Mailman 3 October 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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making systems with translational symmetry perpendicular to the direction of transport
by Maurer, Leon Dec. 13, 2017

Dec. 13, 2017

Hi all, This is a follow up to my post yesterday (where I put a Si tight binding model into Kwant). My goal is to create a 3D system with translational symmetries in a plane so that I can look at transport perpendicular to that (infinite) plane. So, there wouldn’t be a translational symmetry in the direction of transport, but there will be translational symmetry in the two dimensions perpendicular to transport. It’s a little difficult to explain how I’m trying to do this, but hopefully the below explanation mostly conveys the idea. The attached jupyter notebook uses a standard Si primitive cell as the unit cell, and for simplicity, I’ve chosen the axis of the system to be along the first Si primitive vector as defined in the code (1/2, 1/2, 0). There is translational symmetry along the other two primitive vectors (set in “In [5]” of the notebook). Everything seems to work basically as expected. The axis of the system does lie along the first Si primitive vector; I can attach leads with the same symmetries; and the leads have the right band structure: the band structure down the axis of the leads is the band structure between the gamma and L points (calculated in “In [8]”– compare with the full band structure in “In [10]”). I could calculate the transmission down the axis of the structure with something like kwant.smatrix(syst, energy, args=(0,0)).transmission(1, 0), which isn’t shown in the notebook. (I’d also be putting different potentials in the different sites so that the structure isn’t uniform. There’s not much point calculating transport thru the system in the notebook.) Two questions: 1. Can I calculate transport in other directions --- such as the (1,0,0) direction --- using this system? 2. The primitive lattice vectors are not orthogonal, so I don’t really have translational symmetry perpendicular to the axis of the system. Does anyone have an idea for how to fix that? I could create a (larger) non-primitive unit cell with orthogonal primitive vectors by having a bunch of basis vectors (that sounds weird, but I think that the terminology is right), but I like having my unit cell be simple. (I have tried effectively building a larger unit cell from the primitive cells, but I’ve run into problems – a topic for a different email.) -Leon

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Defining hopping in 3D structure with 3 basis atoms
by Sergio Castillo Robles Nov. 8, 2017

Nov. 8, 2017

Hello everyone, i would appreciate any help you could give me to solve this issue. Well, the problem is that i cant find a way to properly show the desired hopppings in this structure, as you could see i've tried usign the lat.neighbors() function showing me wrong hoppings and the HoppingKind function sending a error msg listed below. The hoppings im trying to define are the ones joining the central atom with the 3 nearest neighbors in the top layer and the 3 nearest neighbors in the bottom layer. Im pretty new using kwant so any advice is appreciated. P.D. Sorry for my bad english import kwant from matplotlib import pyplot VectoresPrimitivos = [(3.176, 0, 0), (1.588, 2.7504, 0), (0, 0, 10)] base = [(0, 0, 0), (1.588, 0.9168, 0.8745), (0, 0, 1.749)] lat = kwant.lattice.general(prim_vecs = VectoresPrimitivos, basis = base) a, b, c= lat.sublattices 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[lat.shape(cuboid_shape, (0, 0, 0))] = 4 * t #syst[lat.neighbors(3, 1e-07)] = 3 lead = kwant.Builder(kwant.TranslationalSymmetry((-3.176, 0, 0))) #hoppings = (((1, 0, 0), a, b), ((0, 0, 0), a, b), ((0, 0, 0), c, b), ((-1, 0, 0), c, b)) #syst[[kwant.builder.HoppingKind(*hopping) for hopping in hoppings]] = -1 def lead_shape(pos): return 0 <= pos[1] < b and 0 <= pos[2] < c lead[lat.shape(lead_shape, (0, 0, 0))] = 4 * t #lead[lat.neighbors(3, 1e-07)] = 3 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=19, c=4) def family_colors(site): if site.family == a: return 'yellow' elif site.family == b: return 'gray' else: return 'black' kwant.plot(syst, site_size=0.25, site_lw=0.025, hop_lw=0.05, site_color=family_colors) syst = syst.finalized() plot_conductance(syst, energies=[0.01 * i - 0.3 for i in range(100)]) def print_hop_kind(hop_kind): print ('HoppingKind' + hop_kind.delta.__str__() + ', ' + hop_kind.family_a.name + ', ' + hop_kind.family_b.name ) print ('Nearest neighbors:') for i in lat.neighbors(3): print_hop_kind(i) if __name__ == '__main__': main() ERROR MESSAGE TypeError Traceback (most recent call last)<ipython-input-54-7d65fe171f23> in <module>() 79 80 if __name__ == '__main__':---> 81 main() <ipython-input-54-7d65fe171f23> in main() 48 def main(): 49 ---> 50 syst = make_cuboid() 51 kwant.plot(syst) 52 <ipython-input-54-7d65fe171f23> in make_cuboid(t, a, b, c) 21 22 hoppings = (((1, 0, 0), a, b), ((0, 0, 0), a, b), ((0, 0, 0), c, b), ((-1, 0, 0), c, b))---> 23 syst[[kwant.builder.HoppingKind(*hopping) for hopping in hoppings]] = -1 24 25 def lead_shape(pos): <ipython-input-54-7d65fe171f23> in <listcomp>(.0) 21 22 hoppings = (((1, 0, 0), a, b), ((0, 0, 0), a, b), ((0, 0, 0), c, b), ((-1, 0, 0), c, b))---> 23 syst[[kwant.builder.HoppingKind(*hopping) for hopping in hoppings]] = -1 24 25 def lead_shape(pos): /usr/lib/python3/dist-packages/kwant/builder.py in __init__(self, delta, family_a, family_b) 361 def __init__(self, delta, family_a, family_b=None): 362 self.delta = ta.array(delta, int)--> 363 ensure_isinstance(family_a, SiteFamily) 364 self.family_a = family_a 365 if family_b is None: /usr/lib/python3/dist-packages/kwant/_common.py in ensure_isinstance(obj, typ, msg) 97 if msg is None: 98 msg = "Expecting an instance of {}.".format(typ.__name__)---> 99 raise TypeError(msg) TypeError: Expecting an instance of SiteFamily.

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Majorana polarization
by Antonio Lucas Rigotti Manesco Nov. 3, 2017

Nov. 3, 2017

Dear Kwant users, I am interested to calculate Majorana polarization for a system I am currently studying. I was wondering if it is possible to obtain it from kwant.ldos. The system is constructed as a kronecker product between particle-hole and spin in that order but I am not sure how kwant.ldos orders the internal degrees of freedom. Does any of you have some hint about that? Thanks in advance.

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beyond effective mass (limiting kwant to a range of k)
by Maurer, Leon Oct. 30, 2017

Oct. 30, 2017

Hello, I’m interested in using kwant to look at transport beyond the effective mass approximation. To that end, I’ve entered a Hamiltonian that reproduces silicon’s band structure [specifically, the k.p Hamiltonian from M. Cardona and F. H. Pollak, Phys. Rev. 142, 530 (1966)] into a 1D kwant lattice. When I plot the bands in the leads using kwant.plotter.bands, at first it looks nothing like Si’s band structure (see lead_bands.pdf, attached). However, when zoomed in to an appropriate k range for Si, Si’s band structure is there as expected (see lead_bands_zoom.pdf, attached). To be more specific, this is Si’s band structure in the (100) direction, which is what I was aiming for. However, this is still useless for transport because kwant calculates transmission as a function of energy for all k values – including k values that are meaningless for Si and need to be excluded from the calculation. So, I think that my question boils down to: is there a reasonably simple way to restrict the range of k values that kwant considers? If not, can you think of another way to hack a full band structure into kwant? Thanks. -Leon PS. Just to preempt some non-helpful answers: I am not interested in replies along the lines of “You couldn’t possibly need to include the full band structure. Just use an effective mass.” I have good reasons to want to include the full band structure.

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Compute conductance for different system lengths
by Jan Behrends Oct. 30, 2017

Oct. 30, 2017

Dear all, I'm looking for a workaround for a problem I currently face: when computing the two-terminal conductance for a system of length L, is there a way to get the conductance for the same system of length 1,2,..L-1 on the fly (while keeping everything else the same, i.e., same width, same disorder configuration etc.)? As far as I understand how the scattering matrix calculation works internally, it shouldn't take much longer to compute these intermediate values than just getting the final conductance. Best, Jan -- Jan Behrends Max-Planck-Institut für Physik komplexer Systeme Nöthnitzer Straße 38, 01187 Dresden, Germany E-Mail: jb(a)pks.mpg.de

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voltage drop between any given pair of sites
by Chung Tsai Oct. 26, 2017

Oct. 26, 2017

Dear all, I was wondering if there is a way to calculate the voltage drop between sites i and j (Vj-Vi) for any given pair of sites in the system? I appreciate any help Bests Chung

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