Mailman 3 November 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 07 Mar '22

07 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 07 Mar '22

07 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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Access to eigenvalue, eigenvector and number of points in each unit cell
by Saj.ZiaBorujeni 02 Dec '19

02 Dec '19

Dear all, I need to access to the number of atoms of my unit cell, the eigenvalue and eigenvectors for each eigenvalue of my Hamiltonian. Is there any one to help me and let me know if it is possible in kwan to access them. Best wishes, Sajad

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Diamond structure
by tavakkolidjawad 30 Nov '19

30 Nov '19

Hi dears Based on the code for zincblende structure inside the Kwant website, I want to build a diamond lattice, but I don't know what I need to change in this code to create a diamond structure, also I need to create one lead for this structure. can you help me? Thank you in advance. >>>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)]) >>>a, b = lat.sublattices >>>def make_cuboid(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))] = None >>>syst[lat.neighbors()] = None >>>return syst >>>def main(): >>># the standard plotting style for 3D is mainly useful for >>># checking shapes: >>>syst = make_cuboid() >>>kwant.plot(syst) >>># visualize the crystal structure better for a very small system >>>syst = make_cuboid(a=1.5, b=1.5, c=1.5) >>>def family_colors(site): return 'r' if site.family == a else 'g' >>>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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How to add Hopping to a curved surface?
by EUDES THOMAS GOMES DA SILVA 30 Nov '19

30 Nov '19

Hi dears, I am trying to study curved structures on Kwant and i've already done a code that gives me the coordinates for all atoms. What I have done was to curve a graphene sheet. By now, I am trying to add the hoppings to its structure, but as my structure does not have "symmetry" when I write down: lat = kwant.lattice.general([(1,0,0), (0,1,0), (0,0,1)],norbs=3) syst[lat(surface[0][0],surface[1][0],surface[2][0])]=2*t syst[sites[0], lat(surface[0][0],surface[1][0],surface[2][0])] = -t where surface[0][0], surface[1][0], surface[2][0] are the coordinates x, y and z of the first atom and sites[0] is the first site. I create a curved surface and make my Kwant Ambient as follow: class SURFACE(kwant.builder.SimpleSiteFamily): def normalize_tag(self, tag): return tinyarray.array(tag, float) def pos(self, tag): return tag atoms = SURFACE(norbs=3) syst = kwant.Builder() sites = [] for i in range(int(len(surface[0]))): x = surface[0][i] y = surface[1][i] z = surface[2][i] sites.append(atoms(x,y,z)) My question is: When I write lat(surface[0][0],surface[1][0],surface[2][0]) it does not stay at the real surface[0][0],surface[1][0],surface[2][0] position because it has floats values. When I type lat(surface[0][0],surface[1][0],surface[2][0]) I see: (Site(<class '__main__.SURFACE'>(None, 1), array([-3.472, -9.108, 1.205])), Site(kwant.lattice.Monatomic([[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [0.0, 0.0, 0.0], '', 3), array([-3, -9, 1]))) and array([-3, -9, 1]) should be array([-3.472, -9.108, 1.205]). Why lattices accept only integer values?

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Fwd: Tags and sites
by Adel Belayadi 28 Nov '19

28 Nov '19

---------- Forwarded message --------- De : Adel Belayadi <adelphys(a)gmail.com> Date: mer. 27 nov. 2019 à 20:27 Subject: Re: [Kwant] Tags and sites To: EUDES THOMAS GOMES DA SILVA <eudes.gomes(a)ufrpe.br> Dear EUDES, why can tags assume only integers values? In fact, the tight binding approach works like the discretized Schrodinger equation see Ref [1]. In this context each site is defined by an integer lattice coordinates (𝑖, 𝑗) which provide the real-space coordinates (𝑥, 𝑦) as (a1*n, a2*m ). Once you define the primitive vector of the system let’s say *𝑎*1 and *𝑎*2, so the translation to get the whole lattice leads to write *𝑅* = 𝑛*𝑎*1 + m*𝑎*2. Here n and m are integer which refer to the tag in kwant. So building the whole lattice has nothing to with real space position( since we use *translation as 𝑅* = 𝑛*𝑎*1 + m*𝑎*2 ). Now the most important task is to define the hopping between neighboring atoms. A hopping is created between the main cell (for instance (0, 0) ) and a neighboring cell specified by relative index such as (0, 1) and (1, 0). For more explanation, see the enclosed figure ( in case of square lattice ) Additionally, remember that when we use the Bloch theorem. The wave function for a periodic lattice is defined by a phase factor: For instance let as say φ (n∓q, m∓q ). =exp(±iqakx)*exp(±iqaky) φ (n, m). Where q in an integer that way we deal with integer not with space positions. Ps: Ref[1]: Timothy B. Boykin. The discretized Schrodinger equation and simplemodels for semiconductor quantum wells best, Adel Le mar. 26 nov. 2019 à 20:29, EUDES THOMAS GOMES DA SILVA < eudes.gomes(a)ufrpe.br> a écrit : > Hi Dears, > > why can tags assume only integers values? > > For example: > > lat = kwant.lattice.Polyatomic([(1, 0, 0), (0, 1, 0),(0, 0, 1)], [(1, 0, > 0), (0.0, 1, 0.0),(0.0, 0.0, 1)],norbs=1) > syst = kwant.Builder() > > # it is possible: > syst[a(1,0,0)]=4 > > and syst[a(1.5,0,0)]=4 > > gives me the same result as before? > > Both of them says: > > >>> a(1,0,0) > > Site(kwant.lattice.Monatomic([[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, > 1.0]], [0.0, 0.0, 0.0], '0', 1), array([1, 0, 0])) > > >>> a(1.5,0,0) > > Site(kwant.lattice.Monatomic([[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, > 1.0]], [0.0, 0.0, 0.0], '0', 1), array([1, 0, 0])) > > The later should be: > > Site(kwant.lattice.Monatomic([[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, > 1.0]], [0.0, 0.0, 0.0], '0', 1), array([1.5, 0, 0])) > > best regards. > > Eudes. > > > > > > > > > >

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Tags and sites
by EUDES THOMAS GOMES DA SILVA 27 Nov '19

27 Nov '19

Hi Dears, why can tags assume only integers values? For example: lat = kwant.lattice.Polyatomic([(1, 0, 0), (0, 1, 0),(0, 0, 1)], [(1, 0, 0), (0.0, 1, 0.0),(0.0, 0.0, 1)],norbs=1) syst = kwant.Builder() # it is possible: syst[a(1,0,0)]=4 and syst[a(1.5,0,0)]=4 gives me the same result as before? Both of them says: >>> a(1,0,0) Site(kwant.lattice.Monatomic([[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [0.0, 0.0, 0.0], '0', 1), array([1, 0, 0])) >>> a(1.5,0,0) Site(kwant.lattice.Monatomic([[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [0.0, 0.0, 0.0], '0', 1), array([1, 0, 0])) The later should be: Site(kwant.lattice.Monatomic([[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [0.0, 0.0, 0.0], '0', 1), array([1.5, 0, 0])) best regards. Eudes.

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