Mailman 3 September 2018 - 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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Disconnected Quantum Dot Shape for Black Phosphorous
by Shivang Agarwal Sept. 27, 2018

Sept. 27, 2018

Hello All, I am trying to simulate black phosphorous quantum dots of circular shape, but with their ends (that will be attached to the leads) will be broad. The shape would be something like a circle with two thick lines on either side of the circle. I have the following code for it, but the problem I face is that the two thick lines are disconnected from the circle. I am not able to understand the reason behind it and rectify it. If any of you could help me, it would be of great value to me. ------ CODE ------- *import kwant* *from matplotlib import pyplot* *import numpy as np* *h = 2.707 * np.cos(13.69*np.pi/180)* *dx = 4.43* *dy = 3.27* *shift_x = 2.164 * np.cos(0.5*98.15*np.pi/180)* *shift_y = 2.164 * np.sin(0.5*98.15*np.pi/180)* *r_const = 20* *lat0 = kwant.lattice.general([(dx, 0, 0), (0, dy, 0)], [(0, 0, 0), (shift_x, shift_y, 0)])* *lat1 = kwant.lattice.general([(dx, 0, 0), (0, dy, 0)], [(0.5*dx, 0.5*dy, h), (0.5*dx + shift_x, 0.5*dy + shift_y, h)])* *def cuboid_shape(pos):* * x, y, z = pos* * if -1.2*r_const <= x < -r_const:* * return abs(y) < r_const* * if -r_const <= x <= r_const:* * return x**2 + y**2 <= r_const**2* * if r_const < x <= 1.2*r_const:* * return abs(y) < r_const* *def potential(site):* * x, y, z = site.pos* * return (-tanh(5*(x-r_const)) - tanh(5*(x+r_const))) * pot* *sys = kwant.Builder()* *sys[lat0.shape(cuboid_shape, (0, 0, 0))] = potential* *sys[lat0.neighbors(1)] = 1* *sys[lat0.neighbors(2)] = 1* *sys[lat1.shape(cuboid_shape, (0.5*dx, 0.5*dy, h))] = potential* *sys[lat1.neighbors(1)] = 1* *sys[lat1.neighbors(2)] = 1* *lat0_0 = [ ]* *lat0_1 = [ ]* *lat1_0 = [ ]* *lat1_1 = [ ]* *for site in kwant.Builder.sites(sys):* * if site.family == lat0.sublattices[0]:* * lat0_0.append(site[1])* * elif site.family == lat0.sublattices[1]:* * lat0_1.append(site[1])* * elif site.family == lat1.sublattices[0]:* * lat1_0.append(site[1])* * elif site.family == lat1.sublattices[1]:* * lat1_1.append(site[1])* *for w in lat0_0:* * for v in lat0_1:* * for k in lat1_0:* * for l in lat1_1:* * if v == k:* * sys[lat0.sublattices[1](v[0],v[1]), lat1.sublattices[0](k[0],k[1])] = 2* * if w == l:* * if (w[0]+1,w[1]+1) in lat0_0:* * sys[lat0.sublattices[0](w[0]+1,w[1]+1), lat1.sublattices[1](l[0],l[1])] = 2* * if w == l:* * if (l[0]-1,l[1]-1) in lat1_1:* * sys[lat0.sublattices[0](w[0],w[1]), lat1.sublattices[1](l[0]-1,l[1]-1)] = 2* *kwant.plot(sys, site_size=0.2, hop_lw=0.1)* Any help would be greatly appreciated. Regards, Shivang Agarwal -- *Shivang Agarwal* Senior Undergraduate Coordinator - Academic Discussion Hours Discipline of Electrical Engineering IIT Gandhinagar Contact: +91-9869321451

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Problem in installing Kwant
by Sadeq Bahmani Sept. 20, 2018

Sept. 20, 2018

Hi. Im trying to install kwant on Anaconda 3. The install page said the package is in the conda-forge but it is not there. You can look at this list of package in the conda-forge. Package repository for conda-forge :: Anaconda Cloud | | | | Package repository for conda-forge :: Anaconda Cloud | | | As you can see there is no package by name kwant. Thank you.

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Onsite and hopping values in QHE
by elchatz＠auth.gr Sept. 15, 2018

Sept. 15, 2018

Hello everyone, I am trying to reproduce the QHE bar device calculations http://nbviewer.jupyter.org/github/topocm/topocm_content/blob/master/w3_pum… However, I am having difficulty with the onsite and hopping values as I am using TBModels https://github.com/Z2PackDev/TBmodels and therefore the values are not the same for all sites. The problem is that after the scalar values have been passed on to the Builder, these will then be overriden when using functions for the position-dependent Hamiltonian. I tried making a deep copy of the model, which would then serve as a data structure where to draw the scalar values from when calling the Onsite and Hopping functions. The problem with this is a) I am getting a KeyError which I am still not sure why it happens b) It does not feel very memory-efficient. I am wondering if there is another way that this could be done on the Kwant side that I have not been able to think of. Regards -- Dr. Eleni Chatzikyriakou Computational Physics lab Aristotle University of Thessaloniki elchatz(a)auth.gr - tel:+30 2310 998109

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Error: Hopping from site 407 to site 814 does not match the dimensions of onsite Hamiltonians of these sites
by Sergio Castillo Robles Sept. 7, 2018

Sept. 7, 2018

Hello everyone, i would appreciate any suggestion you could give me to solve this Im trying to plot the conductance for a two dimensional array of 3 basis atoms, i have defined the atoms positions, the onsite energies and hoppings matrices and the leads but it is showing me this error: (i search in the mailing list but theres no info about it) ValueError Traceback (most recent call last)<ipython-input-1-ee484ce5ea50> in <module>() 111 112 if __name__ == '__main__':--> 113 main() <ipython-input-1-ee484ce5ea50> in main() 107 site_color=family_colors) 108 syst = syst.finalized()--> 109 plot_conductance(syst, energies=[0.01 * i - 0.3 for i in range(100)]) 110 111 <ipython-input-1-ee484ce5ea50> in plot_conductance(syst, energies) 85 data = [] 86 for energy in energies:---> 87 smatrix = kwant.smatrix(syst, energy) 88 data.append(smatrix.transmission(1, 0)) 89 pyplot.figure() ~/anaconda3/lib/python3.6/site-packages/kwant/solvers/common.py in smatrix(self, sys, energy, args, out_leads, in_leads, check_hermiticity, params) 370 linsys, lead_info = self._make_linear_sys(syst, in_leads, energy, args, 371 check_hermiticity, False,--> 372 params=params) 373 374 kept_vars = np.concatenate([coords for i, coords in ~/anaconda3/lib/python3.6/site-packages/kwant/solvers/common.py in _make_linear_sys(self, sys, in_leads, energy, args, check_hermiticity, realspace, params) 162 lhs, norb = syst.hamiltonian_submatrix(args, sparse=True, 163 return_norb=True,--> 164 params=params)[:2] 165 lhs = getattr(lhs, 'to' + self.lhsformat)() 166 lhs = lhs - energy * sp.identity(lhs.shape[0], format=self.lhsformat) kwant/_system.pyx in kwant._system.hamiltonian_submatrix() kwant/_system.pyx in kwant._system.make_sparse_full() ValueError: Hopping from site 407 to site 814 does not match the dimensions of onsite Hamiltonians of these sites. Here is the code so far: import kwant import tinyarray import numpy from matplotlib import pyplot %matplotlib notebook VecPrim = [(3.176, 0, 0), (1.588, 2.7504, 0), (0, 0, 17.49)] base = [(0, 0, 0), (1.588, 0.9168, 0.8745), (0, 0, 1.749)] lat = kwant.lattice.general(prim_vecs=VecPrim, basis=base) c1, c2, c3 = lat.sublattices c1_ons = numpy.array([[-1.888842, -0.014064-0.000409j, 0.026908+0.003422j], [-0.014064+0.000409j, -1.784936, -0.031384+0.021565j], [0.026908-0.003422j, -0.031384-0.021565j, 0.710443]]) c2_ons = numpy.array([[7.168134, -0.005189-0.047376j, 0.001352+0.000103j, -0.001189-0.00095j, -0.048166-0.007663j, 0.429882+0.00052j], [-0.005189+0.047376j, 0.245358, 0.113162-0.072937j, 0.660849-0.06348j, -0.017571+0.035587j, 0.020961-0.017679j], [0.001352-0.000103j, 0.113162+0.072937j, 1.338059, -0.003126-0.016285j, -0.624702-0.065652j, 0.002353+0.001639j], [-0.001189+0.00095j, 0.660849+0.06348j, -0.003126+0.016285j, 1.325337, 0.110694+0.01548j, 0.009041+0.004483j], [-0.048166+0.007663j, -0.017571-0.035587j, -0.624702+0.065652j, 0.110694-0.01548j, 0.362102, -0.030934+0.002401j], [0.429882-0.00052j, 0.020961+0.017679j, 0.002353-0.001639j, 0.009041-0.004483j, -0.030934-0.002401j, -0.650839]]) c3_ons = numpy.array([[-3.398186, 0.001839+0.001631j, -0.117366+0.00498j], [0.001839-0.001631j, -3.401815, 0.023339+0.009067j], [-0.117366-0.00498j, 0.023339-0.009067j, -0.637207]]) c1_c3_hop = numpy.array([[-1.852931-0.147524j, -0.274338+0.015064j, -0.103127-0.001438j], [0.274586+0.034451j, -1.796449+0.055331j, 0.004816+0.00237j], [-0.015051+0.001677j, -0.034396-0.019407j, 3.410475-0.001248j]]) c1_c2_hop = numpy.array([[0.003644-0.00088j, -0.046131-0.04229j, 0.23188-0.001924j], [-0.305706+0.050514j, -1.963829+0.280977j, -0.597505+0.078772j], [0.638425+0.083597j, -1.171301+0.088146j, -0.146976+0.012943j], [-1.105645-0.086829j, -1.112788+0.056971j, -0.210584-0.002248j], [1.463462+0.012994j, 0.174769-0.106872j, 0.177022-0.031485j], [-0.01338+0.00264j, -0.058159+0.007987j, 0.953363+0.001855j]]) c2_c3_hop = numpy.array([[0.184152+0.002778j, 0.321743-0.010571j, 0.183538-0.00067j], [0.275145+0.007691j, -0.54144+0.012815j, 0.045847+0.015379j], [0.47922+0.015775j, 1.256012+0.007326j, -0.523174+0.00585j], [1.255561-0.002255j, 1.903063+0.010647j, -0.876392+0.010246j], [1.282837-0.091022j, -0.54898+0.001161j, 0.057341-0.004095j], [0.02765-0.001793j, -0.002902-0.001866j, -0.746426-0.000748j]]) def make_cuboid(t=1.0, a=15, b=10, c=5): def cuboid_shape(pos): x, y, z = pos return 0 <= x < a and 0 <= y < b and 0 <= z < c syst = kwant.Builder() syst[c1.shape(cuboid_shape, (0, 0, 0))] = c1_ons syst[c2.shape(cuboid_shape, (0, 1, 0))] = c2_ons syst[c3.shape(cuboid_shape, (0, 0, 1))] = c3_ons syst[kwant.builder.HoppingKind((0, 0, 0), c2, c1)] = c1_c2_hop syst[kwant.builder.HoppingKind((-1, 0, 0), c2, c1)] = c1_c2_hop syst[kwant.builder.HoppingKind((0, -1, 0), c2, c1)] = c1_c2_hop syst[kwant.builder.HoppingKind((0, 0, 0), c3, c2)] = c2_c3_hop syst[kwant.builder.HoppingKind((1, 0, 0), c3, c2)] = c2_c3_hop syst[kwant.builder.HoppingKind((0, 1, 0), c3, c2)] = c2_c3_hop lead = kwant.Builder(kwant.TranslationalSymmetry((-3.176, 0, 0))) lead[c1.shape(cuboid_shape, (0, 0, 0))] = c1_ons lead[c2.shape(cuboid_shape, (0, 1, 0))] = c2_ons lead[c3.shape(cuboid_shape, (0, 0, 1))] = c3_ons lead[kwant.builder.HoppingKind((0, 0, 0), c2, c1)] = c1_c2_hop lead[kwant.builder.HoppingKind((-1, 0, 0), c2, c1)] = c1_c2_hop lead[kwant.builder.HoppingKind((0, -1, 0), c2, c1)] = c1_c2_hop lead[kwant.builder.HoppingKind((0, 0, 0), c3, c2)] = c2_c3_hop lead[kwant.builder.HoppingKind((1, 0, 0), c3, c2)] = c2_c3_hop lead[kwant.builder.HoppingKind((0, 1, 0), c3, c2)] = c2_c3_hop syst.attach_lead(lead) syst.attach_lead(lead.reversed()) return syst def plot_conductance(syst, energies): data = [] for energy in energies: smatrix = kwant.smatrix(syst, energy) data.append(smatrix.transmission(1, 0)) pyplot.figure() pyplot.plot(energies, data) pyplot.xlabel("energy [t]") pyplot.ylabel("conductance [e^2/h]") pyplot.show() def main(): syst = make_cuboid() kwant.plot(syst) syst = make_cuboid(a=100, b=28, c=4) def family_colors(site): if site.family == c1: return 'yellow' elif site.family == c2: return 'gray' else: return 'blue' kwant.plot(syst, site_size=0.05, site_lw=0.01, hop_lw=0.01, site_color=family_colors) syst = syst.finalized() plot_conductance(syst, energies=[0.01 * i - 0.3 for i in range(100)]) if __name__ == '__main__': main()

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A question about setting different hopping energies in different regions
by kuangyia lee Sept. 5, 2018

Sept. 5, 2018

Dear Developers and Users of Kwant, I have been using Kwant for quantum transport calculations. Recently, I came across a bit complicated model problem, which can be described as follows: Suppose I have two scattering regions (S1 and S2) which are defined with two shape functions (shape_function_1 and shape_function_2) and connected with their interface. So I am wondering a feasible way to implement different hoppings in regions S1 and S2. And after that, how to deal with the hoppings across the interface? I also see Prof. Christoph Groth already giving some solutions on the relevant issue, see here: https://mailman-mail5.webfaction.com/pipermail/kwant-discuss/2016-November/…. <https://mailman-mail5.webfaction.com/pipermail/kwant-discuss/2016-November/…> However, these solutions are still not clear to me. Can you help solve my problem? Your help is greatly appreciated. Best regards, Kuangyia Lee

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Query regarding C-C bond length in honeycomb lattice wref. to Kwant Documentation
by Arunabha Ghoshal Sept. 5, 2018

Sept. 5, 2018

Dear Kwant Developers, I am a graduate student learning Kwant for my academics project related purposes. With reference to the Kwant 1.3.1 Documentation (vide page no.45), the honeycomb lattice for the zig-zag edged graphene has been defined as: > graphene = kwant.lattice.general([(1, 0), (sin_30, cos_30)], [(0, 0), (0, 1 / sqrt(3))]) where, as per my understanding, the first argument to the *general* function is the list of *primitive vectors* of the lattice; the second one is the *coordinates of basis atoms*. According to the physics of graphene, the carbon-carbon bond length is approximately 0.142 nm. But after running the above code, I checked that the C-C bond length of the honeycomb lattice is coming as 1/sqrt(3) nm i.e. ~0.58 nm. Therefore, I am feeling quite confused as I am failing to understand where I am going wrong or whether am overlooking any fundamental concepts. I had also raised my query earlier here, regarding defining the lattice for armchair edged graphene (vide Volume 59, Issue 6), but it seems that unfortunately it has missed your notice. So my understandings on this specific domain are still quite hazy. It would be of great help if you look into the matter and kindly guide me to find solution for the above mentioned queries. Thanks Regards Arunabha Ghoshal

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