# Re: [Kwant] continuous vs discrete leads

```Thank you Joe for pointing out the mistake!
I defined the lead_shape function that return True for sites in the 'lat1'.
I have already added the lat1(0, 0, -1) site to the system.
When I replace the 'if continuous' section with the following section it
will complain.```
```
if continuous:
(x, y, z) = site.pos
return (x == -0.7 and y == 0.0 and z <= -a)
t00=0.0
="t00*sigma_0*k_x**2+t00*sigma_0*k_y**2-t0*sigma_0*k_z**2+(2*t0+e1)*sigma_0"

I attach the full code at the end of this message.

What would be the continuous leads (in the momentum space) equivalent of
two discrete leads (vertical 1D chains) attached to my system?

Regards
Patrik

-------------------------------------------------
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
from matplotlib import pyplot

chiral=True
if chiral:
p = pi/5    #phi
t = 0.66    #theta
a = 0.34
x = 1.4
e1 = 0
e2 = 0.3
t2=0.1
t1=-x*t2
t0 = 2
lam=-0.08
t_so1 = 0.01 #spin-orbit coupling param
t_so2 = x*t_so1 #spin-orbit coupling param
tl=tr=0.3
N = 30
sigma_0 = tinyarray.array([[1, 0], [0, 1]])
sigma_x = tinyarray.array([[0, 1], [1, 0]])
sigma_y = tinyarray.array([[0, -1j], [1j, 0]])
sigma_z = tinyarray.array([[1, 0], [0, -1]])
no=2            #number of orbitals
def sigma_v1(ap):         # pauli metrix along the vertical axis
value=sigma_z*cos(t)+sin(t)*(sigma_x*sin(ap)-sigma_y*cos(ap))
return value

def sigma_v2(ap):         # pauli metrix along the vertical axis
value=sigma_z*cos(t)-sin(t)*(sigma_x*sin(ap)-sigma_y*cos(ap))
return value

def family_color(sites):
return 'black' #if site.family == sites

def hopping_lw(site1, site2):
return 0.08

class Amorphous(kwant.builder.SiteFamily):
def __init__(self, coords):
self.coords = coords
super(Amorphous, self).__init__("amorphous", "",no)

def normalize_tag(self, tag):
try:
tag = int(tag[0])
except:
raise KeyError

if 0 <= tag < len(coords):
return tag
else:
raise KeyError

def pos(self, tag):
return self.coords[tag]

coords=[(0.0000000000, 0.0000000000, 0.0000000000), (-0.1336881039,
0.4114496766, 0.3400000000), (-0.4836881039, 0.6657395614, 0.6800000000),
(-0.9163118961, 0.6657395614, 1.0200000000), (-1.2663118961, 0.4114496766,
1.3600000000), (-1.4000000000, 0.0000000000, 1.7000000000), (-1.2663118961,
-0.4114496766, 2.0400000000), (-0.9163118961, -0.6657395614, 2.3800000000),
(-0.4836881039, -0.6657395614, 2.7200000000), (-0.1336881039,
-0.4114496766, 3.0600000000), (0.0000000000, -0.0000000000, 3.4000000000),
(-0.1336881039, 0.4114496766, 3.7400000000), (-0.4836881039, 0.6657395614,
4.0800000000), (-0.9163118961, 0.6657395614, 4.4200000000), (-1.2663118961,
0.4114496766, 4.7600000000), (-1.4000000000, 0.0000000000, 5.1000000000),
(-1.2663118961, -0.4114496766, 5.4400000000), (-0.9163118961,
-0.6657395614, 5.7800000000), (-0.4836881039, -0.6657395614, 6.1200000000),
(-0.1336881039, -0.4114496766, 6.4600000000), (0.0000000000, -0.0000000000,
6.8000000000), (-0.1336881039, 0.4114496766, 7.1400000000), (-0.4836881039,
0.6657395614, 7.4800000000), (-0.9163118961, 0.6657395614, 7.8200000000),
(-1.2663118961, 0.4114496766, 8.1600000000), (-1.4000000000, 0.0000000000,
8.5000000000), (-1.2663118961, -0.4114496766, 8.8400000000),
(-0.9163118961, -0.6657395614, 9.1800000000), (-0.4836881039,
-0.6657395614, 9.5200000000), (-0.1336881039, -0.4114496766, 9.8600000000),
(-1.4000000000, 0.0000000000, 0.0000000000), (-1.2663118961, -0.4114496766,
0.3400000000), (-0.9163118961, -0.6657395614, 0.6800000000),
(-0.4836881039, -0.6657395614, 1.0200000000), (-0.1336881039,
-0.4114496766, 1.3600000000), (0.0000000000, -0.0000000000, 1.7000000000),
(-0.1336881039, 0.4114496766, 2.0400000000), (-0.4836881039, 0.6657395614,
2.3800000000), (-0.9163118961, 0.6657395614, 2.7200000000), (-1.2663118961,
0.4114496766, 3.0600000000), (-1.4000000000, 0.0000000000, 3.4000000000),
(-1.2663118961, -0.4114496766, 3.7400000000), (-0.9163118961,
-0.6657395614, 4.0800000000), (-0.4836881039, -0.6657395614, 4.4200000000),
(-0.1336881039, -0.4114496766, 4.7600000000), (0.0000000000, -0.0000000000,
5.1000000000), (-0.1336881039, 0.4114496766, 5.4400000000), (-0.4836881039,
0.6657395614, 5.7800000000), (-0.9163118961, 0.6657395614, 6.1200000000),
(-1.2663118961, 0.4114496766, 6.4600000000), (-1.4000000000, 0.0000000000,
6.8000000000), (-1.2663118961, -0.4114496766, 7.1400000000),
(-0.9163118961, -0.6657395614, 7.4800000000), (-0.4836881039,
-0.6657395614, 7.8200000000), (-0.1336881039, -0.4114496766, 8.1600000000),
(0.0000000000, -0.0000000000, 8.5000000000), (-0.1336881039, 0.4114496766,
8.8400000000), (-0.4836881039, 0.6657395614, 9.1800000000), (-0.9163118961,
0.6657395614, 9.5200000000), (-1.2663118961, 0.4114496766, 9.8600000000)]
amorphous_lat = Amorphous(coords)

syst = kwant.Builder()

for i in range(N):
syst[amorphous_lat(i)] = e1*sigma_0
syst[amorphous_lat(N+i)] = e2*sigma_0
syst[amorphous_lat(i), amorphous_lat(N+i)] = lam*sigma_0
if i > 0:
syst[amorphous_lat(i), amorphous_lat(i-1)] = t1*sigma_0 +
1j*t_so1*(sigma_v1(i*p)+sigma_v1((i-1)*p))
syst[amorphous_lat(N+i),amorphous_lat(N+i-1)] = t2*sigma_0 +
1j*t_so2*(sigma_v2(i*p)+sigma_v2((i-1)*p))

prim_vecs=tinyarray.array([(a,0.,0.),(0.,a,0.),(0.,0.,a)])

offset1=tinyarray.array((-0.7, 0.0, 0.0))
lat1=kwant.lattice.Monatomic(prim_vecs, offset1, norbs=no)

syst[lat1(0, 0, -1)] = e1*sigma_0
syst[amorphous_lat(0), lat1(0, 0, -1)] = tl*sigma_0
syst[amorphous_lat(N), lat1(0, 0, -1)] = tl*sigma_0

sym = kwant.TranslationalSymmetry([0, 0, -a])

if discrete:
sym = kwant.TranslationalSymmetry([0, 0, -a])

if continuous:
(x, y, z) = site.pos
return (x == -0.7 and y == 0.0 and z <= -a)
t00=0.0
="t00*sigma_0*k_x**2+t00*sigma_0*k_y**2-t0*sigma_0*k_z**2+(2*t0+e1)*sigma_0"

sym1 = kwant.TranslationalSymmetry([0, 0, a])

syst[lat1(0, 0, N)] = e1*sigma_0
syst[amorphous_lat(N-1), lat1(0, 0, N)] = tr*sigma_0
syst[amorphous_lat(2*N-1), lat1(0, 0, N)] = tr*sigma_0

system=kwant.plot(syst, site_lw=0.1, site_color=family_color,
hop_lw=hopping_lw)

trans=True
if trans:
syst = syst.finalized()
energies = []
datau = []

for ie in range(-320,520):
energy = ie * 0.001
smatrix = kwant.smatrix(syst, energy=energy)
energies.append(energy)
Gu=smatrix.transmission((1, 0), 0)
Gd=smatrix.transmission((1, 1), 0)
datau.append(Gu)

fig = pyplot.figure()
pyplot.plot(energies, datau, 'b--')
pyplot.legend(['Gu'], loc='upper left')
pyplot.xlim([-0.32,0.52])
pyplot.ylim([-0.03,1.05])
pyplot.show()

On 7 August 2017 at 12:27, Joseph Weston <joseph.westo...@gmail.com> wrote:

> Dear Patrik,
>
>
> The line that fails is
>
> dn_lead.fill(template, lat1, lat1(0, 0, -2))
>
> did you read the documentation for the "fill" method of builders? The
> documentation says that the second argument, called "shape", should be a
> function that takes a site and returns true or false depending on whether
> or not the site should be added. Instead of providing such a function, you
> have just provided the lattice itself.
>
>
> Happy Kwanting,
>
>
> Joe
> On 08/07/2017 11:35 AM, Patrik Arvoy wrote:
>
>
> Dear Christoph,
>
> Thank you for the reply!
>
> The code works fine with the switch (discrete=True and continuous=False).
> Now if I change (discrete=False and continuous=True), I want to attach a
> I get the error.
>
> Regards
> Patrik
>
> Here is the code
> -----------------------------------
> 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
> from matplotlib import pyplot
>
>
>
>
>
> chiral=True
> if chiral:
>     p = pi/5    #phi
>     t = 0.66    #theta
>     a = 0.34
>     x = 1.4
>     e1 = 0
>     e2 = 0.3
>     t2=0.1
>     t1=-x*t2
>     t0 = 2
>     lam=-0.08
>     t_so1 = 0.01 #spin-orbit coupling param
>     t_so2 = x*t_so1 #spin-orbit coupling param
>     tl=tr=0.3
>     N = 30
>     sigma_0 = tinyarray.array([[1, 0], [0, 1]])
>     sigma_x = tinyarray.array([[0, 1], [1, 0]])
>     sigma_y = tinyarray.array([[0, -1j], [1j, 0]])
>     sigma_z = tinyarray.array([[1, 0], [0, -1]])
>     no=2            #number of orbitals
>     def sigma_v1(ap):         # pauli metrix along the vertical axis
>         value=sigma_z*cos(t)+sin(t)*(sigma_x*sin(ap)-sigma_y*cos(ap))
>         return value
>
>     def sigma_v2(ap):         # pauli metrix along the vertical axis
>         value=sigma_z*cos(t)-sin(t)*(sigma_x*sin(ap)-sigma_y*cos(ap))
>         return value
>
>     def family_color(sites):
>         return 'black' #if site.family == sites
>
>     def hopping_lw(site1, site2):
>         return 0.08
>
>
>     class Amorphous(kwant.builder.SiteFamily):
>         def __init__(self, coords):
>             self.coords = coords
>             super(Amorphous, self).__init__("amorphous", "",no)
>
>         def normalize_tag(self, tag):
>             try:
>                 tag = int(tag[0])
>             except:
>                 raise KeyError
>
>             if 0 <= tag < len(coords):
>                 return tag
>             else:
>                 raise KeyError
>
>         def pos(self, tag):
>             return self.coords[tag]
>
>     coords=[(0.0000000000, 0.0000000000, 0.0000000000), (-0.1336881039,
> 0.4114496766, 0.3400000000), (-0.4836881039, 0.6657395614, 0.6800000000),
> (-0.9163118961, 0.6657395614, 1.0200000000), (-1.2663118961, 0.4114496766,
> 1.3600000000), (-1.4000000000, 0.0000000000, 1.7000000000), (-1.2663118961,
> -0.4114496766, 2.0400000000), (-0.9163118961, -0.6657395614, 2.3800000000),
> (-0.4836881039, -0.6657395614, 2.7200000000), (-0.1336881039,
> -0.4114496766, 3.0600000000), (0.0000000000, -0.0000000000, 3.4000000000),
> (-0.1336881039, 0.4114496766, 3.7400000000), (-0.4836881039, 0.6657395614,
> 4.0800000000), (-0.9163118961, 0.6657395614, 4.4200000000), (-1.2663118961,
> 0.4114496766, 4.7600000000), (-1.4000000000, 0.0000000000, 5.1000000000),
> (-1.2663118961, -0.4114496766, 5.4400000000), (-0.9163118961,
> -0.6657395614, 5.7800000000), (-0.4836881039, -0.6657395614, 6.1200000000),
> (-0.1336881039, -0.4114496766, 6.4600000000), (0.0000000000, -0.0000000000,
> 6.8000000000), (-0.1336881039, 0.4114496766, 7.1400000000), (-0.4836881039,
> 0.6657395614, 7.4800000000), (-0.9163118961, 0.6657395614, 7.8200000000),
> (-1.2663118961, 0.4114496766, 8.1600000000), (-1.4000000000, 0.0000000000,
> 8.5000000000), (-1.2663118961, -0.4114496766, 8.8400000000),
> (-0.9163118961, -0.6657395614, 9.1800000000), (-0.4836881039,
> -0.6657395614, 9.5200000000), (-0.1336881039, -0.4114496766, 9.8600000000),
> (-1.4000000000, 0.0000000000, 0.0000000000), (-1.2663118961, -0.4114496766,
> 0.3400000000), (-0.9163118961, -0.6657395614, 0.6800000000),
> (-0.4836881039, -0.6657395614, 1.0200000000), (-0.1336881039,
> -0.4114496766, 1.3600000000), (0.0000000000, -0.0000000000, 1.7000000000),
> (-0.1336881039, 0.4114496766, 2.0400000000), (-0.4836881039, 0.6657395614,
> 2.3800000000), (-0.9163118961, 0.6657395614, 2.7200000000), (-1.2663118961,
> 0.4114496766, 3.0600000000), (-1.4000000000, 0.0000000000, 3.4000000000),
> (-1.2663118961, -0.4114496766, 3.7400000000), (-0.9163118961,
> -0.6657395614, 4.0800000000), (-0.4836881039, -0.6657395614, 4.4200000000),
> (-0.1336881039, -0.4114496766, 4.7600000000), (0.0000000000, -0.0000000000,
> 5.1000000000), (-0.1336881039, 0.4114496766, 5.4400000000), (-0.4836881039,
> 0.6657395614, 5.7800000000), (-0.9163118961, 0.6657395614, 6.1200000000),
> (-1.2663118961, 0.4114496766, 6.4600000000), (-1.4000000000, 0.0000000000,
> 6.8000000000), (-1.2663118961, -0.4114496766, 7.1400000000),
> (-0.9163118961, -0.6657395614, 7.4800000000), (-0.4836881039,
> -0.6657395614, 7.8200000000), (-0.1336881039, -0.4114496766, 8.1600000000),
> (0.0000000000, -0.0000000000, 8.5000000000), (-0.1336881039, 0.4114496766,
> 8.8400000000), (-0.4836881039, 0.6657395614, 9.1800000000), (-0.9163118961,
> 0.6657395614, 9.5200000000), (-1.2663118961, 0.4114496766, 9.8600000000)]
>     amorphous_lat = Amorphous(coords)
>
>     syst = kwant.Builder()
>
>     for i in range(N):
>         syst[amorphous_lat(i)] = e1*sigma_0
>         syst[amorphous_lat(N+i)] = e2*sigma_0
>         syst[amorphous_lat(i), amorphous_lat(N+i)] = lam*sigma_0
>         if i > 0:
>             syst[amorphous_lat(i), amorphous_lat(i-1)] = t1*sigma_0 +
> 1j*t_so1*(sigma_v1(i*p)+sigma_v1((i-1)*p))
>             syst[amorphous_lat(N+i),amorphous_lat(N+i-1)] = t2*sigma_0 +
> 1j*t_so2*(sigma_v2(i*p)+sigma_v2((i-1)*p))
>
>     prim_vecs=tinyarray.array([(a,0.,0.),(0.,a,0.),(0.,0.,a)])
>
>     offset1=tinyarray.array((-0.7, 0.0, 0.0))
>     lat1=kwant.lattice.Monatomic(prim_vecs, offset1, norbs=no)
>
>
>     syst[lat1(0, 0, -1)] = e1*sigma_0
>     syst[amorphous_lat(0), lat1(0, 0, -1)] = tl*sigma_0
>     syst[amorphous_lat(N), lat1(0, 0, -1)] = tl*sigma_0
>
>     sym = kwant.TranslationalSymmetry([0, 0, -a])
>
>
>
>
>
>
>     if discrete:
>         sym = kwant.TranslationalSymmetry([0, 0, -a])
>
>         dn_lead[lat1(0, 0, -2)] = e1*sigma_0
>
>     if continuous:
>         t00=0.0
> *2+(2*t0+e1)*sigma_0"
>         dn_lead.fill(template, lat1, lat1(0, 0, -2))
>
>
>
>
>
>
>
>     sym1 = kwant.TranslationalSymmetry([0, 0, a])
>
>
>     syst[lat1(0, 0, N)] = e1*sigma_0
>     syst[amorphous_lat(N-1), lat1(0, 0, N)] = tr*sigma_0
>     syst[amorphous_lat(2*N-1), lat1(0, 0, N)] = tr*sigma_0
>
>
>     up_lead[lat1(0, 0, N+1)] = e1*sigma_0
>
>     system=kwant.plot(syst, site_lw=0.1, site_color=family_color,
> hop_lw=hopping_lw)
>
>
>     trans=True
>     if trans:
>         syst = syst.finalized()
>         energies = []
>         datau = []
>
>         for ie in range(-320,520):
>             energy = ie * 0.001
>             smatrix = kwant.smatrix(syst, energy=energy)
>             energies.append(energy)
>             Gu=smatrix.transmission((1, 0), 0)
>             Gd=smatrix.transmission((1, 1), 0)
>             datau.append(Gu)
>
>         fig = pyplot.figure()
>         pyplot.plot(energies, datau, 'b--')
>         pyplot.legend(['Gu'], loc='upper left')
>         pyplot.xlim([-0.32,0.52])
>         pyplot.ylim([-0.03,1.05])
>         pyplot.show()
>
>
>
>
>
>
> On 7 August 2017 at 10:15, Christoph Groth <christoph.gr...@cea.fr> wrote:
>
>> Patrik, can you please provide a complete script file that demonstrates