Re: [Kwant] Kwant-discuss Digest, Vol 15, Issue 9

Well i am trying this paper: http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.226801 I have one more thing to ask,that in the kwant paper the topological suerconductor example is given.I have seen its band sturcture.How can one say that it is a topological in nature,as its its band stucture overlaps on increasing the onsite values more and more. I mean I am trying same for 2 dimension and as i increse its size or onsite potential the bands overlaps more and more.Which confuses me with this , that whether it is topological insulator or not,I guess that example sincerely means to represent edge states only .Could you guide me doing the same thing for 2 d.? ANANT VIJAY VARMA M.Tech. STUDENT CENTER FOR CONVERGING TECHNOLOGIES UNIVERSITY OF RAJASTHAN JAIPUR On Sun, Nov 23, 2014 at 5:32 PM, <kwant-discuss-request@kwant-project.org> wrote:
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Today's Topics:
1. About kane and mele model like crossover (ANANT) 2. Re: About kane and mele model like crossover (Robert Sokolewicz)
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Message: 1 Date: Sat, 22 Nov 2014 12:27:35 +0000 (UTC) From: ANANT <avterminator@gmail.com> To: kwant-discuss@kwant-project.org Subject: [Kwant] About kane and mele model like crossover Message-ID: <loom.20141122T132433-754@post.gmane.org> Content-Type: text/plain; charset=us-ascii
hello everyone, I am trying to simulate the Kane and mele like crossover of bands in Zigzag geometry. But my bans are not spillting or not I dont get.Bcoz bandstructure show that they are overlapping at all,as shown by colors.Here is my code. # -*- coding: utf-8 -*- # <nbformat>3.0</nbformat>
# <codecell>
#required files are imported import kwant import matplotlib.pyplot import math import numpy as np from cmath import exp import tinyarray
# <codecell>
#lattice defined A,B are sublattices. lat = kwant.lattice.general([(2.46,0), (1.23,1.23*math.sqrt(3))],[(0,0), (0,2.46/ math.sqrt(3))]) A,B= lat.sublattices # All pauli matrices to define spin degree of freedom. s_0=np.identity(2) s_z =np.array([[1, 0], [0, -1]]) s_x = np.array([[0, 1], [1, 0]]) s_y = np.array([[0, -1j], [1j, 0]])
for x in xrange(1): def make(a=50,b=11,t=1,alpha =.09): sym0 = kwant.TranslationalSymmetry(lat.vec((-1,0))) #system building def shape(pos): x, y = pos return (0<= y <=b) sys = kwant.Builder(sym0) #onsite enegies for j in range(b): sys[A(0,j+1)] =.1*s_0 sys[B(0,j)] = -.1*s_0 sys[kwant.builder.HoppingKind((0, 0), A,B )]= - t *s_0 + 1j * alpha *s_z # hopping in y direction sys[kwant.builder.HoppingKind((-1,1), A,B )] =-t *s_0 - 1j * alpha *s_x# hopping in x direction sys[kwant.builder.HoppingKind((0,1), A,B )] = -t *s_0 + 1j * alpha *s_y# hopping in x direction #sys[lat.neighbors()]= -t #sys[lat.neighbors()]= -2.6*s_z return sys #main() function call def main(): sys= make().finalized() #plotting a band structure kwant.plotter.bands(sys,momenta= np.linspace(-5,5,1000),show = False) matplotlib.pyplot.xlabel("S_momentum") matplotlib.pyplot.ylabel("S_energy [t]") matplotlib.pyplot.show() if __name__ == '__main__': main()
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Message: 2 Date: Sat, 22 Nov 2014 20:32:28 +0100 From: Robert Sokolewicz <r.sokolewicz@gmail.com> To: ANANT <avterminator@gmail.com> Cc: kwant-discuss@kwant-project.org Subject: Re: [Kwant] About kane and mele model like crossover Message-ID: <CAP+R9snmUJ-MhxbpQ4J9827RtJ_fMj7fommU=+ vFwih6otV+qQ@mail.gmail.com> Content-Type: text/plain; charset="utf-8"
hi Anant,
could you explain in a bit more detail what you are trying to accomplish? which model are you using specifically? Perhaps you made a mistake implementing the tight binding hamiltonian?
cheers, Robert
On Sat, Nov 22, 2014 at 1:27 PM, ANANT <avterminator@gmail.com> wrote:
hello everyone, I am trying to simulate the Kane and mele like crossover of bands in Zigzag geometry. But my bans are not spillting or not I dont get.Bcoz bandstructure show that they are overlapping at all,as shown by colors.Here is my code. # -*- coding: utf-8 -*- # <nbformat>3.0</nbformat>
# <codecell>
#required files are imported import kwant import matplotlib.pyplot import math import numpy as np from cmath import exp import tinyarray
# <codecell>
#lattice defined A,B are sublattices. lat = kwant.lattice.general([(2.46,0), (1.23,1.23*math.sqrt(3))],[(0,0), (0,2.46/ math.sqrt(3))]) A,B= lat.sublattices # All pauli matrices to define spin degree of freedom. s_0=np.identity(2) s_z =np.array([[1, 0], [0, -1]]) s_x = np.array([[0, 1], [1, 0]]) s_y = np.array([[0, -1j], [1j, 0]])
for x in xrange(1): def make(a=50,b=11,t=1,alpha =.09): sym0 = kwant.TranslationalSymmetry(lat.vec((-1,0))) #system building def shape(pos): x, y = pos return (0<= y <=b) sys = kwant.Builder(sym0) #onsite enegies for j in range(b): sys[A(0,j+1)] =.1*s_0 sys[B(0,j)] = -.1*s_0 sys[kwant.builder.HoppingKind((0, 0), A,B )]= - t *s_0 + 1j * alpha *s_z # hopping in y direction sys[kwant.builder.HoppingKind((-1,1), A,B )] =-t *s_0 - 1j * alpha *s_x# hopping in x direction sys[kwant.builder.HoppingKind((0,1), A,B )] = -t *s_0 + 1j * alpha *s_y# hopping in x direction #sys[lat.neighbors()]= -t #sys[lat.neighbors()]= -2.6*s_z return sys #main() function call def main(): sys= make().finalized() #plotting a band structure kwant.plotter.bands(sys,momenta= np.linspace(-5,5,1000),show = False) matplotlib.pyplot.xlabel("S_momentum") matplotlib.pyplot.ylabel("S_energy [t]") matplotlib.pyplot.show() if __name__ == '__main__': main()

Dear Anant, This mailing list is a forum for exchange about the Kwant code. Everybody is welcome to discuss how to do something with Kwant, i.e. how to best implement some physical system in Kwant, or how Kwant itself could be improved. We're glad to see that recently a few questions were answered by people who are not part of the core Kwant team – we hope that the list will continue to develop in this direction. In order to keep this list useful for everyone, other topics are NOT welcome. This explicitly includes general physics questions. Dear Anant, please stop asking general physics questions on this list. You have been asked to do so already twice. If you do not comply, we will have to ban you from posting to this list. All the best, Christoph
participants (2)
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ANANT VIJAY
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christoph.groth@cea.fr