Dear Adel,

           Many thanks for your kind suggestion. 
           Now I understand why I got the incorrect nanotube spectrum. Indeed the hand-added hopping connects the undesired sites at the ends of nanoribbon.
           It seems by using the translational symmetry parameter, we cannot have the correct periodic connection for armchair nanotubes by the default configuration of honeycomb lattice  (Although I can get correct energy spectra for zigzag nanotubes in this case).
           Do you have any ideas of properly defining the primitive vectors and translational symmetry for armchair nanotubes?
           Of course, one can build a proper tight-binding model defining sites one by one with Bloch phase as an extra parameter without using Translational parameters. But I feel this method is a little bit troublesome... 

Many thanks,
feng

Abbout Adel <abbout.adel@gmail.com>于2016年10月21日周五 下午8:21写道：
Dear Liu Feng,


When you plot the lead cell, as you did it in your program, you can not see if your system is exactly what you were expecting. So I suggest to you,in order to see why you are getting a different spectrum then what you are expecting,  is to do the following:

1) define a central sytem.
2) attach the lead to this sytem.
3) plot the system with many cells of the lead by using the option num_lead_cells:
    kwant.plot(system, num_lead_cells=6)

This way, you will see that the links you put, do not define the nanotube you had in mind.

Best regards,
Adel


On Thu, Oct 20, 2016 at 6:45 AM, Liu Feng <ruserzzz@gmail.com> wrote:
Hi everyone,

I am trying to use Kwant to calculate the band structure of a carbon nanotube.

For example, I build a zigzag nanoribbon with translation symmetry (1,0). Then I  add the hopping between the a and b sites at the ends of  the ribbon by hand.  This usually gives the correct nanotube spectrum in a tight-binding scheme. However, I got incorrect one using Kwant. I cannot figure out what is the missing part in the code. Could anyone help me out here? 



The following is the code, and in the attachments there are the graph of the system and also the incorrect spectrum given by Kwant.
 
From the system plot, the a, b sites at the ends of the ribbon are indeed connected.
The incorrect spectrum looks similar to the correct one, but for all the armchair nanotubes they should be metals not insulators.  

Many thanks in advance!
Best regards,
Feng Liu


import kwant 
import numpy as np 
from types import SimpleNamespace 

w=4 
W=np.sqrt(3)*0.5*w+1/sqrt(3) #width of zigzag nanoribbon
p = SimpleNamespace(t=1.0, mu = 0.0, B=0.0)

    
def ribbon_shape(pos):
    return -W/2<= pos[1] < W/2    

    
def onsite(site,p):
    (x,y)=site.pos
    return 0.0  

    
def hopping(site1,site2,p):
    x1, y1 = site1.pos
    x2, y2 = site2.pos
    return p.t    
          
    
lat = kwant.lattice.honeycomb()

a,b=lat.sublattices

sym_sys = kwant.TranslationalSymmetry((1, 0))

sys = kwant.Builder(sym_sys)
    
sys[lat.shape(ribbon_shape, (0, 0))] = onsite



sys[lat.neighbors()] = hopping

sys[a(0, w/2), b(0, -w/2-1)] = p.t  #connect the ends

kwant.plot(sys)

sys=sys.finalized()

kwant.plotter.bands(sys,args=[p],momenta=600)


 



--
Abbout Adel