Kwant-discuss April 2018

kwant-discuss@python.org

6 participants
13 discussions

Gate-defined Nanowire Quantum Dot
by Jonathan Fields 15 Sep '22

15 Sep '22

Dear Reader, I am new to KWANT and trying to figure out if it is suitable for calculating transport properties of gate-defined quantum dots made out of nanowires, along the lines of the structure used in https://arxiv.org/abs/cond-mat/0609463. Now, I understand that the mailing list is not a place to ask people to do my work for me, and my question is also not for someone to do this. What I am looking for is some insights into if this is possible (and not all that difficult) with the package. At first sight (and going through the tutorials as well as the APS March Meeting material) this does not seem straightforward; what I struggle with is how to define this type of dot in KWANT. Now, one way would of course be to built the entire 3D geometry of the system, but this will be computationally expensive, and probably also rather tricky to do in terms of defining everything, from the hexagonal wire itself to all of the gates and oxide layers and such. Some abstraction would be preferred, perhaps even reducing the dimensionality and making a 2D system, such as often done in the tutorial. Is this a good idea? My problem is that if one does this, then I run into the problem of how to model the 'half wrap-around' type gates typically used in these devices. In the transport through barrier section of the APS March Meeting material there is a section on how to model realistic potentials, but this would not work all that well for these wrap around type gates. On the other hand, in a way they are perhaps not so different from the QPC in that section. One could model the three gates as something like https://i.imgur.com/WZC983c.png as they do essentially form channels in the wire. Apart from if this sacrifices too much of the nanowire nature in favor of a 2DEG system, I do suppose such a system should in principle be able to be treated as a quantum dot. I haven't been able to confirm this as I am not yet sure how one can apply a source-drain voltage in KWANT; I first thought that this would probably be related to the energy of the modes, but then again I have not been able to produce Coulomb diamonds in this way. The question is getting rather lenghty, and also a bit unclear at this point. Perhaps I should finish up by stating it in a concise form; would you think that it is possible to simulate the transport of such a gate defined nanowire quantum dot device with KWANT, and if so, is the approach I am suggesting above a viable one, or would you go about it very differently? Kind regards Jonathan <http://aka.ms/weboutlook>

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How the spin is positioned in the Smatrix?
by Qingtian Zhang 06 Mar '22

06 Mar '22

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 06 Mar '22

06 Mar '22

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 12 Sep '21

12 Sep '21

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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Visualize current through a 2D cut for a 3D system
by elchatz＠auth.gr 04 May '18

04 May '18

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

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Reflectionless contacts
by elchatz＠auth.gr 27 Apr '18

27 Apr '18

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

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ValueError: Number of orbitals not defined.
by elchatz＠auth.gr 27 Apr '18

27 Apr '18

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

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Four leads or six leads in hall bar-How to use " add_site_family" exactly in Kwant
by hui yang 26 Apr '18

26 Apr '18

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 >

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Four leads or six leads in hall bar-How to use " add_site_family" exactly in Kwant
by hui yang 26 Apr '18

26 Apr '18

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()

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Four leads or six leads in hall bar-How to use " add_site_family" exactly in Kwant
by hui yang 25 Apr '18

25 Apr '18

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

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