Mailman 3 March 2022 - Kwant-discuss

Defining uniaxial strain in specified region of graphene
by shrushti.tapar07＠gmail.com 20 Jan '23

20 Jan '23

I want to create the graphene strained superlattice-like structure, having uniaxial strain defined at the specified region. Please, someone can suggest to me how to define the strained region and interface between unstrained and strained graphene regions. Thanks in Advance Shrushti

4 6

Re: How the spin is positioned in the Smatrix?
by Diego Bruno 26 Sep '22

26 Sep '22

Can you disponibilize the code?

4 3

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>

4 4

current-voltage diagram
by loojoo026＠gmail.com 08 Apr '22

08 Apr '22

dear all I have done my project using Kwant and I have drawn a conductance-energy diagram for the system. The question I have is how can I get the current-voltage diagram? thanks Leo

4 4

How to improve the efficiency of simulating the disordered electronic system?
by bishihao＠stu.scu.edu.cn 25 Mar '22

25 Mar '22

Dear developers, dear colleagues, Kwant is a really excellent package and I appreciate what you have done to make the numerical simulation easier. I have been using Kwant for a while. Recently I am simulating the disordered quantum anomalous Hall insulators. The disorder average is time-consuming. In the simulation the Fermi energy of the central scattering region is fixed, and I know that extracting the conductance involves a step of computing modes in the leads from https://www.mail-archive.com/kwant-discuss@kwant-project.org/msg00718.html, thus it came to me that whether I can solve the modes in the leads and store them before, and then I just invoke instead of solving them for every disorder configuration. I have tried to realized a MatLab implementation of Landauer-Buttiker formula based on the recursive Green's function, in which I solved the self energy and line width function of leads for once and performing the disorder average with them invoked and it works fine. I know that the implementation in Kwant is some kind of different, and I was wondering if there was something optimized for simulating disordered system. Below is my code: import kwant import numpy as np import time as ti from mpi4py import MPI comm = MPI.COMM_WORLD k = comm.Get_rank() nprocessor = comm.size import warnings warnings.filterwarnings('ignore') # Pauli matrices s0 = np.eye(2) sx = np.array([[0,1], [1,0]]) sy = np.array([[0, -1j],[1j, 0]]) sz = np.array([[1,0],[0,-1]]) # Parameters A = 364.5 # meV nm B = -686 # meV nm^2 C = 0 # meV D = -512 # meV nm^2 M = -10 # meV L = 256 # Building the system def qwz(a=1, L=L, W=L): hamiltonian_syst = """ (V(x, y) + C-D*(k_x**2+k_y**2))* identity(2) + (M-B*(k_x**2+k_y**2)) * sigma_z + A*k_x*sigma_x + A*k_y*sigma_y """ hamiltonian_lead = """ (C-D*(k_x**2+k_y**2))* identity(2) + (M-B*(k_x**2+k_y**2)) * sigma_z + A*k_x*sigma_x + A*k_y*sigma_y """ template_syst = kwant.continuum.discretize(hamiltonian_syst, grid=a) template_lead = kwant.continuum.discretize(hamiltonian_lead, grid=a) def shape(site): (x, y) = site.pos return (0 <= y < W and 0 <= x < L) def lead_shape(site): (x, y) = site.pos return (0 <= y < W) syst = kwant.Builder() syst.fill(template_syst, shape, (0, 0)) lead = kwant.Builder(kwant.TranslationalSymmetry([-a, 0])) lead.fill(template_lead, lead_shape, (0, 0)) syst.attach_lead(lead) syst.attach_lead(lead.reversed()) # kwant.plot(syst) syst = syst.finalized() return syst def get_conductance(w, Ef, Nc): # w is the disorder strength, Ef is the Fermi energy, and Nc is the cycling times def disorder(x, y): # onsite disorder return np.random.uniform(-w/2, w/2) params = dict(A = A, B = B, C = C, D = D, M = M, Ef = Ef, V = disorder) syst = qwz() data = [] for i in range(Nc): smatrix = kwant.smatrix(syst, Ef, params = params) data.append(smatrix.transmission(1, 0)) G_av = np.mean(data) G_std = np.std(data) return G_av, G_std def main(): t1 = ti.time() syst = qwz() Ef = 100 # meV Nc = 500 # cycle w = k * 20 # meV G_av, G_std = get_conductance(w, Ef, Nc) # pyplot.plot(energies, data) # pyplot.xlabel("energy [t]") # pyplot.ylabel("conductance [e^2/h]") # pyplot.show() # pyplot.savefig('conductance' +str(k)+ '.png') np.savez('cond('+str(L)+')'+str(k)+ '.npz', x = w, y = G_av, ye = G_std) # print('Disorder strength:', w, 'Average conductance:', G_av, 'Conductance fluctuation:', G_std) t2 = ti.time() print('time cost:', t2-t1, 's') if __name__ == '__main__': main() In which I simulated a system of 256*256 atoms and averaged for 500 samples. It will take about 20000 seconds with a dual E5 2696 v3 server with 50 threads working parallely at about 2.7 GHz. I know that part of the developers contributed to the termed Topological Anderson Insulator, and I was wondering if there's some way to improve the efficiency of my code? Thank you for taking your time! Yours sincerely, Shihao, A PhD candidate in cond-mat theory

2 1

Inquiry about extracting boundstate eigenvectors/eigenvalues from kwant
by Zhang, Chi 18 Mar '22

18 Mar '22

Dear Devs, I hope this email finds you well. We are two Master's students trying to calculate Andreev/Majorana transition elements using the kwant boundstate algorithm (doi: 10.21468/SciPostPhys.4.5.026). For our purposes we need to extract the evanescent tails of the boundstates in the leads as well, which we had hoped to obtain from the StabilisedModes object in kwant.InfiniteSystem.modes(). However, in general, the vecs and vecslmbdainv object are not related by a constant eigenvalue, as advertised in the documentation. We wonder if you could tell us how to transform from the vecs and vecslmbdainv objects back to the eigenvectors*eigenvalues and eigenvectors object for our calculations? Many thanks in advance for your response! Sincerely, Chi Zhang & Ryan Tiew MSci Physics with Theoretical Physics Imperial College London ----------------------------------------------------- Some technical details of what we have tried here. Please ignore this if you don't have enough time to read. We are aware that kwant is transforming vecslmbdainv by sqrt(norm(hop))*eigenvectors, and vecs by (hop/sqrt(norm(hop)))@eigenvectors@eigenvalues. However, this does not seem to be the full story and we are not able to reproduce what is stored in vecs and vecslmbdainv when there are more than 1 evanescent modes. In particular, we have tried to do a real generalised Schur decomposition of the two matrices in the lead schroedinger's equation, grabbed the vectors stored in the right unitary, and put them through the basis transformation described above. Still the there is no sign of better agreements. We therefore we believe it would be more productive to inquire directly from you how to transform from vecs and vecslmbdainv to actual eigenvectors and eigenvalues. Many thanks in advance for your reply.

2 2

How to Calculate current-voltage characteristics in graphene nanoribbon in kwant
by sahu.ajit92＠gmail.com 09 Mar '22

09 Mar '22

Dear All, How to calculate the current-voltage characteristics in graphene nanoribbon. calculated the conductance with respect to energy. I have the following code for graphene nanoribbon. how to calculate the current with respect to voltage in this example. import kwant import numpy as np from matplotlib import pyplot import matplotlib.pyplot as plt import numpy as np import numpy.linalg as npl import scipy.sparse.linalg as sla pi=np.pi ############################################## structure ######################## Wnr=10 lnr=30 lat=kwant.lattice.honeycomb(a=2.46,norbs=1) a,b=lat.sublattices ########### functions for structure build def rect(pos): x,y=pos return 0<=x<lnr and 0<=y<Wnr ################################ main structure i.e. rectangle #################### model1 = kwant.Builder() model1[lat.shape(rect,(1,1))] = 0 model1[lat.neighbors()] =2.64 model1.eradicate_dangling() ############### functions for lead structure build ################################ def lead1_shape(pos): x, y = pos return 0< y < Wnr-1 def lead2_shape(pos): x, y = pos return 0< x <Wnr ############first lead codes########## sym = kwant.TranslationalSymmetry(lat.vec((-1,0))) #from the left sym.add_site_family(lat.sublattices[0], other_vectors=[(-1, 2)]) sym.add_site_family(lat.sublattices[1], other_vectors=[(-1, 2)]) lead = kwant.Builder(sym) lead[lat.shape(lead1_shape, (0,1))]=0 lead[lat.neighbors()] = 2.64 model1.attach_lead(lead) model1.attach_lead(lead.reversed()) #second lead attach in reverse manner model1=model1.finalized() kwant.plot(model1) ##hamiltonian mat model1_matrix = model1.hamiltonian_submatrix() eng = npl.eigvalsh(model1_matrix) def plot_conductance(sys, energies): # Compute transmission as a function of energy data = [] for energy in energies: smatrix = kwant.smatrix(sys, energy) data.append(smatrix.transmission(0, 1)) pyplot.figure() pyplot.plot(energies, data) pyplot.xlabel("energy [t]") pyplot.ylabel("conductance [e^2/h]") pyplot.show() plot_conductance(model1,eng)

1 0

Can not add Hopping in a MoS2
by utkarshs＠iitgn.ac.in 08 Mar '22

08 Mar '22

I am making an MoS2 lattice but can add hoppings here is the error. """ ValueError: <Monatomic lattice 0> and <Monatomic lattice 1> are not compatible with delta=[0 0] """ here is my code. a0 = 3.15 graphene = kwant.lattice.general ([(a0*1, 0, 0),(a0*np.sin(np.pi/6),a0*np.cos(np.pi/6), 0), (0, 0, 12.5)], [(0, 0, 0),(0, a0*(1/sqrt(3)), 12.5)]) a, b = graphene.sublattices def ribbona(pos): x,y, z = pos return (0<=x<=10 and 0<= y <=10 and 0<= z <= 1) def ribbonb(pos): x,y, z = pos return (0<=x<=10 and 0<= y <=10 and 10< z <= 13) def ribbonc(pos): x,y, z = pos return (0<=x<=10 and 0<= y <=10 and 24< z <= 26) syst = kwant.Builder() syst[b.shape(ribbona,(0,0, 0))] = 0 syst[a.shape(ribbonb,(0,0, 12))] = 0 syst[b.shape(ribbonc,(0,0, 25))] = 0 %matplotlib qt hoppings = (((0,0),a,b),((0,1),a,b)) syst[[kwant.builder.HoppingKind(*hopping) for hopping in hoppings]] = -1 syst[a.neighbors()] = -1 syst[b.neighbors()] = -1 kwant.plotter.plot(syst, fig_size = (10, 10), site_size=0.18, site_lw=0.01, hop_lw=0.05);

1 0

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))

3 3

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

3 3