Mailman 3 December 2019 - 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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To to separate spins, electron and hole
by Khani Hosein 22 Jun '21

22 Jun '21

Dear all, I am using Kwant to study a system with both spins and electron and hole, so the hopping matrix is 4X4. Now I want to know how to separate the spins, electron and hole. I study this through the "2.6. Superconductors: orbital degrees of freedom, conservation laws and symmetries" smatrix = kwant.smatrix(syst, energy) data.append(smatrix.submatrix((0, 0), (0, 0)).shape[0] -smatrix.transmission((0, 0), (0, 0)) +smatrix.transmission((0, 1), (0, 0))) I do not find more information about this for kwant. For my system, if I have 3 leads, and the hopping and onsite energy is set in this order: (e↑,0,0,0)- spin up electron,first row of the 4X4matrix (0,e↓,0,0)- spin down electron,second row of the 4X4matrix (0,0, h↑ ,0)- spin up hole,third row of the 4X4matrix (0,0, 0, h ↓ )- spin down hole,fourth row of the 4X4matrix I want to obtain the transmissions from 0 →2. smatrix = kwant.smatrix(syst, energy) The transmission from h↑ to e↑ is: smatrix.transmission((2, 1), (0, 2)) The transmission from h ↓ to e↑ is: smatrix.transmission((2, 1), (0, 3)) Is my understanding correct? Thanks very much in advance! Hosein Khani

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Can Kwant calculate density of states of quasi one-dimensional systems?
by Cao Zhan 21 Dec '19

21 Dec '19

Dear Kwant users, In Kwant manual there is a section entitled "Calculating spectral density with the kernel polynomial method". I find that examples in this section are all talking about finite-size systems. I wonder whether Kwant can calculate density of states of a quasi one-dimensional system that is finite along y-direction but is translationally invariant along x-direction. For a minimal test, I have run the following codes but errors occurred. #-------------------------------------------------------------------------------------- import kwant import numpy a=1 W=30 t=1 lat = kwant.lattice.square(a) syst = kwant.Builder(kwant.TranslationalSymmetry((-a, 0))) syst[(lat(0, j) for j in range(W))] = 4 * t syst[lat.neighbors()] = -t fsyst = syst.finalized() energies = numpy.linspace(-0.1,0.1, 10) spectrum = kwant.kpm.SpectralDensity(fsyst) spectrum.add_moments(10) spectrum.add_vectors(5) densities = spectrum(energies) #-------------------------------------------------------------------------------------- What's wrong in above codes? Currently, are we able to employ Kwant to calculate density of states of 3D systems being translationally invariant along one or two directions? Regards, Zhan

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attach lead
by tavakkolidjawad 17 Dec '19

17 Dec '19

Hello everyone I want to create a lead for a 3D structure, but when I run the program, I get the following error: ###No sites close to (0, 0, 14) are inside the desired shape.### Please help me find the mistake. Thanks in advance for your reply. #### import kwant from matplotlib import pyplot lat = kwant.lattice.general([(0, 0.5, 0.5), (0.5, 0, 0.5), (0.5, 0.5, 0)], [(0, 0, 0), (0.25, 0.25, 0.25)], name=['a1', 'a2']) a1, a2 = lat.sublattices def make_cuboid(a=10, b=10, c=15): def cuboid_shape(pos): x, y, z = pos return 0 <= x < a and 0 <= y < b and 0 <= z < c syst = kwant.Builder() syst[a1.shape(cuboid_shape, (0, 0, 0))] = 1 ## the same on-site foar a1 and b1 syst[a2.shape(cuboid_shape, (0, 0, 0))] = 1 syst[lat.neighbors()] = 1 def lead_shape(pos): x,y,z = pos return 0 <= x < a and 0 <= y < b and 14 <= z < c lead = kwant.Builder(kwant.TranslationalSymmetry([1,0,0])) lead[lat.shape(lead_shape, (0, 0, 14))] = 1 lead[lat.neighbors()] = 1 return syst,lead def main(): syst,lead = make_cuboid() kwant.plot(syst) syst = syst.finalized() syst = make_cuboid(a=1.1, b=1.1, c=1.1) def family_colors(site): return 'r' if site.family == a1 else 'g' syst.attach_lead(lead) kwant.plot(syst, site_size=0.18, site_lw=0.01, hop_lw=0.05, site_color=family_colors) if __name__ == '__main__': main() #####

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What is the algorithm for calculating the mode decomposition
by Cao Zhan 16 Dec '19

16 Dec '19

Dear kwant users， In the latest Kwant manual describing the details about kwant.physics.modes, I find a sentence "This function uses the most stable and efficient algorithm for calculating the mode decomposition that the Kwant authors are aware about. Its details are to be published." Do anyone know what the algorithm is? I look forward some references if possible. Regards, Zhan

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Transmission spectrum for a reverse bias
by Paul Anderson 14 Dec '19

14 Dec '19

Hello, I'm trying to study a chain of molecules, say A-B-C-D, each with a unique onsite energy and hopping parameter associated to the adjacent site. Electrodes are connected in the conventional way ...-x-x-x-A-B-C-D-x-x-x.... I would like to produce an I-V curve using Landauer Formula from -1V to +1V. I would think that for negative bias, it would be correct to compute transmission probability from lead 1 to lead 0 (i.e. smatrix.transmission(0,1)) as opposed to lead 0 to lead 1 for the positive bias case. Doing so does not result in any difference in the transmission probability. However, if I reverse the sequence, I do get a different transmission spectrum. Shouldn't a reversed sequence result in the same transmission probability as in switching the direction of measurement lead1 to lead0? Thanks, Paul

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scattering matrix
by simon.flury＠uzh.ch 14 Dec '19

14 Dec '19

Dear kwant users I'm trying to calculate magnetic field dependent conductance of a system. For this I used the scattering matrix and adding temperature dependence by multiplying the transmission value by the derivative of the fermi-dirac function. Because of the results I got, I'm not sure if this is the right way of doing it. Can someone please help me? Thank you very much Best regards Simon Code: fluxes = np.linspace(0, 5, 100) def make_system(a=1, t=1.5, w=15, d=30): lat = kwant.lattice.square(a) syst = kwant.Builder() def onsite(site, U0, salt): return U0 * (uniform(repr(site), repr(salt)) - 0.5) + 4*t syst[(lat(x, y) for x in range(w) for y in range(d))] = onsite def hopping(site_i, site_j, phi): xi, yi = site_i.pos xj, yj = site_j.pos if yi == yj: return -t if xi == xj: return -0.001 * t * exp(-0.5j * phi * (xi + xj) * (yi - yj)) syst[lat.neighbors()] = hopping lead = kwant.Builder(kwant.TranslationalSymmetry((0, -a))) lead[(lat(j, 0) for j in range(w))] = 4 * t lead[lat.neighbors()] = hopping syst.attach_lead(lead) syst.attach_lead(lead.reversed()) return syst def plot_conductance(syst): temp = 0.01 w=15 d=30 U0=0 salt = 0.2 phis = np.linspace(0, (2 * pi / w) * 5, 100) count = 0 values = [] for phi in phis: count += 1 ham_mat = syst.hamiltonian_submatrix(params=dict(phi=phi, U0=U0, salt=salt), sparse=True) evals = np.real(np.sort(np.linalg.eigvals(ham_mat.todense()))) EF = evals[int(len(evals) / 2)] liste = [] for k in range(0,len(evals)): energy = evals[k] if EF-temp <= energy <= EF+temp: df = np.real(exp((energy - EF) / temp) / (temp * (exp((energy - EF) / temp) + 1) ** 2)) Smatrix = kwant.smatrix(syst, energy, params=dict(phi=phi, U0=U0, salt=salt)) liste.append(Smatrix.transmission(0,1)*df) val = sum(liste)/(len(liste)) values.append(val/(w*d)) print(count) plt.plot(fluxes,values, label = w) plt.grid(True) plt.title("Conductance eqhop temp=0.1") plt.legend() plt.ylabel("G_[G_0]") plt.xlabel(r'$\phi [2\pi / L]$') plt.show() def main(): syst = make_system() syst = syst.finalized() plot_conductance(syst) if __name__ == "__main__": main()

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