0.6657395614, 7.4800000000),
> atoms(-0.9163118961, 0.6657395614, 7.8200000000), atoms(-1.2663118961,
> 0.4114496766, 8.1600000000), atoms(-1.4000000000, 0.0000000000,
> 8.5000000000), atoms(-1.2663118961, -0.4114496766, 8.8400000000),
> atoms(-0.9163118961, -0.6657395614, 9.1800000000), atoms(-0.4836881039,
> -0.6657395614, 9.5200000000), atoms(-0.1336881039, -0.4114496766,
> 9.8600000000), atoms(0.0, 0.0, 10.2)
>
> #adding the onsite and hopping to the system
> for i in range(N):
> syst[sites[i]] = 4 * t
> if i > 0:
> syst[sites[i], sites[i-1]] = -t
> syst[sites[N-1], sites[0]] = -t
> kwant.plot(syst)
>
> # If we want to attach to vertical 1D chains to the system
> # we first add a slice of the down lead to the scattering region
> lat=kwant.lattice.cubic(a)
>
> for i in range(2): #number of atoms added to the bottom of the
> chiral chain
> syst[lat(0, 0, -(i+1)*a)] = 4 * t
> syst[lat.neighbors()] = -t
> # now we add the hopping to the chiral chain
> syst[sites[0], lat(0, 0, -a)] = -t
> kwant.plot(syst)
>
> # fWe make a regular down lead and attach it to the system
> dn_lead = kwant.Builder(kwant.TranslationalSymmetry((0, 0, -a)))
> for i in range(2):
> dn_lead[lat(0, 0, -(i+1)*a)] = 4 * t
> dn_lead[lat.neighbors()] = -t
> syst.attach_lead(dn_lead)
> kwant.plot(syst)
>
>
>
> #Here is wwhere the problem arises!!!
> #I want to add a similar 1D chain to the top of the chiral system
> #but instead it is automatically added somewhere in the middle.
>
>
>
> for i in range(N, N+2): #number of atoms added to the top
> syst[lat(0, 0, i*a)] = 4 * t
> syst[lat.neighbors()] = -t
> # now we add the hopping to the systeml
> syst[lat(0, 0, N*a), sites[N-1]] = -t
> kwant.plot(syst)
>
> # finally we make a regular lead and attach it to the top
> up_lead = kwant.Builder(kwant.TranslationalSymmetry((0, 0, a)))
> for i in range(N, N+2):
> up_lead[lat(0, 0, i*a)] = 4 * t
> up_lead[lat.neighbors()] = -t
> syst.attach_lead(up_lead)
>
> kwant.plot(syst)
>
> trans=True
> if trans:
> syst = syst.finalized()
> energies = []
> data = []
>
> for ie in range(0,100):
> energy = ie * 0.01
> smatrix = kwant.smatrix(syst, energy)
> energies.append(energy)
> data.append(smatrix.transmission(1, 0))
> pyplot.figure()
> pyplot.plot(energies, data)
> pyplot.xlabel("energy [t]")
> pyplot.ylabel("conductance [e^2/h]")
> pyplot.show()
>
>
> On 6 July 2017 at 18:13, Anton Akhmerov <anton.akhmerov...@gmail.com>
> wrote:
>
>> Hi Patrik,
>>
>> You can use site coordinates that don't belong to any lattice. For
>> that you need to define your own SiteFamily, see for example the
>> script below that achieves this goal.
>>
>> -------------------
>> from matplotlib import pyplot
>> import kwant
>> import tinyarray
>>
>> class Amorphous(kwant.builder.SimpleSiteFamily):
>> def normalize_tag(self, tag):
>> return tinyarray.array(tag, float)
>>
>> def pos(self, tag):
>> return tag
>>
>>
>> atoms = Amorphous()
>>
>> syst = kwant.Builder()
>> sites = atoms(0.01, 0.05), atoms(1.01, -.5)
>> syst[sites[0]] = syst[sites[1]] = 2
>> syst[sites[1], sites[0]] = 1
>>
>> kwant.plot(syst)
>> ---------------------
>>
>> Of course it's now your responsibility to specify the Hamiltonian,
>> leads, attaching leads, etc.
>>
>> Best,
>> Anton
>>
>> On Thu, Jul 6, 2017 at 4:12 PM, Patrik Arvoy <arv...@gmail.com> wrote:
>> >
>> > Dear users and developers,
>> >
>> > I was wondering if I can import the coordinates of a scattering region
>> > without any particular symmetry and compute the conductance via kwant.
>> > If yes, how does one do that?
>> > Let's say the scattering region does not have any symmetry after
>> optimizing
>> > the structure via MD or ... and I have a list of coordinates of all the
>> > sites.
>> > I appreciate any help.
>> >
>> > Regards
>> > Patrik
>>
>
>
--
Abbout Adel
