Hi Pawel,

It seems that Joe was too fast for me.

In addition to what Joe wrote - the need to rescale the momenta properly -
you also rescaled the energy twice so the energy scale was also wrong.

The following script adapted from yours gives correct results.


from matplotlib import pyplot
import kwant
import numpy
import math

def make_lead(W=30,dx=1.0,m=0.0667):

 sym = kwant.TranslationalSymmetry((-dx, 0))
 lead[(lat(0,y) for y in range(-W+1,W))]=4*t

 return lead

def calculation(mydx,W):
   momenta = numpy.linspace(-numpy.pi, numpy.pi, 101)
   energies = [band(k) for k in momenta]
   for i in range(len(momenta)):
      f.write("%f " % (momenta[i]/mydx))
      for j in range(len(energies[0])):
          f.write("%f " % (energies[i][j]))

Xavier Waintal
SPSMS-INAC-CEA,17 rue des Martyrs, 38054 Grenoble CEDEX 9, FRANCE
Tel: 33 (0)4 38 78 03 27 
email: xavier.waintal@cea.fr

Le 27 févr. 2014 à 14:28, Joseph Weston <joseph.weston@cea.fr> a écrit :

Pawel Wojcik <Pawel.Wojcik <at> fis.agh.edu.pl> writes:

I have just started working with KWANT but at the beginning I have a
problem with the calculation of the
energy band in lead. Blow I paste my code in which a define the lead and
try to calculate the energy vs wave
vector. The definition of the lead comes from the example on the website
documentation. I assume a lattice with the size dx and then t=h/m/dx/dx.

The energy from the function kwant.bands is expresed in units of [t] and
in this point a have a problem
because if I define the lead with W=100 points and dx=0.1 nm and calculate
the E vs k bands, it differs from
the E vs k bands calculated for W=50 points and dx=0.2 nm (of course scale
the energy multiplying it by t),
although the width of the lead W_eff=W*dx is the same for both cases.


The reason that you see different band structures is that you have not
re-scaled the "momenta" correctly when calling the `bands` object returned
by `kwant.physics.Bands`. Concretely, when you call `bands(k)`, the "k" value
you give is in units reciprocal to the distance units which you have chosen
(which manifests in the onsite and hopping parameters). This means that
for the "dx = 0.2" case, the momentum units are twice as small as for the
"dx = 0.1" case. If you want to plot the two band structures on the same
curve then you need to rescale the momentum units::

   lead100 = make_lead(W=100,dx=0.1*f_nm2au).finalized()
   lead50 = make_lead(W=50,dx=0.2*f_nm2au).finalized()
   band100 = kwant.physics.Bands(lead100)
   band50 = kwant.physics.Bands(lead50)

   # define this to be in units corresponding to "dx = 0.1"
   momenta = numpy.linspace(-numpy.pi, numpy.pi, 101)
   energies100 = [band100(k) for k in momenta]
   energies50 = [band50(2 * k) for k in momenta]  # rescale momenta
   pyplot.plot(momenta, energies100, 'k', momenta, energies50)

You should now see that for small "k" the two sets of curves match up.