Mailman 3 January 2020 - Kwant-discuss

To to separate spins, electron and hole
by Khani Hosein Oct. 11, 2024

Oct. 11, 2024

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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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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Problems to add disorder to the Kitaev chain
by Luca Lepori Feb. 6, 2020

Feb. 6, 2020

Hello Kwant community, I write since I am trying to simulate a Kitaev chain with disorder, here distributed uniformly in the range [1,-1], and I am experiencing troubles to implement the disorder itself. In the absence of disorder, the function that defines the tight-binding (open) Hamiltonian can be written e.g. as follows: def kitaev(L ,t, mu, Delta) : syst = kwant.Builder() lat = kwant.lattice.chain(norbs=2) syst[lat(0)] = - (mu/2)*pauli3 for i in range(1,L): syst[lat(i)] = -(mu/2)*pauli3 syst[lat(i), lat(i - 1)] = -(t/2)*pauli3 + 1j*(Delta/2)*pauli2 return syst where the Pauli matrices have been previously defined, t is the hopping, mu is the chemical potential, and Delta is the gap. Now, I want to add disorder, proportional to W and uniformly distributed in [-1,1]. The tutorial online for Kwant states that the function kwant.digest.uniform(input, salt='') creates a random offset in the interval [0,1]. Therefore I thought that the Hamiltonian could be changed e.g. as follows: def kitaev(L ,t, mu, Delta, W) : syst = kwant.Builder() lat = kwant.lattice.chain(norbs=2) syst[lat(0)] = -(1/2)*(mu + W*(2*onsite - 1))*pauli3 for i in range(1,L): syst[lat(i)] = -(1/2)*(mu + W*(2*onsite - 1))*pauli3 syst[lat(i), lat(i - 1)] = -(t/2)*pauli3 + 1j*(Delta/2)*pauli2 return syst after that the onsite function has been defined as def onsite(site, phi, salt): return uniform(repr(site), salt) (I am still trying to follow the tutorial). However, when trying to calculate eigenvalues and eigenvectors, via the code L = 50 W = 0 mub = 3 systb = kitaev(L ,1, mub, 1, W) systb = systb.finalized() hamatb = systb.hamiltonian_submatrix(sparse = False) evalsb, evecsb = la.eigh(hamatb) I encountered the problem ----------------------------------------------------------------------------------------- TypeError Traceback (most recent call last) <ipython-input-10-12a574eefcd0> in <module> 3 4 mub = 3 ----> 5 systb = kitaev(L ,1, mub, 1, W) 6 systb = systb.finalized() 7 hamatb = systb.hamiltonian_submatrix(sparse = False) <ipython-input-9-661d5ddb539a> in kitaev(L, t, mu, Delta, W) 4 lat = kwant.lattice.chain(norbs=2) 5 ----> 6 syst[lat(0)] = -(1/2)*(mu + W*(2*onsite - 1))*pauli3 7 8 for i in range(1,L): TypeError: unsupported operand type(s) for *: 'int' and 'function' —————————————————————————————------ that instead does no occur in the absence of disorder (then when the first definition above for the Kitaev chain is assumed). Probably I did not understand properly how to use the function uniform(repr(site), salt). Can you help me ? Thank you very much in advance and best regards L. L.

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AC voltage drop and spin-current for a spin system
by Thomas Kloss Jan. 26, 2020

Jan. 26, 2020

Dear Rudolf, indeed, manybody expectation values involving thermal averages over the occupied states are only available in tkwant by now. The "voltag_raise" tutorial you mentioned is a good reference, just make sure that you stick with the new version (tkwant's API has slightly changed): https://kwant-project.org/extensions/tkwant/tutorial/AC_josephson_without_s… For spin currents, it should work similar to the kwant operator tutorial you mention, with an operator kwant.operator.Current(syst, sigma_u) and sigma_u = ((1,0),(0,0)) for the upp current, respectively sigma_d = ((0,0),(0,1)) for the down current. Best, Thomas

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Can we solve eigenproblem by finite-element-method?
by Cao Zhan Jan. 25, 2020

Jan. 25, 2020

Dear Kwant users, Solving Schrodinger equantions describing quantum physics of noninteracting systems amounts to solving eigenproblems. As I know, the Kwant package has the superiority at calculating transport properties, and moreover, it can also solve eigenproblems of closed systems. To be precise, firstly, one can use "kwant.continuum.discretize" to discrete continous Hamiltonians into tight-binding models with a specified lattice constant, and secondly, diagonalize the lattice model to obtain the eigen-energies and eigen-wavefunctions. Actually, we can solve Schrodinger equantions, which are essentially second-order partial differential equations, by numerical methods such as the powerful finite-element-method with irregular mesh and specified boudary conditions. I know that many papers in codensed matter community studying finite-size models by the tight-binding method rather than the finite-element-method. Is this due to any restriction of the finite-element-method in solving Schrodinger equantion? Does anyone ever compare the performance of tight-binding-method and finite-element-method on solving eigenproblem of closed Hamiltonian. Is there any literature addressing this issue? Regards, Zhan

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tight-binding Hamiltonian
by simon.flury＠uzh.ch Jan. 23, 2020

Jan. 23, 2020

Dear kwant users I was trying to implement the following Hamiltonian: H_j,j+1 = H_j+1,j = -t, H_j,j = -0.02*t*cos(k_y + 2pi (phi/W)*j) for a square lattice of size W*L with attached leads in y-direction. Unfortunately it doesn't work. Could anyone give me a hint how to do this the right way? Thank you for your answers in advance Best, Simon def make_system(a=1, L=60, W=30): offdiagmat = np.zeros((W, W)) for i in range(W): for j in range(W): if i == j + 1 or j == i + 1: offdiagmat[i][j] = 1 hamiltonian = "-1.0*offdiagmat - identity(4)*2*0.01*cos(k_y + (2*pi*phi/30)*x)" hamiltonian = kwant.continuum.sympify(hamiltonian, locals=dict(offdiagmat=offdiagmat)) template = kwant.continuum.discretize(hamiltonian, grid=a) def shape(site): (x, y) = site.pos return (0 <= x < W and 0 <= y < L) def lead_shape(site): (x, y) = site.pos return (0 <= x < W) syst = kwant.Builder() syst.fill(template, shape, (0, 0)) lead = kwant.Builder(kwant.TranslationalSymmetry([0, -a])) lead.fill(template, lead_shape, (0, 0)) syst.attach_lead(lead) syst.attach_lead(lead.reversed()) syst = syst.finalized() return syst def analyze_system(): params = dict(phi=0.2) syst = make_system() kwant.plotter.bands(syst.leads[0], params=params, momenta=np.linspace(-pi, pi, 200), show=False) plt.grid(True) plt.xlim(-pi, pi) plt.xlabel('momentum [1/A]') plt.ylabel('energy [eV]') plt.show() def main(): analyze_system() if __name__ == '__main__': main()

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Regarding the unit in Hall conductance
by MS. PRIYANKA SINHA Jan. 23, 2020

Jan. 23, 2020

Dear Sir, I was trying to calculate the Integer quantum Hall effect in graphene with the help of Laughlinargument.ipynb. For square lattice the quantization is okay ( ne^2/h). But for graphene it is (2n+1) 2e^2/h. I am getting the quantization like 1, 3, 5, 7 e^2/h in graphene which seems there is missing of factor 2. Is the Hall conductivity I am getting is in 2e^2/h unit or should I multiply the data by 2 to get the quantization like 2, 6, 10 which is well-known IQHE in graphene. It will be really helpful If you kindly clear my doubts regarding this. Thanking You, Priyanka Sinha

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