Mailman 3 May 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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Infinite Slab and wraparound
by Bogusz Bujnowski June 17, 2019

June 17, 2019

Dear everyone, I would like to solve the 3D Schrödinger equation with a 1D potential step. With the material in the mailing list as well as from the tutorial the 2D case works fine. Extending to 3D gives the same when just taking one lattice site in the z direction (H>1). Increasing the hight of the slab (H>1) changes the minimal energy for which transmission is possible thus my code is wrong. Did I define and attach the leads correctly with the wraparound in 3D? The short code is below. Thank you for any hint! Best, B import numpy as np import matplotlib.pyplot as plt import scipy as sp from numpy import * import kwant import sys #calculate the conductance for a sheet (Dim=2) or a Slab (Dim=3) that is translational invariant in y direction a = 1.0 #lattice constant V0 = 0.2 #potential step size L = 2 #Length x-direction the length is a bit useless in this code W = 6 #Width y-direction H = 6 #Hight z-direction t = 1 #hopping parameter Dim=3 #dimension of the system # for H=1, Dim=2 # for H>1, Dim=3 #params for integration and plotting Nky=100 #points in ky space NE=25 #points in energy lat = kwant.lattice.cubic(a) # Define the scattering region # Infinite potential plane/Slab in y direction sys = kwant.Builder(kwant.TranslationalSymmetry(lat.vec((0, W, 0)))) for i in range(L): for j in range(W): for k in range(H): # On-site Hamiltonian sys[lat(i, j, k)] = 2*Dim * t + heaviside(i,0)*V0 #potential step located at the center between the leads sys[lat.neighbors(1)] = -t sys = kwant.wraparound.wraparound(sys) #Left lead leadL = kwant.Builder(kwant.TranslationalSymmetry((-a, 0, 0), lat.vec((0, W, 0)))) #trans inv in transport dir and ky leadL[(lat(0,j,k) for j in range(W) for k in range(H))] = 2*Dim*t #onsite terms in the left lead leadL[lat.neighbors(1)] = -t #Right lead leadR = kwant.Builder(kwant.TranslationalSymmetry(( a, 0, 0), lat.vec((0, W, 0)))) leadR[(lat(0,j,k) for j in range(W) for k in range(H))] = 2*Dim*t+V0 #onsite terms in the right lead leadR[lat.neighbors(1)] = -t leadL = kwant.wraparound.wraparound(leadL, keep=0) #keeping the translational invariance in x direction leadR = kwant.wraparound.wraparound(leadR, keep=0) sys.attach_lead(leadL) sys.attach_lead(leadR) kwant.plot(sys) sys = sys.finalized() # Calculation of the total transmission for a given Energy ky_array = np.linspace(-pi,pi,Nky) dky=ky_array[1]-ky_array[0] energies = np.linspace(0.0, 1.0,NE) Ttot=[] for energy in energies: Tky_array=zeros(Nky) for i in arange(len(ky_array)): ky=ky_array[i] smatrix = kwant.smatrix(sys, energy, [ky]) Tky_array[i]=smatrix.transmission(1, 0) Ttot.append((2*pi)/(W)*(sum(Tky_array)-0.5*Tky_array[0]-0.5*Tky_array[Nky-1])*dky) #cheap trapezodial rule to integrate over ky # Plot transmission plt.plot(energies, Ttot) plt.show()

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Changing Hamiltonian after finalized()
by Pavlo Bulanchuk May 24, 2019

May 24, 2019

Dear Kwant developers, I am trying to calculate conductance of a system with disorder at different chemical potentials. The geometry is constant, so I want to finalize() only once. The question:how do I change onsite potential after finalization? There is an example from the manual with conductance through a well of variable depth, but if I do it that way, I would generate new onsite potential every time I change chemical potential, which I would like to avoid. Thank you, Pavlo

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bug in the installation of kwant (linux mint)
by Victor Fernandez Becerra May 23, 2019

May 23, 2019

Dear Kwant developers I am having problems with the installation of kwant in linux mint 19.1 I tried to installed the pre-build package of kwant on my computer but I faced problems with the dependencies. This is what I did: 1. Inserted the lines below in the sources.list file located in /etc/apt/ deb [trusted=yes] http://ftp.debian.org/debian stretch-backports main deb [trusted=yes] http://downloads.kwant-project.org/debian/ stretch-backports main deb-src [trusted=yes] http://downloads.kwant-project.org/debian/ stretch-backports main 2. Executed the commands below as superuser apt-get update apt-get -t stretch-backports install python3-kwant python-kwant-doc and this was the output The following packages have unmet dependencies: python3-kwant : Depends: python3 (< 3.6) but 3.6.7-1~18.04 is to be installed Depends: libmumps-4.10.0 but it is not installable Depends: libmumps-scotch-4.10.0 but it is not installable E: Unable to correct problems, you have held broken packages. Since the pre-build package option did not work, I decided to try to build the package from source. This is what I did: 1. Move to the /tmp folder 2. Executed successfully the command, apt-get build-dep tinyarray kwant 3. Executed successfully the command, apt-get source --compile tinyarray 3. Had a problem with the command apt-get source --compile kwant, that showed me the following error There is a programable error in your configuration file: Traceback (most recent call last): File "/tmp/kwant-1.4.0/debian/python3-kwant/usr/lib/python3.6/dist-packages/kwant/qsymm.py", line 21, in <module> import qsymm ModuleNotFoundError: No module named 'qsymm' The above exception was the direct cause of the following exception: Traceback (most recent call last): File "/usr/lib/python3/dist-packages/sphinx/config.py", line 157, in __init__ execfile_(filename, config) File "/usr/lib/python3/dist-packages/sphinx/util/pycompat.py", line 150, in execfile_ exec_(code, _globals) File "conf.py", line 22, in <module> import kwant.qsymm File "/tmp/kwant-1.4.0/debian/python3-kwant/usr/lib/python3.6/dist-packages/kwant/qsymm.py", line 30, in <module> raise ImportError(msg) from error ImportError: 'kwant.qsymm' is not available because one or more of its dependencies is not installed. Makefile:72: recipe for target 'html' failed make[2]: *** [html] Error 1 make[2]: Leaving directory '/tmp/kwant-1.4.0/doc' debian/rules:25: recipe for target 'override_dh_installdocs' failed make[1]: *** [override_dh_installdocs] Error 2 make[1]: Leaving directory '/tmp/kwant-1.4.0' debian/rules:7: recipe for target 'binary' failed make: *** [binary] Error 2 dpkg-buildpackage: error: fakeroot debian/rules binary subprocess returned exit status 2 E: Build command 'cd kwant-1.4.0 && dpkg-buildpackage -b -uc' failed. I tried to install separately the module qsymm but I couldn't. The instruction pip install qsymm did not work. Kind regards, Leo

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Kwant 1.4.1 has been released
by Christoph Groth May 23, 2019

May 23, 2019

Kwant 1.4.1 has been released recently. By now the new version should be available on all usual channels. This maintenance release does not introduce any new functionality, but fixes some backwards compatibility issues that were introduced by 1.4.0. Most notably, Kwant 1.4.1 is more tolerant to scripts that use the now deprecated "args" mechanism of passing parameters. For example, value functions may continue to accept *args or **kwargs as long as the new "params" parameter-passing mechanism is not used. Please see the "what's new" document [1] for a detailed list of changes. [1] https://kwant-project.org/doc/1/pre/whatsnew/1.4#changes-in-kwant-1-4-1

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honycomb lattice with hole
by nafise.nour＠sci.ui.ac.ir May 20, 2019

May 20, 2019

Dear all, I’m new in kwant and I want to use this package to calculate transport properties of some graphene-liked materials with multi orbital per atom. In order to define hopping in the form of matrix, we need to determine the relative coordinate of neighbor sites. If we build the system using latt = kwant.lattice.honeycomb Could anyone help me to show how can I make a hole on the center of main region and leadS (I would like to make a graphene nanoribbon which have holes)?like in attached fiqure. Please find attached file. Best, Nafise

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build polyatomic model with different orbital number on each site
by Zang, Hang May 19, 2019

May 19, 2019

Dear Kwant developers, I am a new user of Kwant, and I want to build a polyatomic model by directly loading the coordinate and Hamiltonian file. Since each atom site could have more than one orbital (like s, px, py, pz ..), and different kind of atom sites could have a different number of orbitals. Can I just assign the Hamiltonian for each atom by just giving the exact coordinates? For example, for a model system: H 0.0 0.0 0.0 C 2.0 0.0 0.0 C 8.0 0.0 0.0 with the basis function H(H-1s) C(C-2s,C-2px,C-2py, C-2pz), and I set the "family" of the atomic site first, basis[0] -> H-1s basis[1] -> C-2s basis[2] -> C-2px basis[3] -> C-2py basis[4] -> C-2pz and then I set the onsite energy and offsite coupling for each atom by directly assign the atomic coordinate, i.e. for the 2nd C atom, I use the "family" of basis[1] basis[2] basis[3] basis[4] with the coordinate tag to be '2.0 , 0.0 , 0.0'. Enclosed please find my simple kwant script. Thanks in advance for your help. Hang Zang ================================================================================== import kwant import numpy as np import scipy primitive_vectors = [ (1.0,0.0,0.0), (0.0,1.0,0.0), (0.0,0.0,1.0) ] #coordinates of all atoms # H-1s, C-2s, C-2px, C-3py, C-4pz # index 0 1 2 3 4 basis_sites = [(0.0,0.0,0.0), (0.0,0.0,0.0), (0.0,0.0,0.0), (0.0,0.0,0.0), (0.0,0.0,0.0)] lat = kwant.lattice.Polyatomic(primitive_vectors, basis_sites) syst = kwant.Builder() basis = lat.sublattices #onsite energies, or the diagonal terms of the Hamiltonian matrix syst[basis[0](0.0 , 0.0 , 0.0)] = 1.0 # for H1 at 0.0 0.0 0.0 syst[basis[1](2.0 , 0.0 , 0.0)] = 1.0 # for C1 at 2.0 0.0 0.0 syst[basis[2](2.0 , 0.0 , 0.0)] = 1.0 # for C1 at 2.0 0.0 0.0 syst[basis[3](2.0 , 0.0 , 0.0)] = 1.0 # for C1 at 2.0 0.0 0.0 syst[basis[4](2.0 , 0.0 , 0.0)] = 1.0 # for C1 at 2.0 0.0 0.0 syst[basis[1](8.0 , 0.0 , 0.0)] = 1.0 # for C2 at 8.0 0.0 0.0 syst[basis[2](8.0 , 0.0 , 0.0)] = 1.0 # for C2 at 8.0 0.0 0.0 syst[basis[3](8.0 , 0.0 , 0.0)] = 1.0 # for C2 at 8.0 0.0 0.0 syst[basis[4](8.0 , 0.0 , 0.0)] = 1.0 # for C2 at 8.0 0.0 0.0 #off-site copling, or the off-diagonal terms of the Hamiltonian matrix syst[basis[0](0.0 , 0.0 , 0.0) , basis[1](2.0 , 0.0 , 0.0)] = -2.0 syst[basis[0](0.0 , 0.0 , 0.0) , basis[2](2.0 , 0.0 , 0.0)] = -2.0 syst[basis[0](0.0 , 0.0 , 0.0) , basis[3](2.0 , 0.0 , 0.0)] = -2.0 syst[basis[0](0.0 , 0.0 , 0.0) , basis[4](2.0 , 0.0 , 0.0)] = -2.0 syst[basis[0](0.0 , 0.0 , 0.0) , basis[1](8.0 , 0.0 , 0.0)] = -4.0 syst[basis[0](0.0 , 0.0 , 0.0) , basis[2](8.0 , 0.0 , 0.0)] = -4.0 syst[basis[0](0.0 , 0.0 , 0.0) , basis[3](8.0 , 0.0 , 0.0)] = -4.0 syst[basis[0](0.0 , 0.0 , 0.0) , basis[4](8.0 , 0.0 , 0.0)] = -4.0 kwant.plot(syst) syst = builder.finalized() sparse_mat = syst.hamiltonian_submatrix(sparse=False) print(np.matrix(sparse_mat)) evs = scipy.sparse.linalg.eigs(sparse_mat,3)[0] print(evs.real) ===============================================================================

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