Mailman 3 February 2014 - Kwant-discuss

Problem with bands in the lead
by Pawel Wojcik 27 Feb '14

27 Feb '14

Hello, I have just started working with KWANT but at the beginning I have a problem with the calculation of the energy band in lead. Blow I paste my code in which a define the lead and try to calculate the energy vs wave vector. The definition of the lead comes from the example on the website documentation. I assume a lattice with the size dx and then t=h/m/dx/dx. The energy from the function kwant.bands is expresed in units of [t] and in this point a have a problem because if I define the lead with W=100 points and dx=0.1 nm and calculate the E vs k bands, it differs from the E vs k bands calculated for W=50 points and dx=0.2 nm (of course scale the energy multiplying it by t), although the width of the lead W_eff=W*dx is the same for both cases. I would be grateful for any suggestions ? Code of my program from matplotlib import pyplot import kwant import numpy import math f_nm2au=18.897261 f_eV2au=0.03674932587 f_Ha=27.2114 def make_lead(W=30,dx=1.0,m=0.0667): lat=kwant.lattice.square(dx) #uzupelnianie t=1.0/m/dx/dx sym = kwant.TranslationalSymmetry((-dx, 0)) lead=kwant.Builder(sym) lead[(lat(0,y) for y in range(-W+1,W))]=4*t lead[lat.neighbors()]=-t return lead ########## calculations for W=100 and dx=0.1 ############# lead=make_lead(W=100,dx=0.1*f_nm2au).finalized() band=kwant.physics.Bands(lead) momenta = numpy.linspace(-numpy.pi, numpy.pi, 101) energies = [band(k) for k in momenta] dx=0.1*f_nm2au m=0.0667 wsp=f_Ha/(m*dx*dx) #print len(energies[1]) f=open('mode_W100_dx01.dat','w') for i in range(len(momenta)): f.write("%f " % (momenta[i])) for j in range(len(energies[0])): f.write("%f " % (energies[i][j]*wsp)) f.write("\n") f.close() ########## calculations for W=50 and dx=0.2 ############# lead=make_lead(W=50,dx=0.2*f_nm2au).finalized() band=kwant.physics.Bands(lead) momenta = numpy.linspace(-numpy.pi, numpy.pi, 101) energies = [band(k) for k in momenta] dx=0.2*f_nm2au m=0.0667 wsp=f_Ha/(m*dx*dx) #print len(energies[1]) f=open('mode_W50_dx02.dat','w') for i in range(len(momenta)): f.write("%f " % (momenta[i])) for j in range(len(energies[0])): f.write("%f " % (energies[i][j]*wsp)) f.write("\n") f.close() Best Regards Pawel Wojcik

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Re: [Kwant] [PROVENANCE INTERNET] Re: Problem with bands in the lead
by Xavier Waintal 27 Feb '14

27 Feb '14

Hi Pawel, It seems that Joe was too fast for me. In addition to what Joe wrote - the need to rescale the momenta properly - you also rescaled the energy twice so the energy scale was also wrong. The following script adapted from yours gives correct results. Regards, Xavier from matplotlib import pyplot import kwant import numpy import math def make_lead(W=30,dx=1.0,m=0.0667): lat=kwant.lattice.square(dx) #uzupelnianie t=1.0/m/dx/dx sym = kwant.TranslationalSymmetry((-dx, 0)) lead=kwant.Builder(sym) lead[(lat(0,y) for y in range(-W+1,W))]=4*t lead[lat.neighbors()]=-t return lead def calculation(mydx,W): m=0.0667 lead=make_lead(W=100,dx=mydx).finalized() band=kwant.physics.Bands(lead) momenta = numpy.linspace(-numpy.pi, numpy.pi, 101) energies = [band(k) for k in momenta] f=open("band_W"+str(W)+"_dx"+str(mydx)+".dat",'w') for i in range(len(momenta)): f.write("%f " % (momenta[i]/mydx)) for j in range(len(energies[0])): f.write("%f " % (energies[i][j])) f.write("\n") f.close() calculation(0.1,100) calculation(0.2,50) __________________________________________ Xavier Waintal SPSMS-INAC-CEA,17 rue des Martyrs, 38054 Grenoble CEDEX 9, FRANCE Tel: 33 (0)4 38 78 03 27 email: xavier.waintal(a)cea.fr http://inac.cea.fr/Pisp/xavier.waintal __________________________________________ Le 27 févr. 2014 à 14:28, Joseph Weston <joseph.weston(a)cea.fr> a écrit : > Pawel Wojcik <Pawel.Wojcik <at> fis.agh.edu.pl> writes: > >> >> Hello, >> I have just started working with KWANT but at the beginning I have a > problem with the calculation of the >> energy band in lead. Blow I paste my code in which a define the lead and > try to calculate the energy vs wave >> vector. The definition of the lead comes from the example on the website >> documentation. I assume a lattice with the size dx and then t=h/m/dx/dx. >> >> The energy from the function kwant.bands is expresed in units of [t] and > in this point a have a problem >> because if I define the lead with W=100 points and dx=0.1 nm and calculate > the E vs k bands, it differs from >> the E vs k bands calculated for W=50 points and dx=0.2 nm (of course scale > the energy multiplying it by t), >> although the width of the lead W_eff=W*dx is the same for both cases. > > Hi, > > The reason that you see different band structures is that you have not > re-scaled the "momenta" correctly when calling the `bands` object returned > by `kwant.physics.Bands`. Concretely, when you call `bands(k)`, the "k" value > you give is in units reciprocal to the distance units which you have chosen > (which manifests in the onsite and hopping parameters). This means that > for the "dx = 0.2" case, the momentum units are twice as small as for the > "dx = 0.1" case. If you want to plot the two band structures on the same > curve then you need to rescale the momentum units:: > > lead100 = make_lead(W=100,dx=0.1*f_nm2au).finalized() > lead50 = make_lead(W=50,dx=0.2*f_nm2au).finalized() > band100 = kwant.physics.Bands(lead100) > band50 = kwant.physics.Bands(lead50) > > # define this to be in units corresponding to "dx = 0.1" > momenta = numpy.linspace(-numpy.pi, numpy.pi, 101) > energies100 = [band100(k) for k in momenta] > energies50 = [band50(2 * k) for k in momenta] # rescale momenta > pyplot.plot(momenta, energies100, 'k', momenta, energies50) > > You should now see that for small "k" the two sets of curves match up. > > Regards, > > Joe > >

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Problem with bands
by Pawel Wojcik 27 Feb '14

27 Feb '14

Hello, I have just started working with KWANT but at the beginning I have a problem with the calculation of the energy band in lead. Blow I paste my code in which a define the lead and try to calculate the energy vs wave vector. The definition of the lead comes from the example on the website documentation. I assume a lattice with the size dx and then t=h/m/dx/dx. The energy from the function kwant.bands is expresed in units of [t] and in this point a have a problem because if I define the lead with W=100 points and dx=0.1 nm and calculate the E vs k bands, it differs from the E vs k bands calculated for W=50 points and dx=0.2 nm (of course i scale the energy multiplying it by t), although the width of the lead W_eff=W*dx is the same for both cases. I would be grateful for any suggestions ? from matplotlib import pyplot import kwant import numpy import math f_nm2au=18.897261 f_eV2au=0.03674932587 f_Ha=27.2114 def make_lead(W=30,dx=1.0,m=0.0667): lat=kwant.lattice.square(dx) #uzupelnianie t=1.0/m/dx/dx sym = kwant.TranslationalSymmetry((-dx, 0)) lead=kwant.Builder(sym) lead[(lat(0,y) for y in range(-W+1,W))]=4*t lead[lat.neighbors()]=-t return lead ########## calculations for W=100 and dx=0.1 ############# lead=make_lead(W=100,dx=0.1*f_nm2au).finalized() band=kwant.physics.Bands(lead) momenta = numpy.linspace(-numpy.pi, numpy.pi, 101) energies = [band(k) for k in momenta] dx=0.1*f_nm2au m=0.0667 wsp=f_Ha/(m*dx*dx) #print len(energies[1]) f=open('mode_W100_dx01.dat','w') for i in range(len(momenta)): f.write("%f " % (momenta[i])) for j in range(len(energies[0])): f.write("%f " % (energies[i][j]*wsp)) f.write("\n") f.close() ########## calculations for W=50 and dx=0.2 ############# lead=make_lead(W=50,dx=0.2*f_nm2au).finalized() band=kwant.physics.Bands(lead) momenta = numpy.linspace(-numpy.pi, numpy.pi, 101) energies = [band(k) for k in momenta] dx=0.2*f_nm2au m=0.0667 wsp=f_Ha/(m*dx*dx) #print len(energies[1]) f=open('mode_W50_dx02.dat','w') for i in range(len(momenta)): f.write("%f " % (momenta[i])) for j in range(len(energies[0])): f.write("%f " % (energies[i][j]*wsp)) f.write("\n") f.close() Best Regards Pawel Wojcik

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Spin orbit interaction for honeycomb
by Qingtian Zhang 24 Feb '14

24 Feb '14

Dear all, I note that we can easily consider the next-nearest-neighbor hopping in honeycomb, however, what is the model (Hamiltonian) for this code? In graphene, the intrinsic SOI is included in the reference:PRL 95, 226801 (2005) and we also have that in silicene: PRL 110, 026603 (2013). Is the model for Kwant the same as the two reference papers? Moreover,can we consider the Rashba SOI using the Tinyarray package in honeycomb? the hoppings along x and y direction are more complicated in honeycomb. Regards, Qingtian Zhang

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how to define make_system?
by Qingtian Zhang 18 Feb '14

18 Feb '14

Dear all, I am new to Kwant and python, and I am trying out Kwant by learning the examples. I have tried a simple squre scattering region like this: def make_system(a=1, t=-2.8, W=9, L=10): lat = kwant.lattice.honeycomb() def squre(pos): x, y = pos return 0<=x<=L and 0<=y<=W sys = kwant.Builder() i want to try more complicated shapes, for example 0<=x<=L, 0<=y<=W and 2L<=x<=3L,0<=y<=2W. how shoud i change my programme? i note that in the previous version Knit we can glue two regions easily,can we do this in Kwant similarly？ Thanks! Regards, Qingtian Zhang

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