Mailman 3 July 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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Velocities
by BENJAMIN STREKHA July 29, 2016

July 29, 2016

Hello, Can you point me to the correct direction of where to look at the documentation to figure out how to make a vorticity plot in kwant? Essentially, I want to attach leads to a graphene flake. I want to find the vorticity around each closed hexagon. Which command of kwant should I look at to figure out the velocity between two adjacent atoms so that I can calculate the vorticity in the end? Also, kwant.solvers.default.wave_function(some_sys, some_energy) Where is some_energy a reference to? An excitation energy relative to what? Thanks, Ben

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Issue in display wave function in 3D lattice
by L.M J July 28, 2016

July 28, 2016

Dear all I was trying to plot the wavefunction on each site of a 3-D lattice and each site is described by a 4x4 matrix. However, it turned out the that plotted wave function is overlapped with the surrounding site and I could not identify the magnitude of wave function on each site. The code I had implemented for plotting was the same as the codes in " http://kwant-project.org/doc/1.0/tutorial/tutorial6" with a copy of specific plot command as below. I have varied the value "3" before wf[i] to tune the size however it turned out this value cannot tune the plot size of the wavefunction. I think I'm not doing it correctly. def site_size(i): return 3 * wf[i] / wf.max() kwant.plot(sys, site_size=site_size, site_color=(0, 0, 1, 0.3), hop_lw=0.1) This method works perfectly for 2-D lattice plot. However, it cannot display the wavefunction properly in 3-d lattice. My question is, how can I plot the wavefunction in 3-d lattice clearly? (Or maybe I can force the kwant to plot it in 2-d by configuring the kwant.plot?) Thank you for advance. Sincerely, Liming

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Inconsistent calculation result
by L.M J July 26, 2016

July 26, 2016

Hi Kwant Users I notice an inconsistency in calculation result using Python IDLE (3.5.1, Anaconda3). The issue is that every time I execute the same code, it gives me a different result.The test code that I use is the example code for graphene quantum dot calculation (2.7.1) . First, I used the different parameter (r=3). Each time I executed the same code, it returned different wavefunction. If I use a large r (r=8), the wavefunction(n=225) is consistent. But if I plot the wavefunction 22 instead of 225 as an example, then the wavefunction is different for each time. I tested the code within jupyter notebook and it doesn't show any inconsistencies. Can anyone advise me what raises this issue ? Is it because of Kwant package or Python IDLE or the calculation script itself? If I still want to use Python IDLE to do the calculation. How can I make sure my calculation result is correct? The test code is copied at the end of the email. Thanks in advance. Sincerely, Liming Test code: ================================================================ ================================================================ # Tutorial 2.7.1. 2D example: graphene quantum dot # ================================================ # # Physics background # ------------------ # - graphene edge states # # Kwant features highlighted # -------------------------- # - demonstrate different ways of plotting import kwant from matplotlib import pyplot lat = kwant.lattice.honeycomb() a, b = lat.sublattices def make_system(r=8, t=-1, tp=-0.1): def circle(pos): x, y = pos return x**2 + y**2 < r**2 sys = kwant.Builder() sys[lat.shape(circle, (0, 0))] = 0 sys[lat.neighbors()] = t sys.eradicate_dangling() if tp: sys[lat.neighbors(2)] = tp return sys def plot_system(sys): kwant.plot(sys) # the standard plot is ok, but not very intelligible. One can do # better by playing wioth colors and linewidths # use color and linewidths to get a better plot def family_color(site): return 'black' if site.family == a else 'white' def hopping_lw(site1, site2): return 0.04 if site1.family == site2.family else 0.1 kwant.plot(sys, site_lw=0.1, site_color=family_color, hop_lw=hopping_lw) def plot_data(sys, n): import scipy.linalg as la sys = sys.finalized() ham = sys.hamiltonian_submatrix() evecs = la.eigh(ham)[1] wf = abs(evecs[:, n])**2 # the usual - works great in general, looks just a bit crufty for # small systems kwant.plotter.map(sys, wf, oversampling=10, cmap='gist_heat_r') # use two different sort of triangles to cleanly fill the space def family_shape(i): site = sys.sites[i] return ('p', 3, 180) if site.family == a else ('p', 3, 0) def family_color(i): return 'black' if sys.site(i).family == a else 'white' kwant.plot(sys, site_color=wf, site_symbol=family_shape, site_size=0.5, hop_lw=0, cmap='gist_heat_r') # plot by changing the symbols itself def site_size(i): return 3 * wf[i] / wf.max() kwant.plot(sys, site_size=site_size, site_color=(0, 0, 1, 0.3), hop_lw=0.1) def main(): # plot the graphene system in different styles sys = make_system() plot_system(sys) # compute a wavefunction (number 225) and plot it in different # styles sys = make_system(tp=0) plot_data(sys, 22) # Call the main function if the script gets executed (as opposed to imported). # See <http://docs.python.org/library/__main__.html>. if __name__ == '__main__': main()

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closed graphene system - PBCs in one direction - dispersion
by Tibor Sekera July 20, 2016

July 20, 2016

Dear all, I create Hamiltonian H for a graphene lattice with nn-hopping only, no leads, i.e. closed system. Each a (b) sublattice site is located at r=i*a_1+j*a_2 (r=i*a_1+j*a_2+d), with i,j being integers, a_1,2 being Bravais lattice vectors, and d a vector pointing from a to b sublattice. Hence each site is marked with |i,j,a or b>. My question is, once the nn-hoppings are set, how do I locate the position in H belonging to specific matrix element between two sites, say <2,5,a|H|1,2,b>? My goal is to plot a dispersion relation E(k_y) of such a closed system with periodic boundary conditions in y-direction (I did it by hand) and hard-wall in x-direction. I guess I need to do the Fourier transform in y-direction by hand. Or, are there some built-in functions to do this? Thank you for eventual answer or pointing me to duplicate question. Tibor

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How to calculate supercurrent in superconductors
by 操津津 July 13, 2016

July 13, 2016

Dear members of Kwant Groups, I'm so interested in the calculations of supercurrents in superconductors. As can be seen, Kwant possesses the functionality of investigating superconductivity, but with no obvious sign of the calculations of current or current density in superconductors. Would you please send me some examples or calculation steps to learn the methodology of current density calculations in superconductors by employing Kwant? I really appreciate your assistance. I will be looking forward to your response. Yours sincerely, Jin-Jin Cao ------------------ Jin-Jin Cao Ph.D. student College of Mechanics and Materials, Hohai University 1 Xikang Road, Nanjing, Jiangsu 210098, China

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lead direction
by kamal ghosh July 4, 2016

July 4, 2016

Dear all, Facing a problem to fix lead in a desired direction. In fact, I can't understand how to count the sites and this make trouble. For better, let me refer to to the documentary paper on "Kwant: ---- transport" of C.W.Groth et.al. in example of appendix D4. 1. sys[lat.shape(ring,(10,0))] = 0; > whether the origin (0,0) or the site coordinate specified by (10,0) is to be taken as origin for fixing the location/position of the leads? How then the desired choice of to fix lead position is to be made ? 2. sym=kwant.TranslationalSymmetry((-2,1)); > I am sorry I cannot follow meaning of the symmetry direction vector! I cannot match the idea with the kwant construction of the lead in the direction of (-2,1) 3. lead[lat((x,0) for x in range(-6,6))]=0; > I understand total 13 sites counted from (-6,0) to (6,0); Where I am wrong in understanding ? 4. sys.attach_lead(lead,lat(0,0)); > Is it not possible to use the code "lead.(reversed)" ? Though every question is answered in the paper still my ignorance blockheads my real conception. Unless I have clear conception I cannot use my Kwant, an extremely powerful weapon, flexibly to design my nanosystems. I am waiting for your nice and exemplary advice and instruction from the forum. All regards. K.K.Ghosh

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