Mailman 3 November 2018 - Kwant-discuss

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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Wave function of nanoribbon
by kuangyia lee 29 Nov '18

29 Nov '18

Dear all, I made the following snippets to build the structure of zigzag graphene nanoribbon (basically an infinite zigzag lead) and to calculate its band structure. As expected, everything is correct. ### import numpy as np import kwant from math import pi, sqrt import matplotlib.pyplot as plt def make_lead(r): # r is ribbon width 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 hoppings = (((0, 0), a, b), ((0, 1), a, b), ((-1, 1), a, b)) sym = kwant.TranslationalSymmetry(graphene.vec((-1, 0))) def lead_shape(pos): x, y = pos return (-0.5 * r < y < 0.5 * r) lead = kwant.Builder(sym) lead[graphene.shape(lead_shape, (0, 0))] = 0 lead[[kwant.builder.HoppingKind(*hopping) for hopping in hoppings]] = -1 return lead def main(): lead = make_lead(r=10) # r is ribbon width lead = lead.finalized() kwant.plotter.bands(lead, show=False) plt.xlim(-pi, pi) plt.ylim(-2, 2) plt.xlabel("$ka$") plt.ylabel("$E$ [eV]") plt.show() if __name__ == '__main__': main() ### *Now my concern is how to calculate and plot the wave function of the n^th eigenmode at a given wave vector (e.g. k=0) for this nanoribbon with KWANT. *I tried to search the relevant issues through different resources like tutorial and forum but none of these give useful insights. Can someone help to figure out this problem? Thanks and regards, Kuangyia

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Change conductance step units
by Joseph Weston 28 Nov '18

28 Nov '18

The message below was originall from Sergio Castillo. For some reason neither I nor several other Kwant developers received this message from the mailing list, so I'm reposting it here. > Hello everyone, I would appreciate any suggestion you could give me to > solve this: > > Im trying to plot the conductance for a two dimensional material, > however, I want the y-axis to show conductance in (2e^2/h) units > instead of (e^2/h) units that are shown by default as in the examples. > It could be something obvious but I can't figure it out how to plot > the data in that units > > Thanks in advance. Hi Sergio, You can divide your conductance by 2, that will change the units from (e^2/h) to (2e^2/h) Happy Kwanting, Joe

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How to plot the lead band of non hermitian Hamiltonian with Kwant
by luoxunjiang＠hust.edu.cn 28 Nov '18

28 Nov '18

Dear professor, Have a good day! I am xunjiang Luo, a chinese students coming from Huazhong University of Science and Technology in Wuhan. I am sorry to disturb you and I want to ask some questions. In the kwant, I want to plot the lead band of non hermitian Hamiltonian and I just add some imaginary terms to the onsite term. However, the error "The cell Hamiltonian is not Hermitian" will appear. How can I solve the problem? I am looking forward for your reply and I would appreciate it if you could contact me. luoxunjiang(a)hust.edu.cn

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Change conductance step units
by Sergio Castillo Robles 26 Nov '18

26 Nov '18

Hello everyone, I would appreciate any suggestion you could give me to solve this: Im trying to plot the conductance for a two dimensional material, however, I want the y-axis to show conductance in (2e^2/h) units instead of (e^2/h) units that are shown by default as in the examples. It could be something obvious but I can't figure it out how to plot the data in that units Thanks in advance.

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Error visualizing the zigzag graphene lattice using kwant.plot() in tutorial
by Srilok Srinivasan 20 Nov '18

20 Nov '18

Hello Kwant users, I am very new to kwant and I am still learning to use the code. So my apologizes for any trivial questions. I working on the tutorial notebooks I found in the here ( https://kwant-project.org/mm16). In the tutorial 3.4.graphene_qshe.ipynb I am trying to visualize the zigzag graphene lattice created using the kwant.Builder and .shape() module using kwant.plot(*sys*). I am getting the following error zigzag_ribbon = kwant.Builder(kwant.TranslationalSymmetry([1, 0])) #zigzag_ribbon[graphene.shape((lambda pos: abs(pos[1]) < 9 and pos[1]%2 ==1), (0, 0))] = 0.2 #zigzag_ribbon[graphene.shape((lambda pos: abs(pos[1]) < 9 and pos[1]%2 ==0), (0, 0))] = -0.2 zigzag_ribbon[graphene.shape((lambda pos: abs(pos[1]) < 9), (0, 0))] = 0 zigzag_ribbon[graphene.neighbors(1)] = 1 zigzag_ribbon.finalized() kwant.plotter.plot(zigzag_ribbon) #kwant.plotter.bands(zigzag_ribbon.finalized()); ---------------------------------------------------------------------------KeyError Traceback (most recent call last)<ipython-input-84-0b886d56dec5> in <module> 5 zigzag_ribbon[graphene.neighbors(1)] = 1 6 zigzag_ribbon.finalized()----> 7 kwant.plotter.plot(zigzag_ribbon) 8 #kwant.plotter.bands(zigzag_ribbon.finalized()); ~/anaconda3/lib/python3.6/site-packages/kwant/plotter.py in plot(sys, num_lead_cells, unit, site_symbol, site_size, site_color, site_edgecolor, site_lw, hop_color, hop_lw, lead_site_symbol, lead_site_size, lead_color, lead_site_edgecolor, lead_site_lw, lead_hop_lw, pos_transform, cmap, colorbar, file, show, dpi, fig_size, ax) 962 963 site_size = make_proper_site_spec(site_size, fancy_indexing)--> 964 site_color = make_proper_site_spec(site_color, fancy_indexing) 965 site_edgecolor = make_proper_site_spec(site_edgecolor, fancy_indexing) 966 site_lw = make_proper_site_spec(site_lw, fancy_indexing) ~/anaconda3/lib/python3.6/site-packages/kwant/plotter.py in make_proper_site_spec(spec, fancy_indexing) 907 def make_proper_site_spec(spec, fancy_indexing=False): 908 if callable(spec):--> 909 spec = [spec(i[0]) for i in sites if i[1] is None] 910 if (fancy_indexing and _p.isarray(spec) 911 and not isinstance(spec, np.ndarray)): ~/anaconda3/lib/python3.6/site-packages/kwant/plotter.py in <listcomp>(.0) 907 def make_proper_site_spec(spec, fancy_indexing=False): 908 if callable(spec):--> 909 spec = [spec(i[0]) for i in sites if i[1] is None] 910 if (fancy_indexing and _p.isarray(spec) 911 and not isinstance(spec, np.ndarray)): ~/anaconda3/lib/python3.6/site-packages/kwant/plotter.py in site_color(site) 956 color_mapping = dict(zip(families, cycle)) 957 def site_color(site):--> 958 return color_mapping[site.family] 959 else: 960 # Unknown finalized system, no sites access. KeyError: kwant.lattice.Monatomic([[1.0, 0.0], [0.5, 0.8660254037844386]], [0.0, 0.5773502691896258], '1', None) However, I am able to plot the dispersion and all that. Also, I am able to visualize the square lattice presented in other tutorials. Do we have to do something different to visualize non-square lattice ? Thanks for your help -- Srilok Srinivasan Graduate Student Mechanical Engineering Iowa State University, Ames, IA

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Fixing min and max values of colormap using kwant.plot
by Shivang Agarwal 19 Nov '18

19 Nov '18

Dear All, I am using the kwant.plot and kwant.wavefunction functions to plot the wavefunction's sqaured amplitude on the system. For my work, I need to compare such plots on two different systems. It is tough to compare the values as the max and min is not defined on the colorbar. For example, if system 1 has a max value of 0.9 it will be shown as yellow. However, if system 2 has a max value of 2.4 it will also be shown as yellow because the max value gets automatically assigned to the top of the colorbar (inferno in this case). Would it be possible to assign the max of the colorbar to a fixed number, say 5, for all plots. That way the value 5 will be yellow and 2.4 could be orange while 0.9 could be blue - leading to easier comparison between plots of seen side by side. Any help would be greatly appreciated. Thanks and best regards, Shivang Agarwal -- *Shivang Agarwal* Senior Undergraduate Coordinator - Academic Discussion Hours Discipline of Electrical Engineering IIT Gandhinagar Contact: +91-9869321451

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