Mailman 3 June 2019 - Kwant-discuss

docu2.7 and docu2.3
by kamal ghosh 22 Jun '19

22 Jun '19

.Dear all,         Right now I am working with spin transport. Kwant documentations 2.3 of docu1.0.5 and 2.7 of docu1.3.2 are very much helpful and informative to my study. I have a few questions/ doubts to understand the Hamiltonians meaningfully. Hamiltonian for spin (docu2.7) :-                                                           H= -Σ&lsaquo;ij&rsaquo;Σα│iα&rsaquo;&lsaquo;jα│+ JΣiΣαβ mi. σαβ│iα&rsaquo;&lsaquo;iβ│                                         (1) Hamiltonian for spin (docu2.3) :-                                                   H= (-ħ2/2m)(∂x2+∂y2) – iα(∂xσy - ∂yσx ) + Ezσz + V(y)                        (2)(i) Is there a missing of hopping energy tα (t  alpha) in eqn.(1) because the first term takes care of the hopping ? Further, are the kinetic and potential parts for charge transport not considered. I mean, term like the first term in eqn.(2) ? As both the charge and spin transport are there so should we not consider them simultaneously ? Also, does the J in eqn.(1) signify the magnetic field arising out of Rashba interaction which is clearly expressed in eqn,(2)?(ii) Am I right to understand that the second and third terms in eqn.(2) signify the Zeeman splitting and Rashba interaction? Please bear with me that I cannot derive these two terms from Zeeman splitting term and Rashba interacti on term as found in text books on quantum mechanics. I would be thankful if the origin of these terms be made understood! or else, atleast the reference from where i may get idea.I am earnestly requesting the learned developers of Kwant and / my co-members in the family of Kwant to help solving my problems.All the best and Happy Kwanting.K.K.Ghosh                                                                                   i 

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Density Operator & Current Operator for 3D systems
by Naveen Yadav 22 Jun '19

22 Jun '19

Dear KWANT Depelopers, Following the Kwant documentation, it is easy to plot probability density for 2D systems. But on following the same procedure for the 3D systems it shows an *ValueError: Only 2D systems can be plotted this way.* Please suggest me if there is a way to plot probability density for 3D system having only an orbital degree of freedom per site. Thanks in advance. Naveen Naveen Department of Physics & Astrophysics University of Delhi New Delhi-110007

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Infinite Slab and wraparound
by Bogusz Bujnowski 17 Jun '19

17 Jun '19

Dear everyone, I would like to solve the 3D Schrödinger equation with a 1D potential step. With the material in the mailing list as well as from the tutorial the 2D case works fine. Extending to 3D gives the same when just taking one lattice site in the z direction (H>1). Increasing the hight of the slab (H>1) changes the minimal energy for which transmission is possible thus my code is wrong. Did I define and attach the leads correctly with the wraparound in 3D? The short code is below. Thank you for any hint! Best, B import numpy as np import matplotlib.pyplot as plt import scipy as sp from numpy import * import kwant import sys #calculate the conductance for a sheet (Dim=2) or a Slab (Dim=3) that is translational invariant in y direction a = 1.0 #lattice constant V0 = 0.2 #potential step size L = 2 #Length x-direction the length is a bit useless in this code W = 6 #Width y-direction H = 6 #Hight z-direction t = 1 #hopping parameter Dim=3 #dimension of the system # for H=1, Dim=2 # for H>1, Dim=3 #params for integration and plotting Nky=100 #points in ky space NE=25 #points in energy lat = kwant.lattice.cubic(a) # Define the scattering region # Infinite potential plane/Slab in y direction sys = kwant.Builder(kwant.TranslationalSymmetry(lat.vec((0, W, 0)))) for i in range(L): for j in range(W): for k in range(H): # On-site Hamiltonian sys[lat(i, j, k)] = 2*Dim * t + heaviside(i,0)*V0 #potential step located at the center between the leads sys[lat.neighbors(1)] = -t sys = kwant.wraparound.wraparound(sys) #Left lead leadL = kwant.Builder(kwant.TranslationalSymmetry((-a, 0, 0), lat.vec((0, W, 0)))) #trans inv in transport dir and ky leadL[(lat(0,j,k) for j in range(W) for k in range(H))] = 2*Dim*t #onsite terms in the left lead leadL[lat.neighbors(1)] = -t #Right lead leadR = kwant.Builder(kwant.TranslationalSymmetry(( a, 0, 0), lat.vec((0, W, 0)))) leadR[(lat(0,j,k) for j in range(W) for k in range(H))] = 2*Dim*t+V0 #onsite terms in the right lead leadR[lat.neighbors(1)] = -t leadL = kwant.wraparound.wraparound(leadL, keep=0) #keeping the translational invariance in x direction leadR = kwant.wraparound.wraparound(leadR, keep=0) sys.attach_lead(leadL) sys.attach_lead(leadR) kwant.plot(sys) sys = sys.finalized() # Calculation of the total transmission for a given Energy ky_array = np.linspace(-pi,pi,Nky) dky=ky_array[1]-ky_array[0] energies = np.linspace(0.0, 1.0,NE) Ttot=[] for energy in energies: Tky_array=zeros(Nky) for i in arange(len(ky_array)): ky=ky_array[i] smatrix = kwant.smatrix(sys, energy, [ky]) Tky_array[i]=smatrix.transmission(1, 0) Ttot.append((2*pi)/(W)*(sum(Tky_array)-0.5*Tky_array[0]-0.5*Tky_array[Nky-1])*dky) #cheap trapezodial rule to integrate over ky # Plot transmission plt.plot(energies, Ttot) plt.show()

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bounds on KPM
by Antonio Lucas Rigotti Manesco 17 Jun '19

17 Jun '19

Hello all, I'm trying to do some calculations using KPM method for graphene in a somehow large quantum dot (300ax300a, where a is the lattice constant). Since LDOS calculations uses lot of memory and I need good energy resolution, I redefined my energy bounds to a smaller window, and the behavior is similar to what I expected. However, if I do the same for DOS calculations, I get something that looks very strange, compared with the previous result using the automatically generated bounds. So, my question is: are the LDOS results reliable even though the DOS does not looks right? (I'm calculating the LDOS for energies about the middle of the new window, in case that matters). Thanks Antonio

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Update onsite elements
by Barış Özgüler 13 Jun '19

13 Jun '19

Hi all, I want to assign certain values to some onsite elements of the system. I tried to do it via syst[lat(x, y)] but the shape of the scattering region is altered. The code that creates the system in a certain shape and assigns some onsite elements: lat = kwant.lattice.square(a) syst = kwant.Builder() # shape_func is the function for the shape of the scattering region syst[lat.shape(shape_func, (0, 0))] = onsite syst[kwant.builder.HoppingKind((1, 0), lat, lat)] = hopx syst[kwant.builder.HoppingKind((0, 1), lat, lat)] = hopy # update some part of the system (L and W length and width of the scattering region, which is not necessarily rectangular) for x in range(L): for y in range(W): if -L <= x < -L/20 and -L/2 <= y < -L/5: syst[lat(x, y)] = (4 * par.t - par.mu) * tau_z + par.Delta * tau_x After final step (for loops), the system shape is not the one that is determined by shape_func anymore. How should I reach and update certain onsite elements without any shape change? Thanks, Baris

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translational symmetry for non-integer polyatomic basis
by Zang, Hang 06 Jun '19

06 Jun '19

Dear Kwant developers, I want to calculate the band structure for a system with the polyatomic basis, but since the periodic value is not an integer, there was some problem in finalizing the system. Could you give me some suggestions to solve this problem? Enclose please find my kwant script. Thank you very much for your help. Hang Zang =========================== import kwant from matplotlib import pyplot primitive_vectors = [ (1.0,0.0,0.0) , (0.0,1.0,0.0) , (0.0,0.0,1.0) ] atomic_sites = [ (1.0,1.0,1.0) , (0.0,0.0,0.0) , (-1.0,-1.0,-1.0) ] lat = kwant.lattice.Polyatomic(primitive_vectors , atomic_sites) atoms = lat.sublattices sym_lead = kwant.TranslationalSymmetry((-1.0,0.0,0.0)) lead = kwant.Builder(sym_lead) # inside the lead lead[atoms[0](0.0,0.0,0.0)] = 1 lead[atoms[1](0.0,0.0,0.0)] = 1 lead[atoms[2](0.0,0.0,0.0)] = 1 lead[atoms[0](0.0,0.0,0.0),atoms[1](0.0,0.0,0.0)] = -2 lead[atoms[1](0.0,0.0,0.0),atoms[2](0.0,0.0,0.0)] = -2 # between adjacent leads lead[atoms[0](0.0,0.0,0.0),atoms[0](-2.3,0.0,0.0)] = -4 lead[atoms[1](0.0,0.0,0.0),atoms[1](-2.3,0.0,0.0)] = -4 lead[atoms[2](0.0,0.0,0.0),atoms[2](-2.3,0.0,0.0)] = -4 lead = lead.finalized() kwant.plotter.bands(lead,show=False) pyplot.xlabel("momentum [(lattice constant)^-1]") pyplot.ylabel("energy [t]") pyplot.show() =====================================

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