Kwant-discuss April 2018

kwant-discuss@python.org

6 participants
10 discussions

by ZHANG Bing

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

4 months, 2 weeks

Visualize current through a 2D cut for a 3D system

by elchatz＠auth.gr

Hello everyone, Is there currently way to visualize the current through a 2D cut for a 3D system that does not involve messing with the kwant code? I have a 3D system and would like to see the differences in the current when I switch some specific hoppings on and off. Regards, -- Dr. Eleni Chatzikyriakou Computational Physics lab Aristotle University of Thessaloniki elchatz(a)auth.gr - tel:+30 2310 998109

3 years, 8 months

Reflectionless contacts

by elchatz＠auth.gr

Hello everyone, I have defined two semi-infinite contacts in my system as follows: -------------------------------------------------------------------- def lead_shape(p): x, y, z = p return -10 < x < 10 and -6 < y < 6 and 0 < z < 30 sym_lead = kwant.TranslationalSymmetry(lattice.vec((-6, 0, 0))) lead = kwant.Builder(sym_lead) lead[lattice.shape(lead_shape, (0, 0, 15))] = 0 -------------------------------------------------------------------- Is there an easy way to calculate any reflections from the lead back into the conductor? I mean, ideally, I would like all electrons entering the contacts to stay there. Regards Eleni -- Dr. Eleni Chatzikyriakou Computational Physics lab Aristotle University of Thessaloniki elchatz(a)auth.gr - tel:+30 2310 998109

3 years, 9 months

ValueError: Number of orbitals not defined.

by elchatz＠auth.gr

Hello again, I am having trouble defining the nomber of orbitals in the current operator for an infinite system. --------------------------- model = tbmodels.Model.from_wannier_files( hr_file='seedname_hr.dat', wsvec_file='seedname_wsvec.dat', xyz_file='seedname_centres.xyz', win_file='seedname.win' ) def shape(p): x, y, z = p return -6*model.uc[0][0] < x < 6*model.uc[0][0] and -1*model.uc[1][1] < y < 1*model.uc[1][1] and 0 < z < 30 def lead_shape(p): x, y, z = p return -3*model.uc[0][0] < x < 1*model.uc[0][0] and -1*model.uc[1][1] < y < 1*model.uc[1][1] and 0 < z < 30 lattice = model.to_kwant_lattice() for x in lattice.sublattices: x.norbs=1 kwant_model = kwant.Builder() kwant_model[lattice.shape(shape, (0, 0, 15))] = 0 model.add_hoppings_kwant(kwant_model) sym_lead = kwant.TranslationalSymmetry(lattice.vec((-4, 0, 0))) lead = kwant.Builder(sym_lead) lead[lattice.shape(lead_shape, (0, 0, 15))] = 0 model.add_hoppings_kwant(lead) kwant_model.attach_lead(lead) kwant_model.attach_lead(lead.reversed()) kwant_sys = kwant_model.finalized() psi = kwant.wave_function(kwant_sys)(0)[0] J = kwant.operator.Current(kwant_sys) current = sum(J(p) for p in psi) ValueError Traceback (most recent call last) <ipython-input-37-4d2b8ea6f8e4> in <module>() 1 psi = kwant.wave_function(kwant_sys)(0)[0] ----> 2 J = kwant.operator.Current(kwant_sys) 3 current = sum(J(p) for p in psi) 4 kwant\operator.pyx in kwant.operator.Current.__init__() kwant\operator.pyx in kwant.operator._LocalOperator.__init__() ValueError: Number of orbitals not defined. Declare the number of orbitals using the `norbs` keyword argument when constructing the site families (lattices). for x in lattice.sublattices: print(x.norbs) 1 1 1 1 1 1 1 1 1.... ------------------------------------------------ This worked for a closed system. Regards, -- Dr. Eleni Chatzikyriakou Computational Physics lab Aristotle University of Thessaloniki elchatz(a)auth.gr - tel:+30 2310 998109

3 years, 9 months

Four leads or six leads in hall bar-How to use " add_site_family" exactly in Kwant

by hui yang

Dear Joe I am a freshman about Kwant and I want to use Kwant exactly.I will try to define the lattice differently as you adviced.Aha,thank you for your response and it's really happy to communicate with you. Thank you again. Bill - 2018-04-26 17:26 GMT+08:00 Joseph Weston <joseph.weston08(a)gmail.com>: > Hi Bill, > > Dear Joe > "add_site_family" did work in graphene zigzag nanoribbon.When I use > "add_site_family",the central scattering region would not enlarge after > connected with leads in zigzag nanoribbon.But when I use it in graphene > armchair nanoribbon,the central scattering region will enlarge. If you have > spare time,you can run my code,and you can see the picture that the central > scattering is enlarge a little in up and downd leads,left and right lead is > right. > Thank you > Bill Yang > > > > Ah, I understand now. In your original email you talked about a "triangle > of sites", which I did not see in the images you posted, so I was unsure > what you were talking about. > > I don't think you be able to get rid of the "extra added bit" with a > judicious choice of 'other_vectors'; I think you'll have to define the > lattice differently in order to do what you want. > > On the other hand, is this extra added region such a problem? There will > be no physical consequences, as the extra added piece has the same > Hamiltonian as the leads... > > Happy Kwanting, > > Joe >

3 years, 9 months

Four leads or six leads in hall bar-How to use " add_site_family" exactly in Kwant

by hui yang

Dear Joe "add_site_family" did work in graphene zigzag nanoribbon.When I use "add_site_family",the central scattering region would not enlarge after connected with leads in zigzag nanoribbon.But when I use it in graphene armchair nanoribbon,the central scattering region will enlarge. If you have spare time,you can run my code,and you can see the picture that the central scattering is enlarge a little in up and downd leads,left and right lead is right. Thank you Bill Yang This is my code from math import pi, sqrt, tanh import kwant # For computing eigenvalues import scipy.sparse.linalg as sla # For plotting from matplotlib import pyplot #Paramter LeftLength=0.5 #width of scattering region RightLength=5 UpWidth=0 DownWidth=2*4+1#length of scattering region UnitCell=int((DownWidth-1)/2)+1 #unit cell # Define the graphene lattice sin_30, cos_30 = (1 / 2, sqrt(3) / 2) graphene = kwant.lattice.general([(1, 0), (sin_30, cos_30)], [(0, 0), (0, 1 / sqrt(3))]) a,b=graphene.sublattices #graphene2 = graphene = kwant.lattice.general([(sqrt(3)/2, 1/2), (0, 1)], #[(0, 0), (1 / (2*sqrt(3)),1/2)]) def make_system(LeftLength,RightLength,UpWidth,DownWidth): #### Define the scattering region. #### # circular scattering region def circle(pos): x, y = pos return (-LeftLength <= x <= RightLength and (-(sqrt(3)/2*DownWidth+1/2/sqrt(3))<=y<=sqrt(3)/2*UpWidth)) syst = kwant.Builder() # w: width and pot: potential maximum of the p-n junction def potential(pos): #def potential(pos): (x, y) = pos return 0 syst[graphene.shape(circle, (0, 0))] = potential # specify the hoppings of the graphene lattice in the # format expected by builder.HoppingKind hoppings = (((0, 0), a, b), ((0, 1), a, b), ((-1, 1), a, b)) syst[[kwant.builder.HoppingKind(*hopping) for hopping in hoppings]] = -1 # Lead left and right sym0 = kwant.TranslationalSymmetry(graphene.vec((-1, 0))) sym0.add_site_family(graphene.sublattices[0], other_vectors=[(1, -2)]) sym0.add_site_family(graphene.sublattices[1], other_vectors=[(1, -2)]) def lead0_shape(pos): x, y = pos return (-(sqrt(3)/2*DownWidth+1/2/sqrt(3))<=y<=sqrt(3)/2*UpWidth) lead0= kwant.Builder(sym0) lead0[graphene.shape(lead0_shape, (0, 0))] = 0 lead0[[kwant.builder.HoppingKind(*hopping) for hopping in hoppings]] = -1 #Lead up and down sym1 = kwant.TranslationalSymmetry(graphene.vec((-1, 2))) #sym1.add_site_family(graphene.sublattices[0], other_vectors=[(1,1)]) #sym1.add_site_family(graphene.sublattices[1], other_vectors=[(1,1)]) def lead1_shape(pos): x, y = pos return (-1<x<6) lead1= kwant.Builder(sym1) lead1[graphene.shape(lead1_shape, (0, 0))] = 0 lead1[[kwant.builder.HoppingKind(*hopping) for hopping in hoppings]] = -1 return syst, [lead0,lead0.reversed(),lead1,lead1.reversed()] def compute_evs(syst): # Compute some eigenvalues of the closed system sparse_mat = syst.hamiltonian_submatrix(sparse=True) evs = sla.eigs(sparse_mat, 2)[0] print(evs.real) def plot_conductance(syst, energies): # Compute transmission as a function of energy data = [] for energy in energies: smatrix = kwant.smatrix(syst, energy) data.append(smatrix.transmission(0, 1)) pyplot.figure() pyplot.plot(energies, data) pyplot.xlabel("energy [t]") pyplot.ylabel("conductance [e^2/h]") pyplot.show() def plot_bandstructure(flead, momenta): bands = kwant.physics.Bands(flead) energies = [bands(k) for k in momenta] pyplot.figure() pyplot.plot(momenta, energies) pyplot.xlabel("momentum [(lattice constant)^-1]") pyplot.ylabel("energy [t]") pyplot.show() def main(): pot = 0 syst, leads = make_system(LeftLength,RightLength,UpWidth,DownWidth) # To highlight the two sublattices of graphene, we plot one with # a filled, and the other one with an open circle: def family_colors(site): return 0 if site.family == a else 1 # Plot the closed system without leads. #kwant.plot(syst, site_color=family_colors, site_lw=0.1, colorbar=False) # Attach the leads to the system. for lead in leads: syst.attach_lead(lead) # Then, plot the system with leads. kwant.plot(syst, site_color=family_colors, site_lw=0.1, lead_site_lw=0, colorbar=False) # Finalize the system. syst = syst.finalized() # Plot conductance. '''energies = [] for ie in range(1,400): energy = ie * 0.01 energies.append(energy) plot_conductance(syst, energies)''' # 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()

3 years, 9 months

Four leads or six leads in hall bar-How to use " add_site_family" exactly in Kwant

by hui yang

Dear all I am having a problem defining a system which matches leads I want. '''I start by defining a rectangular graphene lattice of size 0<=x<L in the x direction and 0<=x<W in the y direction. (By "rectangular" I mean in the real space coordinates, not the crystallographic coordinates.) I want to attach a lead to the left-had end of this rectangle, going to minus infinity. Therefore, I define a lead with translational symmetry (-1,0) and the appropriate hopping. I attach the lead and plot the system. When I plot the system, I find that the lead has been attached along the (0,1) crystallographic direction (so, that is along the (1/2, sqrt(3)/3) real space vector). A triangle of extra sites have been added for x<0 (real space) so that the total shape of the scattering region is now not rectangular.''' This is David's question.Link is https://mailman-mail5.webfaction.com/pipermail/kwant-discuss/2014-October/0…. and Anton had givern the answer:"We should use add_site_family" I use "add_site_family",but it didn't work. *In summary,I don't know how to use "add_site_family" exactly in kwant.Then I can't create armchair nonaribbon and four leads* *or six leads hall bar (The up and down leads are wrong.Left and right leads are right according to my code.The central scattering* * region is rectangle）.Can you explain "add_site_family" in detail or * *give me a six leads hall bar code to compare with my code .I have spent a lot of time but I can't solve it.* This is my code from math import pi, sqrt, tanh import kwant # For computing eigenvalues import scipy.sparse.linalg as sla # For plotting from matplotlib import pyplot #Paramter LeftLength=0.5 #width of scattering region RightLength=5 UpWidth=0 DownWidth=2*4+1#length of scattering region UnitCell=int((DownWidth-1)/2)+1 #unit cell # Define the graphene lattice sin_30, cos_30 = (1 / 2, sqrt(3) / 2) graphene = kwant.lattice.general([(1, 0), (sin_30, cos_30)], [(0, 0), (0, 1 / sqrt(3))]) a,b=graphene.sublattices #graphene2 = graphene = kwant.lattice.general([(sqrt(3)/2, 1/2), (0, 1)], #[(0, 0), (1 / (2*sqrt(3)),1/2)]) def make_system(LeftLength,RightLength,UpWidth,DownWidth): #### Define the scattering region. #### # circular scattering region def circle(pos): x, y = pos return (-LeftLength <= x <= RightLength and (-(sqrt(3)/2*DownWidth+1/2/sqrt(3))<=y<=sqrt(3)/2*UpWidth)) syst = kwant.Builder() # w: width and pot: potential maximum of the p-n junction def potential(pos): #def potential(pos): (x, y) = pos return 0 syst[graphene.shape(circle, (0, 0))] = potential # specify the hoppings of the graphene lattice in the # format expected by builder.HoppingKind hoppings = (((0, 0), a, b), ((0, 1), a, b), ((-1, 1), a, b)) syst[[kwant.builder.HoppingKind(*hopping) for hopping in hoppings]] = -1 # Lead left and right sym0 = kwant.TranslationalSymmetry(graphene.vec((-1, 0))) sym0.add_site_family(graphene.sublattices[0], other_vectors=[(1, -2)]) sym0.add_site_family(graphene.sublattices[1], other_vectors=[(1, -2)]) def lead0_shape(pos): x, y = pos return (-(sqrt(3)/2*DownWidth+1/2/sqrt(3))<=y<=sqrt(3)/2*UpWidth) lead0= kwant.Builder(sym0) lead0[graphene.shape(lead0_shape, (0, 0))] = 0 lead0[[kwant.builder.HoppingKind(*hopping) for hopping in hoppings]] = -1 #Lead up and down sym1 = kwant.TranslationalSymmetry(graphene.vec((-1, 2))) #sym1.add_site_family(graphene.sublattices[0], other_vectors=[(1,1)]) #sym1.add_site_family(graphene.sublattices[1], other_vectors=[(1,1)]) def lead1_shape(pos): x, y = pos return (-1<x<6) lead1= kwant.Builder(sym1) lead1[graphene.shape(lead1_shape, (0, 0))] = 0 lead1[[kwant.builder.HoppingKind(*hopping) for hopping in hoppings]] = -1 return syst, [lead0,lead0.reversed(),lead1,lead1.reversed()] def compute_evs(syst): # Compute some eigenvalues of the closed system sparse_mat = syst.hamiltonian_submatrix(sparse=True) evs = sla.eigs(sparse_mat, 2)[0] print(evs.real) def plot_conductance(syst, energies): # Compute transmission as a function of energy data = [] for energy in energies: smatrix = kwant.smatrix(syst, energy) data.append(smatrix.transmission(0, 1)) pyplot.figure() pyplot.plot(energies, data) pyplot.xlabel("energy [t]") pyplot.ylabel("conductance [e^2/h]") pyplot.show() def plot_bandstructure(flead, momenta): bands = kwant.physics.Bands(flead) energies = [bands(k) for k in momenta] pyplot.figure() pyplot.plot(momenta, energies) pyplot.xlabel("momentum [(lattice constant)^-1]") pyplot.ylabel("energy [t]") pyplot.show() def main(): pot = 0 syst, leads = make_system(LeftLength,RightLength,UpWidth,DownWidth) # To highlight the two sublattices of graphene, we plot one with # a filled, and the other one with an open circle: def family_colors(site): return 0 if site.family == a else 1 # Plot the closed system without leads. #kwant.plot(syst, site_color=family_colors, site_lw=0.1, colorbar=False) # Attach the leads to the system. for lead in leads: syst.attach_lead(lead) # Then, plot the system with leads. kwant.plot(syst, site_color=family_colors, site_lw=0.1, lead_site_lw=0, colorbar=False) # Finalize the system. syst = syst.finalized() # Plot conductance. '''energies = [] for ie in range(1,400): energy = ie * 0.01 energies.append(energy) plot_conductance(syst, energies)''' # 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() Thanks in advance. Bill Yang

3 years, 9 months

NNN hopping with periodic BC

by yuhao kang

Hello, I want to create a graphene-like system with periodic BC at transverse direction. I'm following the discussion at https://www.mail-archive.com/kwant-discuss@kwant-project.org/msg00036.html. For nearest-neighbor hopping, it works. There is hopping between the upper and lower side. But when I add NNN hopping using: A,B=graphene.sublattices sys[A.neighbors()]=hopp_qsvh sys[B.neighbors()]=hopp_qsvh The NNN hopping doesn't exist between the upper and lower side. Is there any way to solve it? Thank you, Yuhao Attached is the code: import numpy as np import kwant X,Y = 4, 4 s0=np.identity(2) sz=np.array([[1,0],[0,-1]]) graphene = kwant.lattice.honeycomb(1,'b') A,B=graphene.sublattices def rectangle(pos): x, y = pos return -X/2 < x < X/2 def onsite_qsvh(site): x,y=site.pos if y<0: onsite_a = .4*s0 onsite_b = -.4*s0 return onsite_a if site.family == A else onsite_b else: return np.zeros([2,2]) def hopp_qsvh(site1,site2): x1,y1=site1.pos x2,y2=site2.pos hop_a = .4*1j*sz hop_b = -.4*1j*sz if (y1+0.1)*(y2+0.1)>0 and y1+0.1>0: return hop_a if site1.family == A else hop_b else: return np.zeros([2,2]) sym = kwant.TranslationalSymmetry(graphene.vec((-Y/2,Y))) anc = kwant.Builder(sym) anc[graphene.shape(rectangle,(0, 0))] = None anc[graphene.neighbors()] = None sys = kwant.Builder() sys[anc.sites()] = onsite_qsvh sys[((a, sym.to_fd(b)) for a, b in anc.hoppings())] = -s0 sys[A.neighbors()]=hopp_qsvh sys[B.neighbors()]=hopp_qsvh sys = sys.finalized() kwant.plot(sys,fig_size=(20, 10))

3 years, 9 months

Kwant extension directory

by Joseph Weston

Hello everybody! We recently added a new section to the Kwant website [1] that contains links to pieces of code that "extend" Kwant in some cool way. If you've used Kwant in a way that you feel may be useful to the wider community make sure to get in touch so that we can add it to the website. The best way to do that is to make a post to the Kwant development mailing list [2] with a link to your code and a few sentences describing what it enables you to do. Happy Kwanting, Joe [1]: https://kwant-project.org/extensions [2]: mailto:kwant-devel@kwant-project.org

3 years, 9 months

Re: [Kwant] NNN hopping with periodic BC

by Joseph Weston

Sorry I only just saw this email; please remember to "reply All" so that the email gets sent to the mailing list too! > Thanks. But except the PBC imposed on transverse direction, I need > attach the lead on longitude direction. So I want the transverse size > of sample to be finite. > Ah I see. In this case your could consider using 'kwant.wraparound' [1]. In your case you would want to set the 'keep' paramter to '0' to keep the 0th translational symmetry in the wrapped around system. Using wraparound in this way will produce a Builder with a single (longitudinal) translational symmetry that you may use as a lead. The produced Builder will have an (additional) parameter 'k_y'; the transverse momentum. Don't be confused by the name; it will also work when the "wrapped" symmetry vector was not in the "y" direction! There were already several people on the mailing list who used wraparound, so you could also search the archives. If it's still not clear after this post back to this thread. Happy Kwanting, Joe [1]: https://kwant-project.org/doc/1/reference/generated/kwant.wraparound.wrapar…

3 years, 9 months

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Kwant-discuss April 2018