You are correct, Li. Of course the periodic boundaries introduce additional modes, no idea how I forgot that. And the number of modes matches nicely with the analytical results of the free electron model too.
I plotted the square of the absolute value of the wave function in the last script. For plane waves, this is of course a constant value and what that plot showed was numerical artefacts. Plotting, for example, the real part of the wave function gives nice results. (so *np.real(wf(0)[0]) *instead of *np.abs(wf(0)[0])**2*) Thanks for the help! Kristjan On Wed, Mar 8, 2017 at 7:09 PM, Li Mingkai <mingka...@gmail.com> wrote: > I think your code is correct now. It's reasonable that the propagating > mode changes from 1 to 3 because of the finite periodic width W in stead of > W=0. Please check free electron model in one dimentional case. With > incresing energy, the number of bands at k=0 increases from 1 at energy=0 > to 3 at above a certain energy. > > And the wavefuction is reasonable in this case. For nanowire case, the > transverse wavefunction should be 0 at the edge. Instead of that, your > wavefunction shows the symmetric at the both edge. The high energy > wavefunction is combined by several modes. That makes more complex. > > The transmission per unit width can intergrate transmission by ky from -pi > to pi in > > kwant.smatrix(sys, energies[j], [kys[i]]) > > and then divide by width W. It equals to a intergration of Brillouin zone > from -pi/W to pi/W as mentioned in https://www.mail-archive. > com/kwant-discuss@kwant-project.org/msg00873.html. But in kwant, ky must > be set in range (-pi,pi). > > Mingkai Li > > On Tue, Mar 7, 2017 at 3:02 PM, Kristjan Eimre <kristjanei...@gmail.com> > wrote: > >> Hello Anton and Li, >> >> Thanks for the replies, they have helped me a lot. >> >> Li, I agree with you that my initial code was incorrect: the scattering >> regions were periodic in y direction but the leads were not. >> >> I tried to recreate your idea here: http://pastebin.com/DYUvx0YS >> >> When potential in scattering region is set to 0, then indeed the >> transmission starts directly from 0.0, so there is no transversal >> quantization (for the first mode). But I have one problem with this >> approach: the number of propagating modes changes with increasing energy >> (at roughly energy 4.1 eV, the num_prop jumps from 1 to 3). In ideal case, >> we should have a single mode at all energies. >> >> Additionally, I tried to plot the wave function squared for the system, >> but the results seem wrong. For lower energies and ky=0, the plot shows >> nice plane waves, but for energy 3+ eV, it turns into something else. >> Perhaps WF plotting doesn't work for periodic systems? >> >> Would it be possible for a expert to take a quick look at the code and >> point out any obvious mistakes? Currently it creates the scattering region >> with y direction periodicity and uses wraparound on it. Then creates lead >> with x and y periodicity and uses wraparound on it, keeping the x >> periodicity. And finally the leads are attached to the system. Is this the >> correct way? >> >> Best, >> Kristjan >> >> >> >> >> On Sat, Mar 4, 2017 at 11:56 PM, Li Mingkai <mingka...@gmail.com> wrote: >> >>> Hi Kristjan, >>> >>> I'm working on 3D periodic boundary problem recently. Your code really >>> helps me a lot. I tested your code. It seems working with nanowire leads >>> instead of a periodic repeat in y direction. I changed the leads setting a >>> little as following. A translational symmetry along y direction was added >>> on lead. Then wraparound it with keep=0 >>> >>> lead = kwant.Builder(kwant.TranslationalSymmetry((-a, 0),lat.vec((0, >>> W)))) >>> lead[(lat(0,j) for j in range(W))] = 4*t >>> lead[lat.neighbors(1)] = -t >>> sys.attach_lead(wraparound(lead,keep=0)) >>> sys.attach_lead(wraparound(lead,keep=0).reversed()) >>> >>> It seems working as a periodic boundary condiction. I judge it by >>> settiing all potential to 0 in the scatting region. Then the tramsmittion >>> with energy above 0 should be 1. Without above changes, the transmission at >>> a little positive energy is 0 and the it will jump to 1 at a little higher >>> energy. It implies the transversal energy quantization. >>> >>> I tested the ky under the above flat potential condition. The period of >>> ky is 2Pi instead of 2Pi/L. I don't know why. Maybe some expert can explain >>> it. >>> >>> Anyway, I'm just a newbie with kwant and trying to solve some bulk >>> problem with it. I'm not sure about the above opinion. Let's discuss and >>> figure out how it works in peroidic boundary condiction. >>> >>> -- >>> Mingkai Li >>> >> >> > > > -- > Mingkai Li >
