Mailman 3 May 2014 - Kwant-discuss

How the spin is positioned in the Smatrix?
by Qingtian Zhang 06 Mar '22

06 Mar '22

Dear all, I am trying square lattice with spin-orbit coupling and Zeeman splititng just like the example of Tutorial 2.3.1. Now I want to get the spin-dependent conductance：Guu,Gud,Gdu,and Gdd, where "u" indicates up spin, d indicates down spin. We can have the scattering matrix through Smatrix=kwant.smatrix(sys, energy), but how the spin is positioned in the scattering matrix? I have checked some simple cases, it seems the Smatrix is organized like this: | r t | S= | t' r' | but how the spin is included? Thanks in advance. Qingtiian Zhang The code is: import kwant from matplotlib import pyplot from numpy import matrix import tinyarray 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]]) sys=kwant.Builder() lat=kwant.lattice.square() a=1 t=1.0 alpha=0.5 e_z=0.08 W=2 L=2 sys[(lat(x, y) for x in range(L) for y in range(W))] = \ 4 * t * sigma_0 + e_z * sigma_z # hoppings in x-direction sys[kwant.builder.HoppingKind((1, 0), lat, lat)] = \ -t * sigma_0 - 1j * alpha * sigma_y # hoppings in y-directions sys[kwant.builder.HoppingKind((0, 1), lat, lat)] = \ -t * sigma_0 + 1j * alpha * sigma_x #### Define the left lead. #### lead = kwant.Builder(kwant.TranslationalSymmetry((-a, 0))) lead[(lat(0, j) for j in xrange(W))] = 4 * t * sigma_0 + e_z * sigma_z # hoppings in x-direction lead[kwant.builder.HoppingKind((1, 0), lat, lat)] = \ -t * sigma_0 - 1j * alpha * sigma_y # hoppings in y-directions lead[kwant.builder.HoppingKind((0, 1), lat, lat)] = \ -t * sigma_0 + 1j * alpha * sigma_x #### Attach the leads and return the finalized system. #### sys.attach_lead(lead) sys.attach_lead(lead.reversed()) kwant.plot(sys) sys=sys.finalized() print "Hamiltonian=" print sys.hamiltonian_submatrix() Smatrix=kwant.smatrix(sys, energy=3.) print "The scattering matrix=" print matrix.round((Smatrix.data),2) print "T=",(Smatrix.transmission(1, 0))

3 3

How to caculate hall resistance
by ZHANG Bing 12 Sep '21

12 Sep '21

Dear Sir, I am a PhD student of Hong Kong University of Science and Technology. I want to use KWANT to caculate Hall resistance of a Hall bar structure.We can get the conductance between 6 electrodes, but how to get hall resistance? Can you give me some help? Thank you very much. Best Regards, Zhang Bing

4 3

Quantum transport in system with periodic boundary condition.
by Sebastien Guissart 26 May '14

26 May '14

Dear all, With an other student, we are trying to study transport in infinity system, especially we want study tunnel Klein effect in graphene. We are trying to erase edge effect by add a periodic boundary condition, the system should be like a giant nanotube. We do ancillaries system an copy hopping terms for sytem and lead, it produce some mistake, kwant say: "connects non-neighboring lead unit cells.Only nearest-cell hoppings are allowed (consider increasing the lead period)" when we try to attach lead. I attach the script, It is possible to produce this kind of system easily and compute the transmission? Regards, Sébastien Guissart def main() : X = 20 Y = 10 t=1.0 e0=2 def rectangle(pos): x, y = pos return -X/2-1 < x < X/2-1 graphene = kwant.lattice.honeycomb(1,'b') sym = kwant.TranslationalSymmetry(graphene.vec((-Y/2,Y))) anc = kwant.Builder(sym) ### 2D periodic conditions anc[graphene.shape(rectangle,(0, 0))] = None anc[graphene.neighbors()] = None sys = kwant.Builder() sys[anc.sites()] = e0 sys[((a, sym.to_fd(b)) for a, b in anc.hoppings())] = -t sym_anc = kwant.TranslationalSymmetry(graphene.vec((1,0)),graphene.vec((-Y/2,Y))) anc_left = kwant.Builder(sym_anc) sym_left = kwant.TranslationalSymmetry(graphene.vec((1,0))) lead_left = kwant.Builder(sym_left) anc_left[graphene.shape(lambda p: True,(0, 0))] = None anc_left[graphene.neighbors()] = None lead_left[anc_left.sites()] = e0 lead_left[((a, sym_anc.to_fd(b)) for a, b in anc_left.hoppings())] = -t sys.attach_lead(lead_left) sys.attach_lead(lead_left.reversed()) sys = sys.finalized() kwant.plot(sys)

2 1

Re: [Kwant] 3D structure construction with leads
by Julian Schary 22 May '14

22 May '14

Dear Anton, first, let me thank you for your help. I got some problems with it: 1) If I use the "ugly" way, there is an error popping up as soon as I attach the leads in the manner I wrote in my first mail: ... lead = kwant.Builder(kwant.TranslationalSymmetry((-1, 0, 0))) lead[(sublattice(0, y, z) for sublattice in lat.sublattices for y in xrange(a) for z in xrange(b))] = 4 * t lead[lat.neighbors()] = -t sys.attach_lead(lead) sys.attach_lead(lead.reversed()) ... ERROR: "ValueError: Builder does not interrupt the lead, this lead cannot be attached." 2) If I use the second way, there is a memory error even before attaching the leads. "... lead = kwant.Builder(kwant.TranslationalSymmetry((-1, 0, 0))) def lead_shape(pos): return 0 <= pos[1] < a and 0 <= pos[2] < b sys[lat.shape(lead_shape, (0, 0, 0))] = 4 * t lead[lat.neighbors()] = -t" I dont't know if I'm too stupid/new to kwant/... but I can't solve it. Best Julian > Dear Julian, > > Once you execute make_cuboid(), you see the following error message: > > 12 > 13 lead = kwant.Builder(kwant.TranslationalSymmetry((-1, 0, 0))) > ---> 14 lead[(lat(0, j, i) for j in xrange(a) for i in > xrange(b))] = 4 * t > 15 lead[lat.neighbors()] = -t > 16 > > TypeError: 'Polyatomic' object is not callable > > You wrote `lat(0, j, i)`, which is the correct way to deal with > Monatomic lattices in Kwant. In fact this is just a short hand > notation for a site of the lattice lat with Bravais vectors 0, j, i. > If lat was a monatomic lattice, the code you're using would just add a > bunch of sites of the form lat(0, j, i). In your case lat has several > sublattices, so `lat(0, j, i)` does not have any meaning in Kwant. > There are two ways to fix your code. If you want to stick to generator > expressions [=loops of the form `(f(i) for i in somewhere)`], you can > write e.g. > > lead[(sublattice(0, y, z) for sublattice in lat.sublattices for y in > xrange(a) for z in xrange(b))] = 4 * t > > However, as you see, this becomes ugly. It's better to use shape, > similarly to the way you defined the scattering region: > > def lead_shape(pos): > return 0 <= pos[1] < a and 0 <= pos[2] < b > > sys[lat.shape(lead_shape, (0, 0, 0))] = 4 * t > > Note that here the lead_shape doesn't depend on the x-coordinate of > the site, as required by translation invariance in x-direction. More > generally, the shape function for the lead should respect the lead > translational symmetry, or the results may be not what you would > expect. > > I hope this helps, > Anton On Mon, May 19, 2014 at 9:39 AM, Julian Schary <julian.schary(a)stud-mail.uni-wuerzburg.de> wrote: > Dear all, > > > I'm triying to figure out how to attach symmetrical leads to a 3D zincblende > -structure in kwant. The code I used so far: > > lat = kwant.lattice.general([(0, 0.5, 0.5), (0.5, 0, 0.5), (0.5, 0.5, > 0)], [(0, 0, 0), (0.25, 0.25, 0.25)]) > a, b = lat.sublattices > def make_cuboid(t=1.0, a=15, b=10, c=5): > def cuboid_shape(pos): > x, y, z = pos > return 0 <= x < a and 0 <= y < b and 0 <= z < c > > sys = kwant.Builder() > sys[lat.shape(cuboid_shape, (0, 0, 0))] = 4 * t > sys[lat.neighbors()] = -t > > lead = kwant.Builder(kwant.TranslationalSymmetry((-1, 0, 0))) > lead[(lat(0, j, i) for j in xrange(a) for i in xrange(b))] = 4 * t > lead[lat.neighbors()] = -t > > #sys.attach_lead(lead) > #sys.attach_lead(lead.reversed()) > > return sys > > causes errors. Could you help me and tell me how to attach the leads in > 3D,please? > > Best regards, > > Julian > Depatment of Physics & Astronomy > University of Würzburg (Germany) >

2 3

Problem with 1D stucture
by Pawel Wojcik 21 May '14

21 May '14

Dear all, I would like to simulate transport through a simple 1D structure, and i used chain() function to define the lattice but i dont know how to define leads. I tried to use transationalsymmetry() function but it does not work. Below i paste part of my simple code def make_system(L=100,dx=1.0,m=0.0667): lat=kwant.lattice.chain(dx) sys=kwant.Builder() sys[(lat(i) for i in range(L))]=onsite sys[lat.neighbors()]=hopping sym = kwant.TranslationalSymmetry((-dx,0)) #here i also tried to use kwant.TranslationalSymmetry((-dx)) l_lead=kwant.Builder(sym) l_lead[(lat(0,0))]=onsite l_lead[lat.neighbors()]=hopping sys.attach_lead(l_lead) sys.attach_lead(l_lead.reversed()) return sys.finalized() I would be greatfull for advises. Thank you in advance Best Regards Pawel

2 1

3D structure construction with leads
by Julian Schary 19 May '14

19 May '14

Dear all, I'm triying to figure out how to attach symmetrical leads to a 3D zincblende -structure in kwant. The code I used so far: lat = kwant.lattice.general([(0, 0.5, 0.5), (0.5, 0, 0.5), (0.5, 0.5, 0)], [(0, 0, 0), (0.25, 0.25, 0.25)]) a, b = lat.sublattices def make_cuboid(t=1.0, a=15, b=10, c=5): def cuboid_shape(pos): x, y, z = pos return 0 <= x < a and 0 <= y < b and 0 <= z < c sys = kwant.Builder() sys[lat.shape(cuboid_shape, (0, 0, 0))] = 4 * t sys[lat.neighbors()] = -t lead = kwant.Builder(kwant.TranslationalSymmetry((-1, 0, 0))) lead[(lat(0, j, i) for j in xrange(a) for i in xrange(b))] = 4 * t lead[lat.neighbors()] = -t #sys.attach_lead(lead) #sys.attach_lead(lead.reversed()) return sys causes errors. Could you help me and tell me how to attach the leads in 3D,please? Best regards, Julian Depatment of Physics & Astronomy University of Würzburg (Germany)

2 1

graphene nano ribbon
by Sumit Ghosh 14 May '14

14 May '14

I am trying to repeat the same calculation as the nanowire, but with graphene nanoribbon. How can I do that? I tried to replace the square lattice with hexagonal, but it is not working as there are two atoms per unit cell. what would be the best way to do this? I would like to study both band structure and conductance. Best, Sumit -- ------------------------------ This message and its contents, including attachments are intended solely for the original recipient. If you are not the intended recipient or have received this message in error, please notify me immediately and delete this message from your computer system. Any unauthorized use or distribution is prohibited. Please consider the environment before printing this email.

2 1

Kwant error
by Bas Nijholt 06 May '14

06 May '14

Dear kwant developers, I got the following error message when installing kwant. Anton already helped me, but told me to send these error messages. *bas@bas-HP-EliteBook-8530w:~$ sudo pip install kwant* *Downloading/unpacking kwant* * Downloading kwant-1.0.0.tar.gz (803kB): 803kB downloaded* * Running setup.py (path:/tmp/pip_build_root/kwant/setup.py) egg_info for package kwant* * Traceback (most recent call last):* * File "<string>", line 17, in <module>* * File "/tmp/pip_build_root/kwant/setup.py", line 39, in <module>* * int(n) for n in Cython.__version__.split('-')[0].split('.'))* * File "/tmp/pip_build_root/kwant/setup.py", line 39, in <genexpr>* * int(n) for n in Cython.__version__.split('-')[0].split('.'))* * ValueError: invalid literal for int() with base 10: '1post0'* * Complete output from command python setup.py egg_info:* * Traceback (most recent call last):* * File "<string>", line 17, in <module>* * File "/tmp/pip_build_root/kwant/setup.py", line 39, in <module>* * int(n) for n in Cython.__version__.split('-')[0].split('.'))* * File "/tmp/pip_build_root/kwant/setup.py", line 39, in <genexpr>* * int(n) for n in Cython.__version__.split('-')[0].split('.'))* *ValueError: invalid literal for int() with base 10: '1post0'* *----------------------------------------* *Cleaning up...* *Command python setup.py egg_info failed with error code 1 in /tmp/pip_build_root/kwant* *Storing debug log for failure in /home/bas/.pip/pip.log* I used *In [3]: cython.__version__* *Out[3]: '0.20.1post0'* Reinstalling cython gave me the following error after successfully installing kwant trough pip. Upon running kwant.test() It gave me the following error: *...........................................................................................E.... ====================================================================== ERROR: kwant.tests.test_plotter.test_plot ---------------------------------------------------------------------- Traceback (most recent call last): File "/usr/lib/python2.7/dist-packages/nose/case.py", line 197, in runTest self.test(*self.arg) File "/usr/local/lib/python2.7/dist-packages/kwant/tests/test_plotter.py", line 102, in test_plot fig = plot(sys, site_color=color, cmap='binary', file=out) File "/usr/local/lib/python2.7/dist-packages/kwant/plotter.py", line 1361, in plot return output_fig(fig, file=file, show=show) File "/usr/local/lib/python2.7/dist-packages/kwant/plotter.py", line 663, in output_fig canvas.print_figure(file, *savefile_opts[0], **savefile_opts[1]) File "/usr/local/lib/python2.7/dist-packages/matplotlib/backend_bases.py", line 2192, in print_figure **kwargs) File "/usr/local/lib/python2.7/dist-packages/matplotlib/backends/backend_agg.py", line 513, in print_png FigureCanvasAgg.draw(self) File "/usr/local/lib/python2.7/dist-packages/matplotlib/backends/backend_agg.py", line 461, in draw self.figure.draw(self.renderer) File "/usr/local/lib/python2.7/dist-packages/matplotlib/artist.py", line 59, in draw_wrapper draw(artist, renderer, *args, **kwargs) File "/usr/local/lib/python2.7/dist-packages/matplotlib/figure.py", line 1079, in draw func(*args) File "/usr/local/lib/python2.7/dist-packages/matplotlib/artist.py", line 59, in draw_wrapper draw(artist, renderer, *args, **kwargs) File "/usr/local/lib/python2.7/dist-packages/matplotlib/axes/_base.py", line 2075, in draw a.draw(renderer) File "/usr/local/lib/python2.7/dist-packages/kwant/plotter.py", line 117, in draw return collections.Collection.draw(self, renderer) File "/usr/local/lib/python2.7/dist-packages/matplotlib/artist.py", line 59, in draw_wrapper draw(artist, renderer, *args, **kwargs) File "/usr/local/lib/python2.7/dist-packages/matplotlib/collections.py", line 301, in draw self._offset_position) File "/usr/local/lib/python2.7/dist-packages/matplotlib/backends/backend_agg.py", line 119, in draw_path_collection return self._renderer.draw_path_collection(*kl, **kw) ValueError: Transforms must be a Nx3x3 numpy array ---------------------------------------------------------------------- Ran 96 tests in 13.670s FAILED (errors=1)* I use: matplotlib.__version__ u'1.4.x' Cheers, Bas

2 1