Mailman 3 April 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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Regarding the NNN term in bilayer graphene across the layer
by MS. PRIYANKA SINHA April 30, 2019

April 30, 2019

Dear Kwant developers, I am trying to put next nearest neighbor hopping terms across the layer in bilayer graphene. In that case, how can I get those hopping kind directions for the NNN hopping for the interlayer or can I use sys [ lat.neighbor(3)] or sys[ lat.neighbor(4)]? Kindly help me in this regard. Thanking You, Priyanka Sinha

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[KWANT] Diagonalization of hamiltonian
by Naveen Yadav April 29, 2019

April 29, 2019

Dear KWANT developers, I want to diagonalize the model hamiltonian containing sine and cosine functions with momentum operators as their argument. H(k) = tx*σx* sin kx + ty*σy*sin ky + mk*σz + λ*σ0 *sin kz, mk = tz(cos β − cos kz) + t'(2 − cos kx − cos ky) Then I want to plot the energy dispersion as a function of kz in the presence of perpendicular magnetic field. Here perpendicular direction is x. Could anybody suggest me how to do this using kwant? I am new to kwant. Thanks in advance. Best,Naveen Naveen Department of Physics & Astrophysics University of Delhi New Delhi-110007

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band structure for a one-dimensional diatomic chain
by Hanning Chen April 26, 2019

April 26, 2019

Dear Kwant developers, I am trying to plot the band structure for a one-dimensional diatomic chain. It turns out that kwant only plots one band. But two bands are expected because I set very different onsite energies for the two atoms. Enclosed please find my python code, and let me know if anything is missing. Thanks. Hanning Chen, Ph.D. Assistant Professor Department of Chemistry George Washington University Washington, DC 20052 http://www.chenlagbwu.net import kwant import matplotlib.pyplot as plt import numpy a=1.0 device=kwant.Builder() lat_device = kwant.lattice.chain(a=a,name='1D_chain_Diatomic',norbs=1) #build electrode L = 2 symmetry_lead = kwant.TranslationalSymmetry([-1]) lead = kwant.Builder(symmetry_lead) lead[lat_device(0)] = 1.0 lead[lat_device(1)] = 100.0 lead[lat_device(0),lat_device(1)]=-1 lead = lead.finalized() bands = kwant.physics.Bands(lead); momenta = numpy.linspace(-numpy.pi, numpy.pi, 101); energies = [bands(k) for k in momenta] plt.plot(momenta,energies) plt.show()

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overlap matrix besides Hamiltonian matrix
by Hanning Chen April 24, 2019

April 24, 2019

Dear Kwant developers, I am wondering if it is possible to designate overlap matrix between sites in Kwant, similar to the construction of Hamiltonian matrix? Or, in Kwant, we always assume non-overlapping sites. Thanks. Hanning Chen, Ph.D. Assistant Professor Department of Chemistry George Washington University Washington, DC 20052 http://www.chenlagbwu.net

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Re: [Kwant] 答复: Problem in Kwant1.4
by Abbout Adel April 23, 2019

April 23, 2019

Dear Yan, It is better to plot your system before you attach the leads. Think also about plotting the leads separately (kwant.plot(lead)). This may give you some clues. In your case, you have to issues: 1) Increase the bottom limit of your lead condition: in_lead = -NL_wid/2*ay+.1 <= y <= NL_wid/2*ay-0.1 in fact, the system needs to interrupt the lead. (in your case, you have an extra layer in the lead) 2) Change the starting point where you build your leads: lead1[lat.shape(lead1_shape, ( 40, 0))] = onsite lead0[lat.shape(lead0_shape, (- 40, 0))] = onsite With these corrections, your program will work fine. I hope this helps. Regards, Adel On Mon, Apr 22, 2019 at 8:17 PM X.F.Yan <yxf0125(a)aliyun.com> wrote: > Dear Anton > > > > Sorry, I am a beginner. Although I have read the full error message, I can > ’t understand the error code. If I try change the hopping site, the > RunningtimeError will go away. > > Could you explain the error to me in detail? Thanks! > > > > Best regards, > > Yan > > *发件人: *Anton Akhmerov <anton.akhmerov+kd(a)gmail.com> > *发送时间: *2019年4月22日 16:48 > *收件人: *X.F.Yan <yxf0125(a)aliyun.com> > *抄送: *kwant-discuss(a)kwant-project.org > *主题: *Re: [Kwant] Problem in Kwant1.4 > > > > Dear F.X. Yan, > > > > Please read the full error message, not just the last lines. The full > error message clearly explains what goes wrong. > > > > Best regards, > > Anton > > > > > > > > On Mon, Apr 22, 2019 at 9:47 AM X.F.Yan <yxf0125(a)aliyun.com> wrote: > > Dear Professor, > > > > I encountered problems during my recent use of kwant. I had a running time > error while writing the black phosphorus ring structure.This is erroe. > > > > RuntimeError: All sites of this builder have been deleted because an > exception > > occurred during the execution of fill(): see above. > > > > [image: cid:16a44372e27afc7934e1] > > > > I find the problem in the line 138. If I replace *lead0 *with* sys, * the > error will be solved. But this structure is false, there is a hopping > integral missing in the left lead. > > > > Otherwise, I writing the same lead which I don’t replace *lead1* with* > sys* in the symmetric direction, there is no error here. > > > > Please help me solve this problem,Thanks! > > > > In the attachment, I will attach my program. > > > > Sincerely yours, > > F.X. Yan > > > > 发送自 Windows 10 版邮件 <https://go.microsoft.com/fwlink/?LinkId=550986>应用 > > > > > -- Abbout Adel

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leads not properly attached in a one-dimensional system
by Hanning Chen April 23, 2019

April 23, 2019

Dear KWANT developers, I am a new user of KWANT, and is building my first one-dimensional toy system that consists of a 20-site central device and two 2-site leads. After constructing the two leads, I found that both are not properly attached to the central device by using the “attach_lead” function. First, the “kwant.plot” only shows one site for each lead. Second, the calculated conductance is always zero regardless of energy. Enclosed please find my simple kwant script. Any comments and suggestions are highly appreciated.. Thanks. Hanning Chen, Ph.D. Assistant Professor Department of Chemistry George Washington University Washington, DC 20052 http://www.chenlagbwu.net import kwant import matplotlib.pyplot as plt import scipy import numpy as np #build central device L = 20 a = 1 alpha = 0 beta = -1 device=kwant.Builder() lat_device = kwant.lattice.chain(a=a,name='20_site_1D_chain',norbs=1) device[(lat_device(i) for i in range(L))]=alpha for i in range(L): if i > 0: device[lat_device(i),lat_device(i-1)]=beta #build left electrode L_left = 2 alpha_left = 0 beta_left = -1 symmetry_left_lead = kwant.TranslationalSymmetry([-1]) left_lead = kwant.Builder(symmetry_left_lead) left_lead[(lat_device(i) for i in range(L_left))]=alpha_left for i in range(L_left): left_lead[lat_device(i),lat_device(i+1)]=beta_left #build right electrode L_right = 2 alpha_right = 0 beta_right = -1 symmetry_right_lead = kwant.TranslationalSymmetry([+1]) right_lead = kwant.Builder(symmetry_right_lead) right_lead[(lat_device(i) for i in range(L_right))]=alpha_right for i in range(L_right): right_lead[lat_device(i),lat_device(i+1)]=beta_right #attach the left electrode to the central device device.attach_lead(left_lead) #attach the right electrode to the central device device.attach_lead(right_lead) #plot the system kwant.plot(device) #finalize the whole system, which consists of left eletrode, device and right electrode device = device.finalized() #eigenvalues and eigevectors of device's Hamiltonian sparse_mat = device.hamiltonian_submatrix(sparse=False) print(np.matrix(sparse_mat)) evs = scipy.sparse.linalg.eigs(sparse_mat,10)[0] print(evs.real) #conductance calculation through transmission matrix energies = [] transmission = [] for ie in range(100): energy = ie * 0.01 smatrix = kwant.smatrix(device, energy) energies.append(energy) transmission.append(smatrix.transmission(1,0)) plt.figure() plt.plot(energies,transmission) plt.xlabel("energy") plt.ylabel("conductance") plt.show()

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