Mailman 3 May 2017 - 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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lead_info
by Prof. CHAN Kwok Sum Sept. 20, 2017

Sept. 20, 2017

Dear Kwant developer, Thank you for your effort in developing Kwant. I have a question about the definition of the direction of momentum in the smatrix.lead_info. Assume a lead lies along the y direction with primitive vector (0,1). The symmetry operation of a lead is (0,1) if the lead goes towards the positive direction and is (0,-1) if the lead goes towards the negative direction. For the momenta contained in smatrix.lead_info for these two leads , do they use the same coordinate system? Positive momenta mean the direction (0,1), negative momenta mean the direction (0,-1). For velocity, in smatrix.lead_info, it has nothing to do with the coordinate system. Positive means outgoing, negative means incoming in the lead. Thank you KS Chan Disclaimer: This email (including any attachments) is for the use of the intended recipient only and may contain confidential information and/or copyright material. If you are not the intended recipient, please notify the sender immediately and delete this email and all copies from your system. Any unauthorized use, disclosure, reproduction, copying, distribution, or other form of unauthorized dissemination of the contents is expressly prohibited.

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reproducing simple analytical solution (chain of atoms)
by Jambulat Basaev June 1, 2017

June 1, 2017

Dear Kwant Community, In my research work I've come to the simple test problem which can be solved both using Kwant and analytically. It's about scattering of the electron wave in the chain of atoms in which hopping integral is t1 for x < 0 and t2 for x > 0. Almost all the solution is in the picture in the attachments. Realization of this analytical solution is presented in testChain.py which plots the dependence on scattering energy of the transmission coefficient |tau|**2 * v2/v1, vj = -2*tj*sin(phi_j) - velocity of the electron. The testChain-kwant.py also plots transmission coefficient versus energy in the same system, but the results are not coincide. So, my question, is it possible to reach the accordance between the solutions in both cases? P.S. Analytical solution seems to be correct, at least |rho|**2 + |tau|**2 * v2/v1 is 1 identically. P.P.S. Is it possible to draw the different hopping kinds with different colors and line styles? It can be useful for controlling errors when building the geometries with hoppings between second-neighbors... Sincerely, Jambulat

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Re: [Kwant] kwant.builder.BuilderLead
by Татьяна Матусевич June 1, 2017

June 1, 2017

Yes, this problem is still relevant. T hank you for your help -- Tatsiana Matusevich

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Re: [Kwant] kwant.builder.BuilderLead
by Татьяна Григоренко May 31, 2017

May 31, 2017

As a lead I want to use the left boundary atoms of graphene (please see attached photo). I use class kwant.builder.BuilderLead(builder, interface). I define a builder in the following way: #The tight-binding system of a left lead. left_lead = kwant.Builder() left_lead[lat(- 90.26501 , 13.2107 )] = 1.5 left_lead[lat(- 91.60269 , 12.67463 )] = 1.5 left_lead[lat(- 91.59045 , 11.58774 )] = 1.5 left_lead[lat(- 90.26237 , 11.08828 )] = 1.5 etc. And add hoppings left_lead[lat(- 91.60269 , 12.67463 ) , lat(- 90.26501 , 13.2107 )] = 2j left_lead[lat(- 91.59045 , 11.58774 ) , lat(- 91.60269 , 12.67463 )] = 2j left_lead[lat(- 90.26237 , 11.08828 ) , lat(- 91.59045 , 11.58774 )] = 2j left_lead[lat(- 90.26083 , 10.04835 ) , lat(- 90.26237 , 11.08828 )] = 2j etc The same way I define the interface (which called left_sequence) but without the hoppings. left_sequence = kwant.Builder() left_sequence[lat(- 88.99753 , 12.6423 )] = 1.5 left_sequence[lat(- 89.0014 , 11.61135 )] = 1.5 left_sequence[lat(- 88.9998 , 9.535691 )] = 1.5 left_sequence[lat(- 89.00571 , 8.504004 )] = 1.5 left_sequence[lat(- 88.99628 , 6.424798 )] = 1.5 etc l_lead = kwant.builder.BuilderLead(left_lead , left_sequence) sys .leads.append(l_lead) kwant.plot(sys) While I try to plot sys I have encountered an error: IndexError: Index 0 out of range (-0 <= index < 0) in dimension 0. I think that this error may appear because I incorrectly pass parameters builder and interface to a class. С уважением, Татьяна Григоренко

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performance of mumps solver and sparse solver.
by Prof. CHAN Kwok Sum May 31, 2017

May 31, 2017

Dear Kwant Develop I have compared the performance of default, mumps solvers in windows and Ubuntu machines. Their performance is very similar without significant gain when using mumps. Do I miss anything in the installation? For example, not installing the mumps. Similar performance is found for the sparse solver. The system I considered has 10^5 to 6X10^5 sites and machine has a quad core i7 cpu with 16G RAM. My installation procedures are those found in the website for pre complled packages. KS Disclaimer: This email (including any attachments) is for the use of the intended recipient only and may contain confidential information and/or copyright material. If you are not the intended recipient, please notify the sender immediately and delete this email and all copies from your system. Any unauthorized use, disclosure, reproduction, copying, distribution, or other form of unauthorized dissemination of the contents is expressly prohibited.

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Problems with tinyarray
by Camilla Espedal May 24, 2017

May 24, 2017

Hi again, I had to reinstall Kwant 1.3 and Tinyarray, but I get the following error message when I try to run a script using conservation_laws (script is included at the end): /usr/local/lib/python3.5/dist-packages/matplotlib-2.0.2+4130.g8ae0dbf-py3.5-linux-x86_64.egg/matplotlib/backends/backend_gtk3agg.py:18: UserWarning: The Gtk3Agg backend is known to not work on Python 3.x with pycairo. Try installing cairocffi. "The Gtk3Agg backend is known to not work on Python 3.x with pycairo. " Traceback (most recent call last): File "/home/camilla/spinHall/Kwant/Tests/spin_kwant13.py", line 45, in <module> syst = make_system(t=1.0, W=10, L=10) File "/home/camilla/spinHall/Kwant/Tests/spin_kwant13.py", line 37, in make_system syst.attach_lead(lead) File "/home/camilla/.local/lib/python3.5/site-packages/kwant/builder.py", line 1402, in attach_lead self.leads.append(BuilderLead(lead_builder, tuple(interface))) File "/home/camilla/.local/lib/python3.5/site-packages/kwant/builder.py", line 566, in __init__ self.interface = tuple(sorted(interface)) TypeError: unorderable types: tinyarray.ndarray_int() < tinyarray.ndarray_int() I used pip to install both kwant and tinyarray, using the commands in the notebook here: http://nbviewer.jupyter.org/url/antonakhmerov.org/misc/spin_conductance.ipy… The versions that pip tells me I have is: Name: kwant Version: 1.3.0a0.dev123+g3961899 Summary: Package for numerical quantum transport calculations (Python 3 version) Home-page: http://kwant-project.org/ Author: C. W. Groth (CEA), M. Wimmer, A. R. Akhmerov, X. Waintal (CEA), and others Author-email: authors(a)kwant-project.org License: BSD Location: /home/camilla/.local/lib/python3.5/site-packages Requires: numpy, scipy, tinyarray Name: tinyarray Version: 1.2.0 Summary: Arrays of numbers for Python, optimized for small sizes Home-page: https://gitlab.kwant-project.org/kwant/tinyarray Author: Christoph Groth (CEA) and others Author-email: christoph.groth(a)cea.fr License: Simplified BSD license Location: /usr/local/lib/python3.5/dist-packages Requires: I got into a similar problem earlier, but then it was because I had the wrong version of tinyarray (not dev), but now I think I have installed it correctly. Can you help me? Best, Camilla

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