Mailman 3 October 2019 - Kwant-discuss

Gate-defined Nanowire Quantum Dot
by Jonathan Fields Sept. 15, 2022

Sept. 15, 2022

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 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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(no subject)
by Khani Hosein Nov. 4, 2019

Nov. 4, 2019

Dear all, I am using kwant to calculate the transmission of a bulk system. I use " sys = kwant.wraparound.wraparound(sys) and lead = kwant.wraparound.wraparound(lead, keep=0)" to change my tight-binding ribbon system to a bulk system. The transmission is obtained using: kys = np.arange(-0.5, 0.5, 0.001) for ky in kys: smatrix = kwant.smatrix(sys, energy, [ky]) transmission.append(smatrix.transmission(1, 0)) I want to obtain the Transmission vs the incident angle of an electron, and I also need to do the integration ∫T(ky, E) dky or ∫T(θ,E)cosθdθ. I do not undstand the ky in the system with kwant.wraparoun, what is the unit of ky, what is k here for the system. Can you give me some advices on this?Thanks in advance. The definition of incident angle is shown in the attached Fig.1， the band structure for my bulk system is shown in attached Fig.2 and the Tranmission vs ky is shown in Fig.3 (I do not know how the set the values for ky). Regards, Hosein Khani

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Re: [Kwant] question
by Nafise Nouri Oct. 31, 2019

Oct. 31, 2019

Dear all, Now I am trying to understand kwant specially for hexagonal structure. If you look at my code as the following, import kwant import matplotlib.pyplot as plt import math d=1.42; a1=d*math.sqrt(3); t=-0.033; latt = kwant.lattice.general([(a1,0),(a1*0.5,a1*math.sqrt(3)/2)], [(a1/2,-d/2),(a1/2,d/2)]) a,b = latt.sublattices syst= kwant.Builder() #................................................................................... def rectangle(pos): x, y = pos z=x**2+y**2 return -4.75*a1<x<4.75*a1 and -8*d<y<8*d syst[latt.shape(rectangle, (1,1))]=0 def delet(pos): x, y = pos z=x**2+y**2 return z<(1*a1)**2 del syst[latt.shape(delet, (1,1))] #nearest neighbors............................................................. syst[[kwant.builder.HoppingKind((0,0),a,b)]] =t syst[[kwant.builder.HoppingKind((0,1),a,b)]] =t syst[[kwant.builder.HoppingKind((-1,1),a,b)]] =t sym = kwant.TranslationalSymmetry(latt.vec((-4,0))) sym.add_site_family(latt.sublattices[0], other_vectors=[(-1, 2)]) sym.add_site_family(latt.sublattices[1], other_vectors=[(-1, 2)]) lead = kwant.Builder(sym) def lead_shape(pos): x, y = pos return -8*d<y<8*d lead[latt.shape(lead_shape, (1,1))] = 0 def delet_lead(pos): x, y = pos z=x**2+y**2 return z<(1*a1)**2 del lead[latt.shape(delet_lead, (1,1))] lead[[kwant.builder.HoppingKind((0,0),a,b)]] =t lead[[kwant.builder.HoppingKind((0,1),a,b)]] =t lead[[kwant.builder.HoppingKind((-1,1),a,b)]] =t syst.attach_lead(lead,add_cells=3) syst.attach_lead(lead.reversed(),add_cells=3) ax=kwant.plot(syst); I used sym.add_site_family(latt.sublattices[0], other_vectors=[(2,1)]) sym.add_site_family(latt.sublattices[1], other_vectors=[(2,1)]) but I do not exactly why I used these vectors. These vectors are for zigzag nanoribbon, can we use them for armchair nanoribbon? Do you know any information about an armchair nanoribbon? Best, Nafise On Thu, Oct 31, 2019 at 1:08 AM Adel Belayadi <adelphys(a)gmail.com> wrote: > Hey naffisse. > Sure!. I have prepared a detailed explanation with codes as illustrations. > Please ask the question publicly (I mean add kwant.discuss) and I will > answer you so maybe others will benefit and my efforts would be fruitful > for others. > Waiting you question again > Regards > > Le mar. 22 oct. 2019 à 14:03, Nafise Nouri <nafise.nour(a)gmail.com> a > écrit : > >> Hi Adel, >> >> Of course, maybe in future we can have a good collaboration. Now I am >> trying to understand kwant specially for hexagonal structure. >> >> If you look at my code in the proviso emails, I used >> sym.add_site_family(latt.sublattices[0], other_vectors=[(2,1)]) >> sym.add_site_family(latt.sublattices[1], other_vectors=[(2,1)]) >> but I do not exactly why I used these vectors. These vectors are for >> zigzag nanoribbon, can we use them for armchair nanoribbon? >> Do you know any information about an armchair nanoribbon? >> >> Best, >> Nafise >> >> On Mon, Oct 21, 2019 at 10:17 PM Adel Belayadi <adelphys(a)gmail.com> >> wrote: >> >>> Hello Nafise >>> Sorry for my late reply.Yes, that is correct. >>> About the result, my be because of the tight-binding parameters, or due >>> to the masse terme (inversion symmetry) or other things such as SOC. >>> I connot help from now thing. maybe if you email the paper would be >>> better. >>> If you are interested in collaboration, I am willing to work and >>> collaborate. >>> Best regards, Adel >>> >>> Le mer. 16 oct. 2019 à 09:42, Nafise Nouri <nafise.nour(a)gmail.com> a >>> écrit : >>> >>>> Dear Adel Belayadi >>>> >>>> That is very kind of you for your explanation. >>>> As I understand that the definition of limitation of scattering >>>> region in direction of x (the direction that we exert periodic border >>>> condition, here is x direction) is not important because the number of >>>> symmetry vector defines the limitation of x direction in the scattering >>>> region. Am I right? >>>> >>>> I am trying to reproduce of the result of a article for graphene >>>> nanoribbon with hole, the shape of structure in kwant is OK,but the band >>>> structure is not the same as article's. I do not know where is the problem. >>>> >>>> Best, >>>> Nafise >>>> >>>> On Fri, Oct 11, 2019 at 11:22 PM Adel Belayadi <adelphys(a)gmail.com> >>>> wrote: >>>> >>>>> Hey again, >>>>> >>>>> I am so glad that my contribution was beneficial to you. >>>>> >>>>> *1- * *Why did you choose a new super cell. What is a problem when we >>>>> use honeycomb unit cell?* >>>>> >>>>> In fat, it is the same thing since we have (i) a finite system and >>>>> (ii) the obtained system has the honeycomb shape >>>>> >>>>> whether using honeycomb lattice or the provides supercell. >>>>> >>>>> In fact, the supercell where created carefully to provide the same >>>>> shape of honeycomb lattice. >>>>> >>>>> However, if the case of a periodic system, the use of supercell will >>>>> be wrong since the number of atom in the unit cell is a key factor. >>>>> >>>>> *2-If we change symmetry vector (for **example try it by simple >>>>> graphene nanoribbon) some physical properties like* >>>>> >>>>> * band structure IS changed? why does it happen?* >>>>> >>>>> I have small experience in kwant since I am a new user, but >>>>> technically let us say: >>>>> >>>>> (a) The lead is considered as an infinite system, so the number of >>>>> atom in the unit cell should be carefully selected or we will get extra >>>>> usefulness >>>>> >>>>> modes in bands. For example, In the case of perfect lead, we do have >>>>> to set sym = kwant.TranslationalSymmetry(Super_cell_latt.vec((Num=-1,0))) >>>>> >>>>> since for Num =1 is the primitive unit cell which provide the whole >>>>> lead. However, If we set (Num=-2 or more), we will get the same lead >>>>> >>>>> but with non primitive cell (or let's say Conventional lattice). In >>>>> this case, you will get extract evanescent and propagating modes >>>>> which are unnecessary. >>>>> >>>>> >>>>> (b) in your case the lead is not perfect since it contains some holes >>>>> in. For this reason you have to define Conventional lattice or shape which >>>>> provide >>>>> >>>>> or insure periodicity to get the whole lead. >>>>> >>>>> >>>>> Please see attached Pdf.file to have an idea about primitive cell and >>>>> conventional cell (see the fcc case). >>>>> >>>>> >>>>> Ps1 few examples of bands using primitive and conventional unit cell >>>>> >>>>> >>>>> ### Primitive unit cell where Num is set to -1. Here 6 bands are found >>>>> >>>>> import kwant >>>>> >>>>> import matplotlib.pyplot as plt >>>>> >>>>> import math >>>>> >>>>> >>>>> d=1.42; >>>>> >>>>> a1=d*math.sqrt(3); >>>>> >>>>> t=-0.033; >>>>> >>>>> latt = kwant.lattice.general([(a1,0),(a1*0.5,a1*math.sqrt(3)/2)], >>>>> >>>>> [(a1/2,-d/2),(a1/2,d/2)]) >>>>> >>>>> a,b = latt.sublattices >>>>> >>>>> syst= kwant.Builder() >>>>> >>>>> def lead_shape(pos): >>>>> >>>>> return -3<pos[1]<3 >>>>> >>>>> Num = -1 >>>>> >>>>> sym = kwant.TranslationalSymmetry(latt.vec((Num,0))) >>>>> >>>>> sym.add_site_family(latt.sublattices[0], other_vectors=[(-1, 2)]) >>>>> >>>>> sym.add_site_family(latt.sublattices[1], other_vectors=[(-1, 2)]) >>>>> >>>>> lead = kwant.Builder(sym) >>>>> >>>>> >>>>> lead[latt.shape(lead_shape, (1,1))] = 0 >>>>> >>>>> lead[[kwant.builder.HoppingKind((0,0),a,b)]] =t >>>>> >>>>> lead[[kwant.builder.HoppingKind((0,1),a,b)]] =t >>>>> >>>>> lead[[kwant.builder.HoppingKind((-1,1),a,b)]] =t >>>>> >>>>> kwant.plot(lead) >>>>> >>>>> plt.show() >>>>> >>>>> >>>>> ## The unit cell of the lead is composed of 6 atoms, hence 6 bands >>>>> could be find >>>>> >>>>> lead_Num1 = lead.finalized() >>>>> >>>>> kwant.plotter.bands(lead_Num1, show=False) >>>>> >>>>> plt.xlabel("momentum [(lattice constant)^-1]") >>>>> >>>>> plt.ylabel("energy [t]") >>>>> >>>>> plt.show() >>>>> >>>>> >>>>> >>>>> ## the conventional unit cell where Num is set to -2. Here 6*2=12 >>>>> bands are found. We have 6 extrat bands which have nothing >>>>> >>>>> ##to do in the case of a perfect lead >>>>> >>>>> import kwant >>>>> >>>>> import matplotlib.pyplot as plt >>>>> >>>>> import math >>>>> >>>>> >>>>> d=1.42; >>>>> >>>>> a1=d*math.sqrt(3); >>>>> >>>>> t=-0.033; >>>>> >>>>> latt = kwant.lattice.general([(a1,0),(a1*0.5,a1*math.sqrt(3)/2)], >>>>> >>>>> [(a1/2,-d/2),(a1/2,d/2)]) >>>>> >>>>> a,b = latt.sublattices >>>>> >>>>> syst= kwant.Builder() >>>>> >>>>> def lead_shape(pos): >>>>> >>>>> return -3<pos[1]<3 >>>>> >>>>> Num = -2 >>>>> >>>>> sym = kwant.TranslationalSymmetry(latt.vec((Num,0))) >>>>> >>>>> sym.add_site_family(latt.sublattices[0], other_vectors=[(-1, 2)]) >>>>> >>>>> sym.add_site_family(latt.sublattices[1], other_vectors=[(-1, 2)]) >>>>> >>>>> lead = kwant.Builder(sym) >>>>> >>>>> >>>>> lead[latt.shape(lead_shape, (1,1))] = 0 >>>>> >>>>> lead[[kwant.builder.HoppingKind((0,0),a,b)]] =t >>>>> >>>>> lead[[kwant.builder.HoppingKind((0,1),a,b)]] =t >>>>> >>>>> lead[[kwant.builder.HoppingKind((-1,1),a,b)]] =t >>>>> >>>>> kwant.plot(lead) >>>>> >>>>> plt.show() >>>>> >>>>> >>>>> ## The unit cell of the lead is composed of 6*2 atoms, hence 6 bands >>>>> could be find >>>>> >>>>> lead_Num1 = lead.finalized() >>>>> >>>>> kwant.plotter.bands(lead_Num1, show=False) >>>>> >>>>> plt.xlabel("momentum [(lattice constant)^-1]") >>>>> >>>>> plt.ylabel("energy [t]") >>>>> >>>>> plt.show() >>>>> >>>>> >>>>> >>>>> Ps2 few examples of bands using honycomb or supper celll >>>>> >>>>> >>>>> ##In the following we will compare the your honycombe lattice Num =-1 >>>>> and the proposed supper cell. >>>>> >>>>> ##You will see that we will get the same results in terms of bands >>>>> >>>>> >>>>> import kwant >>>>> >>>>> import matplotlib.pyplot as plt >>>>> >>>>> from math import sqrt >>>>> >>>>> >>>>> d = 1.42; >>>>> >>>>> t=-0.033; >>>>> >>>>> ## So let us start >>>>> >>>>> a1 = d*sqrt(3); >>>>> >>>>> a2 = 3*d; >>>>> >>>>> primitive_vector_1 = (a1, 0); >>>>> >>>>> primitive_vector_2 = (0, a2); >>>>> >>>>> ### here premitive vectors are perpondicular: >>>>> primitive_vector_1.primitive_vector_1 = 0 >>>>> >>>>> >>>>> ## Now let us define the atoms positions of the unit cell >>>>> >>>>> Pos_A1 = ( 0, -d/2) >>>>> >>>>> Pos_B1 = ( 0, d/2) >>>>> >>>>> Pos_A2 = ( a1/2, d) >>>>> >>>>> Pos_B2 = ( a1/2, 2*d) >>>>> >>>>> >>>>> Super_cell_latt = kwant.lattice.general([primitive_vector_1, >>>>> primitive_vector_2], >>>>> >>>>> [Pos_A1, Pos_B1, Pos_A2, Pos_B2]) >>>>> >>>>> Sub_A1, Sub_B1, Sub_A2, Sub_B2 = Super_cell_latt.sublattices >>>>> >>>>> >>>>> syst= kwant.Builder() >>>>> >>>>> Num = -1; >>>>> >>>>> sym = kwant.TranslationalSymmetry(Super_cell_latt.vec((Num,0))) >>>>> >>>>> lead = kwant.Builder(sym) >>>>> >>>>> >>>>> def lead_shape(pos): >>>>> >>>>> return -3<pos[1]<3 >>>>> >>>>> >>>>> lead[Super_cell_latt.shape(lead_shape, (1,1))] = 0 >>>>> >>>>> >>>>> >>>>> ## ========================================================= >>>>> >>>>> ## Hopping within unit cell ================================ >>>>> >>>>> lead[[kwant.builder.HoppingKind((0,0),Sub_A1,Sub_B1)]] = t >>>>> >>>>> lead[[kwant.builder.HoppingKind((0,0),Sub_B1,Sub_A2)]] = t >>>>> >>>>> lead[[kwant.builder.HoppingKind((0,0),Sub_A2,Sub_B2)]] = t >>>>> >>>>> ## Hopping between neighbouring unit cell======================= >>>>> >>>>> lead[[kwant.builder.HoppingKind((+1, +1),Sub_A1,Sub_B2)]] = t >>>>> >>>>> lead[[kwant.builder.HoppingKind(( 0, +1),Sub_A1,Sub_B2)]] = t >>>>> >>>>> lead[[kwant.builder.HoppingKind((+1, 0),Sub_B1,Sub_A2)]] = t >>>>> >>>>> >>>>> kwant.plot(lead) >>>>> >>>>> plt.show() >>>>> >>>>> >>>>> ## The unit cell of the lead is composed of 6 atoms, hence 6 bands >>>>> could be find >>>>> >>>>> lead_Num1 = lead.finalized() >>>>> >>>>> kwant.plotter.bands(lead_Num1, show=False) >>>>> >>>>> plt.xlabel("momentum [(lattice constant)^-1]") >>>>> >>>>> plt.ylabel("energy [t]") >>>>> >>>>> plt.show() >>>>> >>>>> Le ven. 11 oct. 2019 à 09:24, Nafise Nouri <nafise.nour(a)gmail.com> a >>>>> écrit : >>>>> >>>>>> Dear Adel Belayadi >>>>>> Thank you so much for your benefit response. But I did not >>>>>> understand completely. Why did you choose a new super cell? What is a >>>>>> problem when we use honeycomb unit cell? >>>>>> >>>>>> Also I have one more question, That is very kind of you if you help m: >>>>>> * If we change symmetry vector (for **example** try it by simple >>>>>> graphene nanoribbon) some physical properties like band structure IS >>>>>> changed? why does it happen?* >>>>>> * Do you know what is the concept of symmetry vector in kwant?* >>>>>> >>>>>> *Thank you in advance for your help.* >>>>>> >>>>>> *Best wishes,* >>>>>> *Nafise* >>>>>> >>>>>> On Fri, Oct 11, 2019 at 3:56 AM Adel Belayadi <adelphys(a)gmail.com> >>>>>> wrote: >>>>>> >>>>>>> Dear Abbout, Josef and Nafiss, >>>>>>> >>>>>>> Good day. As it was stated by Mr. Abbout adel, it seems somehow >>>>>>> tricky to do it. In my point of view this is because we are dealing with no >>>>>>> orthogonal primitive vectors. >>>>>>> I have fixed this issue by ussing orthogonal primitive vectors. >>>>>>> However in this case, we have to use super-cell instead of a simple >>>>>>> honeycomb lattice. >>>>>>> >>>>>>> Please, In the script bellow we will find the code.In the comment, a >>>>>>> little explanation of each part of the code is provided. Additionally, you >>>>>>> might find the enclosed file which contains the python script of the code. >>>>>>> >>>>>>> On think to care about. In the >>>>>>> sym = kwant.TranslationalSymmetry(Super_cell_latt.vec((-Num,0))), >>>>>>> Num should be carefully chosen since it depends on the boundaries >>>>>>> rectangle shape. >>>>>>> >>>>>>> Finally, If you need to have only two families in the plot. Simply >>>>>>> use >>>>>>> >>>>>>> def family_colors(site): return 0 or give a color you like if >>>>>>> site.family == Sub_A1 or Sub_A2 else 1 or give another color you like >>>>>>> >>>>>>> Finally, I hope this is useful for you. Here you are the script >>>>>>> >>>>>>> >>>>>>> ############################################################################################# >>>>>>> >>>>>>> ### I think to solve the problem we need to creat supercell with >>>>>>> orthogonal primitive vector >>>>>>> import kwant >>>>>>> import matplotlib.pyplot as plt >>>>>>> from math import sqrt >>>>>>> >>>>>>> d = 1.42; >>>>>>> hbar_square_over_m = 7.62 >>>>>>> Ep = -11.07; >>>>>>> Vpppi = -0.63*hbar_square_over_m*(1/d)*2 >>>>>>> >>>>>>> ## In the following, we will define a super cell of 4 atoms >>>>>>> ## we define four atoms in the unit cell where A2 equivalent(==) to >>>>>>> A1 and B2==B1. >>>>>>> ## Bear in minde that this kind ofthinking is generally used in >>>>>>> python as aliases >>>>>>> ## In kwant i dont know how to use aliases but we will assume the A2 >>>>>>> and A1 have the same on-site energy >>>>>>> ## (or let us say the same familly). Also the the B2 and B1 have the >>>>>>> same on-site energy >>>>>>> >>>>>>> ## So let us start >>>>>>> a1 = d*sqrt(3); >>>>>>> a2 = 3*d; >>>>>>> primitive_vector_1 = (a1, 0); >>>>>>> primitive_vector_2 = (0, a2); >>>>>>> ### here premitive vectors are perpondicular: >>>>>>> primitive_vector_1.primitive_vector_1 = 0 >>>>>>> >>>>>>> ## Now let us define the atoms positions of the unit cell >>>>>>> Pos_A1 = ( 0, -d/2) >>>>>>> Pos_B1 = ( 0, d/2) >>>>>>> Pos_A2 = ( a1/2, d) >>>>>>> Pos_B2 = ( a1/2, 2*d) >>>>>>> >>>>>>> >>>>>>> Super_cell_latt = kwant.lattice.general([primitive_vector_1, >>>>>>> primitive_vector_2], >>>>>>> [Pos_A1, Pos_B1, Pos_A2, >>>>>>> Pos_B2]) >>>>>>> Sub_A1, Sub_B1, Sub_A2, Sub_B2 = Super_cell_latt.sublattices >>>>>>> >>>>>>> syst= kwant.Builder() >>>>>>> >>>>>>> #................................................................................... >>>>>>> def rectangle(pos): >>>>>>> x, y = pos >>>>>>> z=x**2+y**2 >>>>>>> return -4.75*a1<x<4.75*a1 and -8*d<y<8*d >>>>>>> >>>>>>> syst[Super_cell_latt.shape(rectangle, (1,1))]=Ep >>>>>>> >>>>>>> def delet(pos): >>>>>>> x, y = pos >>>>>>> z=x**2+y**2 >>>>>>> return z<(1*a1)**2 >>>>>>> >>>>>>> del syst[Super_cell_latt.shape(delet, (1,1))] >>>>>>> >>>>>>> #nearest >>>>>>> neighbors............................................................. >>>>>>> ## Be carfull if you consider second nearest neighbors >>>>>>> ## ========================================================= >>>>>>> ## Hopping within unit cell ================================ >>>>>>> syst[[kwant.builder.HoppingKind((0,0),Sub_A1,Sub_B1)]] = Vpppi >>>>>>> syst[[kwant.builder.HoppingKind((0,0),Sub_B1,Sub_A2)]] = Vpppi >>>>>>> syst[[kwant.builder.HoppingKind((0,0),Sub_A2,Sub_B2)]] = Vpppi >>>>>>> ## Hopping between neighbouring unit cell======================= >>>>>>> syst[[kwant.builder.HoppingKind((+1, +1),Sub_A1,Sub_B2)]] = Vpppi >>>>>>> syst[[kwant.builder.HoppingKind(( 0, +1),Sub_A1,Sub_B2)]] = Vpppi >>>>>>> syst[[kwant.builder.HoppingKind((+1, 0),Sub_B1,Sub_A2)]] = Vpppi >>>>>>> >>>>>>> # Plot the closed system without leads. >>>>>>> kwant.plot(syst) >>>>>>> >>>>>>> Num = 8; >>>>>>> sym = kwant.TranslationalSymmetry(Super_cell_latt.vec((-Num,0))) >>>>>>> lead = kwant.Builder(sym) >>>>>>> >>>>>>> def lead_shape(pos): >>>>>>> x, y = pos >>>>>>> return -8*d<y<8*d >>>>>>> >>>>>>> lead[Super_cell_latt.shape(lead_shape, (1,1))] = Ep >>>>>>> >>>>>>> del lead[Super_cell_latt.shape(delet, (1,1))] >>>>>>> >>>>>>> ## ========================================================= >>>>>>> ## Hopping within unit cell ================================ >>>>>>> lead[[kwant.builder.HoppingKind((0,0),Sub_A1,Sub_B1)]] = Vpppi >>>>>>> lead[[kwant.builder.HoppingKind((0,0),Sub_B1,Sub_A2)]] = Vpppi >>>>>>> lead[[kwant.builder.HoppingKind((0,0),Sub_A2,Sub_B2)]] = Vpppi >>>>>>> ## Hopping between neighbouring unit cell======================= >>>>>>> lead[[kwant.builder.HoppingKind((+1, +1),Sub_A1,Sub_B2)]] = Vpppi >>>>>>> lead[[kwant.builder.HoppingKind(( 0, +1),Sub_A1,Sub_B2)]] = Vpppi >>>>>>> lead[[kwant.builder.HoppingKind((+1, 0),Sub_B1,Sub_A2)]] = Vpppi >>>>>>> >>>>>>> >>>>>>> syst.attach_lead(lead,add_cells=3) >>>>>>> syst.attach_lead(lead.reversed(),add_cells=3) >>>>>>> >>>>>>> # Plot the closed system without leads. >>>>>>> kwant.plot(syst) >>>>>>> plt.show() >>>>>>> >>>>>>> >>>>>>> Best >>>>>>> >>>>>>> A. BELAYADI >>>>>>> >>>>>>> Le jeu. 10 oct. 2019 à 22:44, Abbout Adel <abbout.adel(a)gmail.com> a >>>>>>> écrit : >>>>>>> >>>>>>>> Dear Nafise, >>>>>>>> >>>>>>>> You are right, this might be annoying when you try to construct a >>>>>>>> uniform system (central+leads). Indeed, a lot of concentration is needed in >>>>>>>> some cases because the lead usually adds some extra sites until it meats >>>>>>>> the system. >>>>>>>> There is an easy trick to overcome this small issue. >>>>>>>> >>>>>>>> 1) Create a system which can stop a lead (any shape for the system). >>>>>>>> 2) Attach one lead: syst.attach_lead(lead,add_cells=0) >>>>>>>> 3) Save the sites of the system: sites=list(syst.finalized().sites) >>>>>>>> 4) Delete the lead: del syst.leads[0] >>>>>>>> 5) Attach again the lead with one extra >>>>>>>> cell: syst.attach_lead(lead,add_cells=1) >>>>>>>> 6) Delete the previous sites of the system: del syst[sites] >>>>>>>> >>>>>>>> By doing this last step, all the previous sites are deleted and >>>>>>>> only one full unit cell remains in the central system (the one added by the >>>>>>>> lead). >>>>>>>> 7) the last step is : syst.attach_lead(lead.reversed(),add_cells=1) >>>>>>>> >>>>>>>> And that is it! >>>>>>>> Your program is summarized below. >>>>>>>> I hope this helps, >>>>>>>> >>>>>>>> Regards, >>>>>>>> Adel >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> ######################################################################################### >>>>>>>> import kwant >>>>>>>> import matplotlib.pyplot as plt >>>>>>>> import math >>>>>>>> >>>>>>>> d=1.42; >>>>>>>> a1=d*math.sqrt(3); >>>>>>>> t=-0.033; >>>>>>>> >>>>>>>> latt = kwant.lattice.general([(a1,0),(a1*0.5,a1*math.sqrt(3)/2)], >>>>>>>> [(a1/2,-d/2),(a1/2,d/2)]) >>>>>>>> a,b = latt.sublattices >>>>>>>> syst= kwant.Builder() >>>>>>>> >>>>>>>> >>>>>>>> #................................................................................... >>>>>>>> def rectangle(pos): >>>>>>>> x, y = pos >>>>>>>> z=x**2+y**2 >>>>>>>> return -4.75*a1<x<4.75*a1 and -8*d<y<8*d >>>>>>>> >>>>>>>> syst[latt.shape(rectangle, (1,1))]=0 >>>>>>>> >>>>>>>> def delet(pos): >>>>>>>> x, y = pos >>>>>>>> z=x**2+y**2 >>>>>>>> return z<(1*a1)**2 >>>>>>>> >>>>>>>> del syst[latt.shape(delet, (1,1))] >>>>>>>> >>>>>>>> >>>>>>>> #nearest >>>>>>>> neighbors............................................................. >>>>>>>> syst[[kwant.builder.HoppingKind((0,0),a,b)]] =t >>>>>>>> syst[[kwant.builder.HoppingKind((0,1),a,b)]] =t >>>>>>>> syst[[kwant.builder.HoppingKind((-1,1),a,b)]] =t >>>>>>>> >>>>>>>> >>>>>>>> sym = kwant.TranslationalSymmetry(latt.vec((-4,0))) >>>>>>>> >>>>>>>> sym.add_site_family(latt.sublattices[0], other_vectors=[(-1, 2)]) >>>>>>>> sym.add_site_family(latt.sublattices[1], other_vectors=[(-1, 2)]) >>>>>>>> lead = kwant.Builder(sym) >>>>>>>> >>>>>>>> >>>>>>>> def lead_shape(pos): >>>>>>>> x, y = pos >>>>>>>> return -8*d<y<8*d >>>>>>>> >>>>>>>> lead[latt.shape(lead_shape, (1,1))] = 0 >>>>>>>> >>>>>>>> def delet_lead(pos): >>>>>>>> x, y = pos >>>>>>>> z=x**2+y**2 >>>>>>>> return z<(1*a1)**2 >>>>>>>> >>>>>>>> del lead[latt.shape(delet_lead, (1,1))] >>>>>>>> >>>>>>>> lead[[kwant.builder.HoppingKind((0,0),a,b)]] =t >>>>>>>> lead[[kwant.builder.HoppingKind((0,1),a,b)]] =t >>>>>>>> lead[[kwant.builder.HoppingKind((-1,1),a,b)]] =t >>>>>>>> >>>>>>>> syst.attach_lead(lead,add_cells=0) >>>>>>>> del syst.leads[0] >>>>>>>> sites=list(syst.finalized().sites) >>>>>>>> syst.attach_lead(lead,add_cells=1) >>>>>>>> >>>>>>>> del syst[sites] >>>>>>>> #syst.attach_lead(lead.reversed(),add_cells=3) >>>>>>>> syst.attach_lead(lead.reversed(),add_cells=1) >>>>>>>> ax=kwant.plot(syst); >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> del syst[sites] >>>>>>>> >>>>>>>> On Thu, Oct 10, 2019 at 11:01 AM Nafise Nouri < >>>>>>>> nafise.nour(a)gmail.com> wrote: >>>>>>>> >>>>>>>>> Dear Joseph Weston >>>>>>>>> Thank you very much for your quick response. >>>>>>>>> Of course, I can post you my cod example. It is in the following: >>>>>>>>> >>>>>>>>> import kwant >>>>>>>>> import matplotlib.pyplot as plt >>>>>>>>> import math >>>>>>>>> >>>>>>>>> d=1.42; >>>>>>>>> a1=d*math.sqrt(3); >>>>>>>>> t=-0.033; >>>>>>>>> >>>>>>>>> latt = kwant.lattice.general([(a1,0),(a1*0.5,a1*math.sqrt(3)/2)], >>>>>>>>> [(a1/2,-d/2),(a1/2,d/2)]) >>>>>>>>> a,b = latt.sublattices >>>>>>>>> syst= kwant.Builder() >>>>>>>>> >>>>>>>>> >>>>>>>>> #................................................................................... >>>>>>>>> def rectangle(pos): >>>>>>>>> x, y = pos >>>>>>>>> z=x**2+y**2 >>>>>>>>> return -4.75*a1<x<4.75*a1 and -8*d<y<8*d >>>>>>>>> >>>>>>>>> syst[latt.shape(rectangle, (1,1))]=0 >>>>>>>>> >>>>>>>>> def delet(pos): >>>>>>>>> x, y = pos >>>>>>>>> z=x**2+y**2 >>>>>>>>> return z<(1*a1)**2 >>>>>>>>> >>>>>>>>> del syst[latt.shape(delet, (1,1))] >>>>>>>>> >>>>>>>>> >>>>>>>>> #nearest >>>>>>>>> neighbors............................................................. >>>>>>>>> syst[[kwant.builder.HoppingKind((0,0),a,b)]] =t >>>>>>>>> syst[[kwant.builder.HoppingKind((0,1),a,b)]] =t >>>>>>>>> syst[[kwant.builder.HoppingKind((-1,1),a,b)]] =t >>>>>>>>> >>>>>>>>> >>>>>>>>> sym = kwant.TranslationalSymmetry(latt.vec((-4,0))) >>>>>>>>> >>>>>>>>> sym.add_site_family(latt.sublattices[0], other_vectors=[(-1, 2)]) >>>>>>>>> sym.add_site_family(latt.sublattices[1], other_vectors=[(-1, 2)]) >>>>>>>>> lead = kwant.Builder(sym) >>>>>>>>> >>>>>>>>> >>>>>>>>> def lead_shape(pos): >>>>>>>>> x, y = pos >>>>>>>>> return -8*d<y<8*d >>>>>>>>> >>>>>>>>> lead[latt.shape(lead_shape, (1,1))] = 0 >>>>>>>>> >>>>>>>>> def delet_lead(pos): >>>>>>>>> x, y = pos >>>>>>>>> z=x**2+y**2 >>>>>>>>> return z<(1*a1)**2 >>>>>>>>> >>>>>>>>> del lead[latt.shape(delet_lead, (1,1))] >>>>>>>>> >>>>>>>>> lead[[kwant.builder.HoppingKind((0,0),a,b)]] =t >>>>>>>>> lead[[kwant.builder.HoppingKind((0,1),a,b)]] =t >>>>>>>>> lead[[kwant.builder.HoppingKind((-1,1),a,b)]] =t >>>>>>>>> >>>>>>>>> syst.attach_lead(lead,add_cells=3) >>>>>>>>> syst.attach_lead(lead.reversed(),add_cells=3) >>>>>>>>> >>>>>>>>> ax=kwant.plot(syst); >>>>>>>>> >>>>>>>>> Best wishes, >>>>>>>>> Nafise >>>>>>>>> >>>>>>>>> Sorry for double email. The first email was not as reply. >>>>>>>>> >>>>>>>>> Best, >>>>>>>>> Nafise >>>>>>>>> >>>>>>>>> >>>>>>>>> On Tue, Oct 8, 2019 at 3:08 PM Nafise Nouri <nafise.nour(a)gmail.com> >>>>>>>>> wrote: >>>>>>>>> >>>>>>>>>> Hi, >>>>>>>>>> Of course. >>>>>>>>>> I sent it to you and also to the mailing list, >>>>>>>>>> >>>>>>>>>> Best regards, >>>>>>>>>> Nafise >>>>>>>>>> >>>>>>>>>> On Tue, Oct 8, 2019 at 11:31 AM Joseph Weston < >>>>>>>>>> joseph.weston08(a)gmail.com> wrote: >>>>>>>>>> >>>>>>>>>>> Hi, >>>>>>>>>>> >>>>>>>>>>> Can you post this as a reply to your query in the mailing list? >>>>>>>>>>> I accidentally replied directly to you when I should have CC'd the mailing >>>>>>>>>>> list also. >>>>>>>>>>> >>>>>>>>>>> Thanks, >>>>>>>>>>> >>>>>>>>>>> Joe >>>>>>>>>>> On 10/6/19 7:43 AM, Nafise Nouri wrote: >>>>>>>>>>> >>>>>>>>>>> Dear Joseph Weston >>>>>>>>>>> Thank you very much for your quick response. >>>>>>>>>>> Of course, I can post you my cod example. It is in the >>>>>>>>>>> following: >>>>>>>>>>> >>>>>>>>>>> import kwant >>>>>>>>>>> import matplotlib.pyplot as plt >>>>>>>>>>> import math >>>>>>>>>>> >>>>>>>>>>> d=1.42; >>>>>>>>>>> a1=d*math.sqrt(3); >>>>>>>>>>> t=-0.033; >>>>>>>>>>> >>>>>>>>>>> latt = kwant.lattice.general([(a1,0),(a1*0.5,a1*math.sqrt(3)/2)], >>>>>>>>>>> [(a1/2,-d/2),(a1/2,d/2)]) >>>>>>>>>>> a,b = latt.sublattices >>>>>>>>>>> syst= kwant.Builder() >>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> #................................................................................... >>>>>>>>>>> def rectangle(pos): >>>>>>>>>>> x, y = pos >>>>>>>>>>> z=x**2+y**2 >>>>>>>>>>> return -4.75*a1<x<4.75*a1 and -8*d<y<8*d >>>>>>>>>>> >>>>>>>>>>> syst[latt.shape(rectangle, (1,1))]=0 >>>>>>>>>>> >>>>>>>>>>> def delet(pos): >>>>>>>>>>> x, y = pos >>>>>>>>>>> z=x**2+y**2 >>>>>>>>>>> return z<(1*a1)**2 >>>>>>>>>>> >>>>>>>>>>> del syst[latt.shape(delet, (1,1))] >>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> #nearest >>>>>>>>>>> neighbors............................................................. >>>>>>>>>>> syst[[kwant.builder.HoppingKind((0,0),a,b)]] =t >>>>>>>>>>> syst[[kwant.builder.HoppingKind((0,1),a,b)]] =t >>>>>>>>>>> syst[[kwant.builder.HoppingKind((-1,1),a,b)]] =t >>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> sym = kwant.TranslationalSymmetry(latt.vec((-4,0))) >>>>>>>>>>> >>>>>>>>>>> sym.add_site_family(latt.sublattices[0], other_vectors=[(-1, 2)]) >>>>>>>>>>> sym.add_site_family(latt.sublattices[1], other_vectors=[(-1, 2)]) >>>>>>>>>>> lead = kwant.Builder(sym) >>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> def lead_shape(pos): >>>>>>>>>>> x, y = pos >>>>>>>>>>> return -8*d<y<8*d >>>>>>>>>>> >>>>>>>>>>> lead[latt.shape(lead_shape, (1,1))] = 0 >>>>>>>>>>> >>>>>>>>>>> def delet_lead(pos): >>>>>>>>>>> x, y = pos >>>>>>>>>>> z=x**2+y**2 >>>>>>>>>>> return z<(1*a1)**2 >>>>>>>>>>> >>>>>>>>>>> del lead[latt.shape(delet_lead, (1,1))] >>>>>>>>>>> >>>>>>>>>>> lead[[kwant.builder.HoppingKind((0,0),a,b)]] =t >>>>>>>>>>> lead[[kwant.builder.HoppingKind((0,1),a,b)]] =t >>>>>>>>>>> lead[[kwant.builder.HoppingKind((-1,1),a,b)]] =t >>>>>>>>>>> >>>>>>>>>>> syst.attach_lead(lead,add_cells=3) >>>>>>>>>>> syst.attach_lead(lead.reversed(),add_cells=3) >>>>>>>>>>> >>>>>>>>>>> ax=kwant.plot(syst); >>>>>>>>>>> >>>>>>>>>>> Best wishes, >>>>>>>>>>> Nafise >>>>>>>>>>> >>>>>>>>>>> On Sat, Oct 5, 2019 at 12:57 PM Joseph Weston < >>>>>>>>>>> joseph.weston08(a)gmail.com> wrote: >>>>>>>>>>> >>>>>>>>>>>> Hi Nafise >>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> I need to make a periodic lattice with hole. In fact I should make holes on the scattering region and also on the leads. Although I can make this kind of lattice by kwant, I have problem about the distances between holes. I want to make a periodic holes on the nanoribbon but the distance between holes in the scattering region is different from the distance between holes in the other regions. Would you please let me know How Can I make a same distance between holes? Should I work on the translational symmetry in the leads? >>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> Because the leads need to be translationally invariant if you >>>>>>>>>>>> want a very large distance between defects then your unit cell in the leads >>>>>>>>>>>> needs to be correspondingly large. >>>>>>>>>>>> >>>>>>>>>>>> If you post a code example of what your problem is specifically >>>>>>>>>>>> we may be able to help more. >>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> Happy Kwanting, >>>>>>>>>>>> >>>>>>>>>>>> Joe >>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> P.S. sorry for the double reply; I forgot to send to the >>>>>>>>>>>> mailing list also >>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>> >>>>>>>> -- >>>>>>>> Abbout Adel >>>>>>>> >>>>>>>

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Re transmission for bulk system
by Khani Hosein Oct. 29, 2019

Oct. 29, 2019

Dear Adel, Thank you very much for your kind help.I want to use kwant to calculate the transmission for bulk system because of the paper Phys. Rev. B 86, 115455. However, ky for the lead and the scattering region is not very clear in Kwant when we use kwant.wraparound. When we use smatrix = kwant.smatrix(sys, energy, [ky]) to calculate the transmission of the bulk system,we do not know if the ky here can affect the scattering region or not. I have tried a system with more args, for example smatrix = kwant.smatrix(sys, energy, [VG1,VG2,ky]), (Here ky must be put as the third one), the definition of the onsite potential should be given as “def onsitepotential(site,VG1,VG2)”. I do not know if it is a bug or I just do not find the right way to use the kwant.wraparound. I think the developers may know the reason. Best, Khani Hosein

1 0

armchair nanoribbon with defect
by Saj.ZiaBorujeni Oct. 27, 2019

Oct. 27, 2019

Dear all, I am trying to make an armchair nanoribbon as following: import kwant from math import sqrt import matplotlib.pyplot as plt import tinyarray import numpy as np import math import cmath #import scipy.linalg as la import matplotlib d=1.42; a1=d*math.sqrt(3); #on-site energy................................................... t=-2.7; latt = kwant.lattice.general([(0,a1),(a1*math.sqrt(3)/2,a1*0.5)], [(-d/2,a1/2),(d/2,a1/2)]) a,b = latt.sublattices syst= kwant.Builder() def rectangle(pos): x, y = pos return -2.4*a1<x<2.4*a1 and -3*d<y<3*d syst[latt.shape(rectangle, (1,1))]=0 #nearest neighbors............................................................. syst[[kwant.builder.HoppingKind((0,0),a,b)]] =t syst[[kwant.builder.HoppingKind((0,1),a,b)]] =t syst[[kwant.builder.HoppingKind((-1,1),a,b)]] =t ax=kwant.plot(syst); sym = kwant.TranslationalSymmetry(latt.vec((-1,2))) lead = kwant.Builder(sym) def lead_shape(pos): x, y = pos return -3*d<y<3*d lead[latt.shape(lead_shape, (1,1))]=0 lead[[kwant.builder.HoppingKind((0,0),a,b)]]=t lead[[kwant.builder.HoppingKind((0,1),a,b)]]=t lead[[kwant.builder.HoppingKind((-1,1),a,b)]]=t syst.attach_lead(lead,add_cells=0) syst.attach_lead(lead.reversed(),add_cells=0) ax=kwant.plot(syst); It is ok and I have no problem with it. I have problem when I tried to make a defect (like making a hole) on the scattering rigion and also lead. I used a same method for making a defect on both scattering region and lead but the results are not same. Would you please help me what is a problem. Would you please let me know if symmetry vector (sym = kwant.TranslationalSymmetry(latt.vec((-1,2)))) used is ok? Best wishes, Sajad

2 1

transmission for bulk system
by Khani Hosein Oct. 26, 2019

Oct. 26, 2019

Dear all, I am using kwant to calculate the transmission of a bulk system. I use " sys = kwant.wraparound.wraparound(sys) and lead = kwant.wraparound.wraparound(lead, keep=0)" to change my tight-binding ribbon system to a bulk system. The transmission is obtained using: kys = np.arange(-0.5, 0.5, 0.001) for ky in kys: smatrix = kwant.smatrix(sys, energy, [ky]) transmission.append(smatrix.transmission(1, 0)) I want to obtain the Transmission vs the incident angle of an electron, and I also need to do the integration ∫T(ky, E) dky or ∫T(θ,E)cosθdθ. I do not undstand the ky in the system with kwant.wraparoun, what is the unit of ky, what is k here for the system, how to obtain T(θ,E) .Can you give me some advices on this?Thanks in advance. The definition of incident angle is shown in the attached Fig.1， the band structure for my bulk system is shown in attached Fig.2 and the Tranmission vs ky is shown in Fig.3 (I do not know how to set the values for ky). Regards, Hosein Khani

1 0

Get .tex file for the studied system
by aheuchamps＠student.uliege.be Oct. 20, 2019

Oct. 20, 2019

Hello, I previously asked how to get the corresponding .tex file of the system I want to study. For example, using the tikzplolib package, I can write the following code: figLattice = kwant.plot( sys ) tikzplotlib.save( nameGeometry+'.tex' ) However, the corresponding .tex file is empty (see the attached file). How can I solve that problem ? Thank you and have a good day, Alexandre

2 1