Mailman 3 January 2024 - Kwant-discuss

Hall conductivity from kwant.kpm.conductivity scaled?
by adiptapal7＠gmail.com 31 Jan '24

31 Jan '24

Hello, I was calculating the Hall conductivity for the QWZ model of the Chern insulator using kwant.kpm.conductivity as shown in the tutorial and the result shows that the Hall conductivity within the energy gap is 0.5 when it should have been 1 if it was scaled by the conductance quantum. Is the result scaled by some other factor? I am providing my code below, L = 21; W = 21 M = -1.0 def ChernIns(L,W,M): lat = kwant.lattice.square(norbs=2) sys = kwant.Builder() for i in range(L): for j in range(W): sys[lat(i,j)] = (2+M)*sz if i>0: sys[lat(i,j),lat(i-1,j)] = -0.5*sz+0.5j*sx if j>0: sys[lat(i,j),lat(i,j-1)] = -0.5*sz+0.5j*sy return lat, sys.finalized() where = lambda s: np.linalg.norm(s.pos-np.array([L/2,W/2]))<2 lat, syst_topo = ChernIns(L,W,M) s_factory = kwant.kpm.LocalVectors(syst_topo,where) cond_xy = kwant.kpm.conductivity(syst_topo, alpha='y',beta='x',mean=True,num_vectors=None,vector_factory=s_factory,rng=0)#,mean=True,num_vectors=None,vector_factory=s_factory,rng=0) energies = cond_xy.energies Sigma_xy = np.array([cond_xy(mu=e,temperature=0.01).real for e in energies]) area_per_site = np.linalg.norm(np.cross(*lat.prim_vecs))/len(lat.sublattices) Sigma_xy = Sigma_xy/area_per_site fig = plt.figure(dpi=150) plt.plot(energies,Sigma_xy,'-k') plt.xlabel('Energy') plt.ylabel(r'$\sigma_{xy}$') plt.show() Any help is appreciated. Best, Adipta.

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shape mismatch occuers when computing smatrix in 1-D chain
by 1223234765＠qq.com 15 Jan '24

15 Jan '24

Dear Kwant Community I am new in Kwant and trying to compute a simple 1-D system's conductance. However something strange confuse me that when the Fermi energy gets adjusted into some specific range (like (0,1) or (-1,2)), the Jupyter says: "shape mismatch: value array of shape (2,2) could not be broadcast to indexing result of shape (2,4)". More mystical, if I tuned it to other range (like(-5,5)) or considered 2-D condition，the error would disappear. I don't know what happend QAQ , could anyone please give me some explanation? This is my code: import kwant # For plotting from matplotlib import pyplot import numpy as np sigma_0=np.array([[1,0],[0,1]]) sigma_x=np.array([[0,1],[1,0]]) sigma_y=np.array([[0,-1j],[1j,0]]) sigma_z=np.array([[1,0],[0,-1]]) U=4 def make_system(a=1, t=1.0, L=5): lat = kwant.lattice.chain(a,norbs=2) syst = kwant.Builder() #### Define the scattering region. #### for x in range (L): syst[(lat(x))] = (2*t+U)*sigma_0 syst[lat.neighbors()] = -t*sigma_0 #### Define and attach the leads. #### lead0 = kwant.Builder(kwant.TranslationalSymmetry([-a])) lead0[(lat(0))] = 2*t*sigma_0 lead0[lat.neighbors()] = -t*sigma_0 lead1 = kwant.Builder(kwant.TranslationalSymmetry([a])) lead1[(lat(0))] = 2*t*sigma_0 lead1[lat.neighbors()] = -t*sigma_0 syst.attach_lead(lead0) syst.attach_lead(lead1) return syst #================================================================ def plot_conductance(sys,energies): data=[] for energy in energies: #<-Fermi energy smatrix=kwant.smatrix(sys,energy) data.append(smatrix.transmission(1,0)) plt.figure() plt.plot(energies, data) plt.xlabel("energy") plt.ylabel("conductance [e^2/h]") plt.show() def main(): syst=make_system() kwant.plot(syst) sys=syst.finalized() Es = np.linspace(-1,1, 100) #<-Fermi energy plot_conductance(sys,Es) if __name__ == '__main__': main() I guess it occuers because zero energy may causes some singular conditions, but I badly don't know why XD. Thanks for reading. Sincerely, Intpret

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Inconsistancy in result for generating Triangular shape graphene
by sahu.ajit92＠gmail.com 07 Jan '24

07 Jan '24

Dear sir, I am trying to generate a triangular graphene structure by using Kwant by giving three real space coordinates for three vertices. 1. However, the code does not work for specific coordinates. i.e., the structure doesn't plot as per the given coordinates. is there any problem with my code? 2. Additionally, I am unable to know what the function of giving one real space position is while calling the shape function i.e., model1[lat.shape(lower_tri,(40,40))] = 0 Please find the code below ################################### code ###### import kwant import numpy as np lat=kwant.lattice.honeycomb(a=2.46,norbs=1) a,b=lat.sublattices def lower_tri(pos): x,y=pos ################# #Real space position it works xl2 = 20 yl2 = 0 xl1 = 20 yl1 = 60 yl3 = 0 xl3 = 0 ####################### #Real space position it does not work # xl2 = 50 # yl2 = 0 # xl1 = 50 # yl1 = 60 # yl3 = 0 # xl3 = 25 ######################## Triangle equation ######### D = xl1*yl2 - xl2*yl1+ yl3*xl2 - xl3*yl2 + xl3*yl1 -xl1*yl3 k1 = (2*yl1 - yl2 -yl3)*x + (-2*xl1+xl2+xl3)*y + xl1*yl2 - xl2*yl1 + xl1*yl3 - xl3*yl1 m1 = (2*yl2-2*yl3)*x + (-2*xl2 + 2*xl3)*y - xl1*yl2 + xl2*yl1 + xl2*yl3 + xl3*yl2 + xl1*yl3 -xl3*yl1 K = k1/D M = m1/D return np.abs(K) + np.abs(M + np.abs(K))<=1 model1 = kwant.Builder() model1[lat.shape(lower_tri,(1,1))]=0 #model1[lat.shape(lower_tri,(40,40))] = 0 model1[lat.neighbors()] = 2.64 kwant.plot(model1) ################################### pls find attached image https://drive.google.com/file/d/123qsy_HiA0dlCT8nwhC9JdaJgJnvQ3P3/view?usp=…

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Re: kwant.continuum.discretize scale factors?
by Anton Akhmerov 06 Jan '24

06 Jan '24

Hi Chagaan, The dispersion of the discretized model cannot fully match that of the continuum model, rather it is only an approximation. We explain it in more detail in this section of Kwant documentation: https://kwant-project.org/doc/1/tutorial/discretize#limitations-of-discreti… Best, Anton On Thu, 4 Jan 2024 at 05:48, Chagaan Baatar <chagaan.baatar(a)gmail.com> wrote: > > Hi Anton, > Happy New Year and hope all is well with you! > Thanks for responding to my inquiry. But I’m still a bit puzzled and I > think I might be misunderstanding something very simple. > I ran your code snippet (after cell 7, as you suggested) and got this > plot, where the original plots from cell 5 and 7 are simply overlaid, but > not overlapping. > I thought your two plot.spectrum statements are plotting the exact same > thing, only difference being one is a discretized version of the other > (continuum), and therefore should produce 4 overlapping bands instead of > the 8 shown here. > Do you see what I am missing here? > Thanks again. > Chagaan > > > > On Dec 28, 2023, at 8:13 PM, Anton Akhmerov <anton.akhmerov(a)gmail.com> > wrote: > > Hi Chagaan, > > kwant.continuum.discretize doesn't change the scale. Indeed, plotting the > two dispersions on the same plot shows that they agree quite well. To > confirm, try adding the code below after cell 7. As a note here, the Fermi > momentum is around pi/2a, which is rather high, and if one wanted to make a > more accurate approximation, reducing the lattice constant would be the way > to go. > > Best, > Anton > > from matplotlib import pyplot as plt > > params = dict( > B_x=0, > mu=1, > alpha=0.5, > Delta=0 > ) > > fig, ax = plt.subplots(figsize=(8, 6)) > kwant.plotter.spectrum(h_cont, ('k_x', momenta), params=params, > show=False, ax=ax) > kwant.plotter.spectrum( > infinite_wire, > ('k_x', np.linspace(-np.pi, np.pi, 301)), > params=params, > ax=ax > ) > > >

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3d structure model and add 3d leads
by araya0sun＠gmail.com 02 Jan '24

02 Jan '24

Dear kwant users, Hello, I am a new user of kwant, I want to build a 3d structure model, and add leads, I refer to a similar code, but I keep getting errors during the process, the program says "RuntimeError: All sites of this builder have been deleted because an exception occurred during the execution of fill(): see above. ", I feel that it may be the position of the lead, but I do not know how to modify it, can you give me some suggestions to modify it? Thank you very much! *This is the code I have errors in: ---------------------------------------- import kwant import numpy as np from matplotlib import pyplot #3d test def syst_3d(a=16, b=16, c=10,t=1): 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 syst = kwant.Builder() def cuboid_shape(pos): x, y, z = pos return 0 <= x < a and 0 <= y < b and 0 <= z < c syst[lat.shape(cuboid_shape, (0, 0, 0))] = 4 * t syst[lat.neighbors()] = -t sym_lead0 = kwant.TranslationalSymmetry(lat.vec((1, 0, 0))) lead0 = kwant.Builder(sym_lead0) lead_shape = lambda pos: (-b / 2 <= pos[1] < b / 2) and abs(pos[2]) < c lead0[lat.shape(lead_shape, (-1, 0, 0))] = 4 * t lead0[lat.neighbors()] = -t lead1 = lead0.reversed() syst.attach_lead(lead0) syst.attach_lead(lead1) return syst def main(): syst = syst_3d() kwant.plot(syst) if __name__ == '__main__': main() --------------------------------------------------- *This is the code I refer to, as if this works correctly: ------------------------------------------------------- import kwant import numpy as np from matplotlib import pyplot def syst_3d(W=3, r1=2, r2=4, a=1, t=1.0): lat = kwant.lattice.general(((a, 0, 0), (0, a, 0), (0, 0, a))) syst = kwant.Builder() def ring(pos): (x, y, z) = pos rsq = x**2 + y**2 return (r1**2 < rsq < r2**2) and abs(z) < 2 syst[lat.shape(ring, (0, -r2 + 1, 0))] = 4 * t syst[lat.neighbors()] = -t sym_lead0 = kwant.TranslationalSymmetry(lat.vec((-1, 0, 0))) lead0 = kwant.Builder(sym_lead0) lead_shape = lambda pos: (-W / 2 < pos[1] < W / 2) and abs(pos[2]) < 2 lead0[lat.shape(lead_shape, (0, 0, 0))] = 4 * t lead0[lat.neighbors()] = -t lead1 = lead0.reversed() syst.attach_lead(lead0) syst.attach_lead(lead1) return syst def main(): syst = syst_3d() kwant.plot(syst) if __name__ == '__main__': main() Sincerely, Yue Xiang

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