Dear John,

The solution I am proposing is not very clean, but at least it works fine.

To plot the wavefunction of a system for a fixed slice, you need to save the result of the wavefunction for the desired sites, and then define a new 2D system recovering the slice you chose, and by reordering the results of the wavefunction to fit the new order of the sites in the new system, the plot becomes straightforward.

for your program it works like this:

# plots for the mode 0 and 1

sys = make_system_cyl(a=1, s=50, L = 15)

kwant.plot(sys)

sysf = sys.finalized()

params = SimpleNamespace(t=1)

wf = kwant.wave_function(sysf, 1.5, args=[params])

#define a new system for the desired slice.

lat2 = kwant.lattice.square()

sys_b = kwant.Builder() #new 2D system used for the plot

slice_x=5

mode=1

def Plot_mode(sys_b,slice_x,mode):

wavefunction = wf(1)[mode]

Sites= [site for (index,site) in enumerate(sysf.sites) if site.pos[0]==slice_x ]

Indexes=[index for (index,site) in enumerate(sysf.sites) if site.pos[0]==slice_x ]

waves=[wavefunction[index] for index in Indexes]

Sites2=[lat2(site.pos[1],site.pos[2]) for site in Sites] #used to define the new system sys_b

sys_b[Sites2]=0

sys_b[lat2.neighbors()]=-1

Sites_b=[site for site in sys_b.finalized().sites] # sites of the new system: with a different order!

Index_b=[Sites2.index(site) for site in Sites_b]

waves_b=[waves[index] for index in Index_b] # results is reordered according to the new order of the sites.

return sys_b, waves_b

sys_b, waves_b= Plot_mode(sys_b=sys_b,slice_x=5,mode=0)

kwant.plotter.map(sys_b.finalized(),abs(array(waves_b))**2)

sys_b, waves_b= Plot_mode(sys_b=sys_b,slice_x=5,mode=1)

kwant.plotter.map(sys_b.finalized(),abs(array(waves_b))**2)

I hope this helps.

Regards,

Adel

On Tue, Apr 25, 2017 at 5:43 PM, John Eaves <johneaves02@gmail.com> wrote:

Good day,

I'm trying to reconstruct something discussed in http://www.mail-archive.com/kwant-discuss@kwant-project.org/msg00432.html. In this answer it is described how to take the wavefunction from a 3D system and plot it in a 2D slice. This turned out to be something different than what the OP was asking for, but that is not so important. It is also mentioned that this has been asked before, but I couldn't find the right search terms. If my question has already been answered, I'd be very grateful for a referral to the relevant discussion!

Now, as it turns out, I can't seem to get the above to work. I take some small cylinder, I calculate the wavefunction, but then I get stuck at how to extract for example the y = 0 plane and plot this in 2D. Below I'll post how far I got, perhaps the fix would be rather simple.

def onsite(site, p):
    return 6*p.t

def hopping(site0, site1, p):
    return -p.t

def make_system_cyl(a=1, s=10, L = 15):
    lat = kwant.lattice.general([(0, 0, a), (a, 0, 0), (0, a, 0)])


    sys = kwant.Builder()


    def cyl_shape(pos):
        x, y, z = pos
        rsq = y ** 2 + z ** 2
        return rsq < s^2 and 0 <= x < L


    sys[lat.shape(cyl_shape, (1,1,1))] = onsite
    sys[lat.neighbors()] = hopping


    def lead_shape(pos):
        x, y, z = pos
        rsq = y ** 2 + z ** 2
        return rsq < s^2

    sym_lead = kwant.TranslationalSymmetry((-a,0,0))
    lead = kwant.Builder(sym_lead)

    lead[lat.shape(lead_shape, (-a,1,1))] = onsite
    lead[lat.neighbors()] = hopping

    sys.attach_lead(lead)
    sys.attach_lead(lead.reversed())

    return sys

and I extract the wavefunction at some energy

sys = make_system_cyl(a=1, s=10, L = 15)
kwant.plot(sys)
sysf = sys.finalized()
params = SimpleNamespace(t=1)
wf = kwant.wave_function(sysf, 1.5, args=[params])

And then I try to extract the relevant parts

wavefunction = wf(0)
projected_wavefunction = np.empty((wavefunction.size, 1), dtype=np.complex)

def in_sheet(index, site):
    return site.pos[1] == 0 # site in x-z plane

sheet_idx_sites = filter(in_sheet, enumerate(sys.sites)

for i, (idx, site) in enumerate(sheet_idx_sites):
    projected_wavefunction[i] = wavefunction[idx]

Now this last part I took from the post referenced at the start, and it gives a syntax error. I'm not really sure how to fix it as it looks fine to me. What's wrong there?

And more importantly, once this is fixed, how can one then make a kwant.plotter.map type of plot at this x-z plane?

Abbout Adel