Mailman 3 October 2016 - Kwant-discuss

How the spin is positioned in the Smatrix?
by Qingtian Zhang March 6, 2022

March 6, 2022

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))

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Spin polarized transport calculation
by L.M J March 6, 2022

March 6, 2022

Dear Kwant users and developers I have two questions related to the spin calculation using kwant. 1. I'm wondering if we can do spin-polarized transport in kwant? For example, can we can get the separate Conductance Vs Energy diagram for spin up and spin down terms. I'm thinking one way of doing this is to set up the Rashba Hamiltonian as a whole. And then manually extract the spin up and spin down hamiltonian and do the transport calculation separately. But this will eliminate some extra terms that I don't know whether this is correct anymore. Any suggestions? 2. How can we set up the spin polarization for a particular site? For example, in some of the topological insulator, can we set up spin polarization on the edge as up and the other side of the edge as down, and then do the transport? Or this question is completely wrong? Thanks for advance. Sincerely, Liming

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How to caculate hall resistance
by ZHANG Bing Sept. 12, 2021

Sept. 12, 2021

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

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Hopping between different lattices and families
by Camilla Espedal Nov. 4, 2016

Nov. 4, 2016

Hi, To explain what I mean. I have a system where I have separated spin-up and spin-down into two lattices (like electron and hole in the example at the kwant site) so that it is would be easier to extract spin-resolved information (G_up/up, Gup/down etc.). In addition, these two lattices consists of two sublattices (A and B). The code is like this lat_up = kwant.lattice.general([(1,0),(s,c)],[(0,0),(0,1/sqrt(3))], name='up') A_up, B_up = lat_up.sublattices lat_down = kwant.lattice.general([(1,0),(s,c)],[(0,0),(0,1/sqrt(3))], name='down') A_down, B_down = lat_down.sublattices What I want to do now, is to add a hopping term between say A_up (i,j) and B_down (i.j). So a hopping term between the two different lattices and sublattices. How can I implement this? Or is there a better way to achieve what I want? Best Camilla Espedal

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kkghosh
by kamal ghosh Oct. 30, 2016

Oct. 30, 2016

Hi all, Many thanks to all the developers of kwant not only for the strong potential development of the code but very specially also for the help to solve coding and related physics problems. Presently, I am wondering how to calculate current in a device, say a QWR, connected to source and drain through two infinite leads! Applying the Landauer relation, I require no. of channels M upto the level of Fermi and Transmission probabilities per channel. To me, this appears very involved programming; because (i) first to find the Fermi first and next to find the no. of channels below that (ii) secondly, for any channel the all energies upto the Fermi I have to calculate and (iii) finally to sum up. Then we may get the total transmission probability. I am not sure that is it right to think of a constant probability in a particular channel? I think it is "no". However, I noticed a tutoring correspondence from Joe and Akhmerov in a correspondence with an user working with calculating the current like me. I could not understand the solution because current carried by scattering state is written by a code which I am afraid how to write that code in high level python text? Please, bear with me on this trifling matter. Should we wait for the version kwant2? All the best wishes and awaiting your wise advise. K.K.Ghosh

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Re: [Kwant] Family-dependent onsite potential
by Camilla Espedal Oct. 28, 2016

Oct. 28, 2016

Thanks, I now changed the order, but I still get the same error message. So now the code reads kwant.plotter.map(sys, V) sys = sys.finalized() but now it seems to be in a different place the error message is now 'int' object has no attribute 'site', and the V-function is still def V(sys): Hd = onsite(site) return (Hd[0,0] - Hd[1,1]).real Best, Camilla

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Family-dependent onsite potential
by Camilla Espedal Oct. 27, 2016

Oct. 27, 2016

Hello, I am making a system with 2 sublattices, so they belong to different families (a and b), and I wish to define a sublattice-dependent onsite energy. I tried using the following code for the onsite function. def onsite(site): onsite_a = 2 onsite_b = 2 return onsite_a if site.family == a else onsite_b but it does not work. I get error message: 'int' object has no attribute 'family'. How can I solve this, or what am I doing wrong? Best, Camilla

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Is the transmission/conductance matrix at zero temperature calculated at E = 0?
by Jiuning Hu Oct. 25, 2016

Oct. 25, 2016

Hi All, I have a general question about kwant package. In the kwant paper (https://downloads.kwant-project.org/doc/kwant-paper.pdf), I presume the conductance matrix given in Eq. (10) is for zero temperature calculation. I also presume that the conductance matrix G should be dependent on energy E, i.e., G(E). I am wondering if the output from the transmission matrix t(E) (used to calculate G(E)) of kwant is calculated at E = 0, i.e., what we have is actually t(E=0) and G(E=0). Although this looks like that the Fermi level is fixed at E = 0, the actual Fermi level (e.g., relative to charge neutral point) can be changed via the onsite potential. Please correct me if I have the wrong understanding. Thanks! -- Jiuning Hu

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energy spectrum of carbon nanotube
by Liu Feng Oct. 24, 2016

Oct. 24, 2016

Hi everyone, I am trying to use Kwant to calculate the band structure of a carbon nanotube. For example, I build a zigzag nanoribbon with translation symmetry (1,0). Then I add the hopping between the a and b sites at the ends of the ribbon by hand. This usually gives the correct nanotube spectrum in a tight-binding scheme. However, I got incorrect one using Kwant. I cannot figure out what is the missing part in the code. Could anyone help me out here? The following is the code, and in the attachments there are the graph of the system and also the incorrect spectrum given by Kwant. >From the system plot, the a, b sites at the ends of the ribbon are indeed connected. The incorrect spectrum looks similar to the correct one, but for all the armchair nanotubes they should be metals not insulators. Many thanks in advance! Best regards, Feng Liu import kwant import numpy as np from types import SimpleNamespace w=4 W=np.sqrt(3)*0.5*w+1/sqrt(3) #width of zigzag nanoribbon p = SimpleNamespace(t=1.0, mu = 0.0, B=0.0) def ribbon_shape(pos): return -W/2<= pos[1] < W/2 def onsite(site,p): (x,y)=site.pos return 0.0 def hopping(site1,site2,p): x1, y1 = site1.pos x2, y2 = site2.pos return p.t lat = kwant.lattice.honeycomb() a,b=lat.sublattices sym_sys = kwant.TranslationalSymmetry((1, 0)) sys = kwant.Builder(sym_sys) sys[lat.shape(ribbon_shape, (0, 0))] = onsite sys[lat.neighbors()] = hopping sys[a(0, w/2), b(0, -w/2-1)] = p.t #connect the ends kwant.plot(sys) sys=sys.finalized() kwant.plotter.bands(sys,args=[p],momenta=600)

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P-wave superconductivity in Kwant
by antoniolrm＠usp.br Oct. 24, 2016

Oct. 24, 2016

Hello everyone, I am trying to implement Kitaev model in Kwant via the Hamiltonian: H = -\mu \sum_{n=1}^{N} c_{n}^{\dagger}c_{n} - t \sum_{n=1}^{N-1}(c_{n+1}^{\dagger}c_n + h.c.) + \Delta \sum_{n=1}^{N-1}(c_{n}c_{n+1} + h.c.) The first two terms are simple, but I am stucked in the superconducting p-wave pairing term. I've tried to implement it by doing sys[((lat_e(x+1, 0), lat_h(x, 0)) for x in range(0,L-1))] = Delta which seems somehow correct once I got the zero modes at the edges for the Kitaev limit \mu=0 and t=\Delta. But once I vary \mu I lost one of the edge states, and also it does not close the gap, which makes me belive that I am dealing with a trivial phase. Does anyone ever done it? Can you see something wrong with my approach? Cheers, Antônio. The complete code is the following: ==================================================== from cmath import exp import numpy as np import kwant # For eigenvalue computation import scipy.sparse.linalg as sla # For plotting from matplotlib import pyplot def make_system(a=1.0, W=1, L=50, mu=1.5, Delta=1.0, t=1.0): # Start with an empty tight-binding system and two square lattices, # corresponding to electron and hole degree of freedom lat_e = kwant.lattice.square(a=1.0, name='e') lat_h = kwant.lattice.square(a=1.0, name='h') sys = kwant.Builder() #### Define the scattering region. #### sys[(lat_e(x, y) for x in range(L) for y in range(W))] = - mu sys[(lat_h(x, y) for x in range(L) for y in range(W))] = mu # hoppings for both electrons and holes sys[lat_e.neighbors()] = -t sys[lat_h.neighbors()] = t # Superconducting order parameter enters as hopping between # electrons and holes sys[((lat_e(x+1, y), lat_h(x, y)) for x in range(0,L-1) for y in range(W))] = Delta #### Define the leads. #### # Symmetry for the left leads. sym_left = kwant.TranslationalSymmetry((-a, 0)) # left electron lead lead0 = kwant.Builder(sym_left) lead0[(lat_e(0, j) for j in range(W))] = - mu lead0[lat_e.neighbors()] = t lead0[lat_h.neighbors()] = -t # left hole lead lead1 = kwant.Builder(sym_left) lead1[(lat_h(0, j) for j in range(W))] = mu lead1[lat_e.neighbors()] = t lead1[lat_h.neighbors()] = -t # Then the lead to the right # this one is superconducting and thus is comprised of electrons # AND holes sym_right = kwant.TranslationalSymmetry((a, 0)) lead2 = kwant.Builder(sym_right) lead2 += lead0 lead2 += lead1 lead2[((lat_e(1, j), lat_h(0, j)) for j in range(W))] = Delta #### Attach the leads and return the system. #### sys.attach_lead(lead2) sys.attach_lead(lead2.reversed()) return sys def plot_wave_function(sys, L=100): # Calculate the wave functions in the system. ham_mat = sys.hamiltonian_submatrix(sparse=True) evecs = sla.eigsh(ham_mat, k=50, which='SM')[1] # Plot the probability density of the 1st eigenmode. kwant.plotter.map(sys, np.abs(evecs[:, 0])**2, colorbar=False, a=1.0, oversampling=2) def main(): sys = make_system() # Check that the system looks as intended. kwant.plot(sys) # Finalize the system. sys = sys.finalized() plot_wave_function(sys) if __name__ == '__main__': main() =================================================================

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