Kwant-discuss June 2016

kwant-discuss@python.org

17 participants
19 discussions

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

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

4 3

LDOS and added lead sites to the scattering region
by Tibor Sekera 29 Jun '16

29 Jun '16

Dear all, I want to plot the local density of states (LDOS) for a honeycomb system of a rectangular shape modeled by Hamiltonian H. Because the Bravais lattice vectors are non-orthogonal, the honeycomb leads (but modeled by different Hamiltonian H') are attached in such a way, that sites have to be added to the scattering region. This added part, however, is modeled by H' whereas the rest (original scattering region) by H. I know that I can just say that the added part is actually part of the leads (matter of definition). But, if I want to plot LDOS using "kwant.ldos(sys, energy)", it plots LDOS also on this added part modeled by H', which obscures the LDOS of my interest on the original scattering region modeled by H. How to make KWANT not to plot the LDOS on the artificially added part to the scattering region? Thanks for an advice, Tibor

2 1

CNT lead
by Roohollah Hafizi 26 Jun '16

26 Jun '16

Dear all Hello I want to introduce a deformed Carbon Nanotube (with no symmetry) lead. I should note that a CNT supercell consists of at least (in my case, exactly) four rows of Carbon atoms in the unit cell. I appreciate general remarks on how to do it on KWANT? ?Hafizi

3 7

Hooping from sites does not match the dimensions of onsite
by james edward hernandez 23 Jun '16

23 Jun '16

Hi. I tried to modify the tutorial for spin orbit coupling by replacing the system with a honeycomb lattice. However, I got this error, which came from bands: "Hopping from site 0 to site 12 does not match the dimensions of onsite Hamiltonians of these sites."Part of the code is attached. sys[lat.shape(rectangle, (1, 1))] = 0 #next nearest sys[lat.neighbors()] = 1.04 #nearest #### Define the left lead. #### sym = kwant.TranslationalSymmetry((-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) def lead1_shape(pos): x, y = pos return 0 < y < 10 for j in range(W): lead[lat.shape(lead1_shape, (0,j))] = 4 * t * identitymat + e_z * sigma_z lead[lat.neighbors()] = 0 #lead[(lat(0, j) for j in range(W))] = 4 * t * sigma_0 + e_z * sigma_z #hoppings in x-direction #lead[kwant.builder.HoppingKind((1, 0), 1, 1)] = \ # -t * identitymat - 1j * alpha * sigma_y # hoppings in y-directions #lead[kwant.builder.HoppingKind((0, 1), 1, 1)] = \ # -t * identitymat + 1j * alpha * sigma_x sys.attach_lead(lead) sys.attach_lead(lead.reversed()) return sys,lead def plot_bandstructure(sys, momenta): bands = kwant.physics.Bands(sys) energies = [bands(k) for k in momenta] plt.figure() plt.plot(momenta, energies) plt.xlabel("momentum [(lattice constant)^-1]") plt.ylabel("energy [t]") plt.show() def main(): sys,lead = make_system() honeycomb = sys.finalized() kwant.plot(sys) momenta = [0.01* pi * i for i in range(200)] plot_bandstructure(honeycomb.leads[1], momenta) #leads because of the attribute of silicene # We should see non-monotonic conductance steps. #plot_conductance(sys, energies=[0.01 * i - 0.3 for i in range(100)]) if __name__ == '__main__': main() James

2 1

Gamma, M and K points in Kwant
by james edward hernandez 21 Jun '16

21 Jun '16

Hello, I saw in the tutorial 'Band structure calculations' that Kwant is able to display band structures for each lead. This applies also to Graphene nanoribbons. I was wondering if kwant.plotter.Bands() could also plot the band structure of graphene (or any honeycomb lattice), noting specific points in the Brillouin Zone, particularly Gamma->M->K->K'->Gamma? Regards, James

2 1

conductance in large-voltage regime
by Sergey Slizovskiy 18 Jun '16

18 Jun '16

Dear all, Kwant is by default computing the linear Ohmic conductance in the regime where left and right chemical potentials differ infinitesimally. Do I get it right that to obtain ballistic conductance in the case of finite difference of chemical potentials, I can simply integrate the Kwant conductance result over a range of chemical potentials between the left and right contacts? This seems like a very natural thing to do to me. Am I right? Also, one can smoothen this integration with derivative of Fermi function to account for temperature. Best wishes, Sergey

2 1

Adding leads on rectangular sheet
by james edward hernandez 17 Jun '16

17 Jun '16

Hi. I tried to add leads on the rectangular honeycomb scattering region. I was able to add two leads (the first one is from the left from 0 < y < 10, and the second one is from the right 0 < y < 4). But when I tried add another lead on the right from 7 < y < 10, it gives an error: ValueError: No sites close to (1, 1) are inside the desired shape. Here is the code for the setup: import matplotlib.pyplot import kwant lat = kwant.lattice.honeycomb() sys = kwant.Builder() def rectangle(pos): x, y = pos return 0 < x < 20 and 0 < y < 10 sys[lat.shape(rectangle, (1, 1))] = 0 #next nearest sys[lat.neighbors()] = -1 #nearest sym = kwant.TranslationalSymmetry((-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) def lead1_shape(pos): x, y = pos return 0 < y < 10 lead[lat.shape(lead1_shape, (1,1))] = 0 lead[lat.neighbors()] = -1 sym2 = kwant.TranslationalSymmetry((1, 0)) #to the right, botttom sym2.add_site_family(lat.sublattices[0], other_vectors=[(-1, 2)]) sym2.add_site_family(lat.sublattices[1], other_vectors=[(-1, 2)]) def lead2_shape(pos): x, y = pos return 0 < y < 4 # bottom lead2 = kwant.Builder(sym2) lead2[lat.shape(lead2_shape, (1,1))] = 0 lead2[lat.neighbors()] = -1 sym3 = kwant.TranslationalSymmetry(lat.vec((1, 0))) #to the right, top sym3.add_site_family(lat.sublattices[0], other_vectors=[(-1, 2)]) sym3.add_site_family(lat.sublattices[1], other_vectors=[(-1, 2)]) def lead3_shape(pos): #tried to add this lead and gives an error x, y = pos return 7 < y < 10 # top lead3 = kwant.Builder(sym3) lead3[lat.shape(lead3_shape, (1,1))] = 0 lead3[lat.neighbors()] = -1 sys.attach_lead(lead) sys.attach_lead(lead2) sys.attach_lead(lead3) kwant.plot(sys); Thanks, James

2 1

kwant applicability
by Bibek Bhandari 16 Jun '16

16 Jun '16

I was doing some project on thermoelectric transport in quantum dots. I wanted to know whether I can use the kwant package to study the transport properties. If so, is there any materials that may support my project. Thanks a lot. Most Sincerely, Bibek Bhandari

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Kwant-discuss June 2016