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,
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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
To: kwant-discuss@kwant-project.org Subject: [Kwant] About kane and mele model like crossover Message-ID: 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
To: ANANT Cc: kwant-discuss@kwant-project.org Subject: Re: [Kwant] About kane and mele model like crossover Message-ID: 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
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()
participants (2)
-
ANANT VIJAY
-
christoph.groth@cea.fr