Mailman 3 March 2017 - Kwant-discuss

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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lead_info
by Prof. CHAN Kwok Sum Sept. 20, 2017

Sept. 20, 2017

Dear Kwant developer, Thank you for your effort in developing Kwant. I have a question about the definition of the direction of momentum in the smatrix.lead_info. Assume a lead lies along the y direction with primitive vector (0,1). The symmetry operation of a lead is (0,1) if the lead goes towards the positive direction and is (0,-1) if the lead goes towards the negative direction. For the momenta contained in smatrix.lead_info for these two leads , do they use the same coordinate system? Positive momenta mean the direction (0,1), negative momenta mean the direction (0,-1). For velocity, in smatrix.lead_info, it has nothing to do with the coordinate system. Positive means outgoing, negative means incoming in the lead. Thank you KS Chan Disclaimer: This email (including any attachments) is for the use of the intended recipient only and may contain confidential information and/or copyright material. If you are not the intended recipient, please notify the sender immediately and delete this email and all copies from your system. Any unauthorized use, disclosure, reproduction, copying, distribution, or other form of unauthorized dissemination of the contents is expressly prohibited.

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forking smatrix.transmission
by Sergey Slizovskiy March 31, 2017

March 31, 2017

Dear all, I have tried a primitive forking of kwant computation with joblib package. This worked well for bands computation, here's the code, but it fails for smatrix.transmission. I would be grateful for any hints and examples. Thank you, Sergey from joblib import Parallel, delayed def plot_bandstructure(flead, momenta, args, max=0.05): global processors switch=False cutoff=0.001 bands = kwant.physics.Bands(flead, args=args) energies = Parallel(n_jobs=processors)(delayed(bands)(k) for k in momenta) pyplot.figure() pyplot.plot(momenta, energies) pyplot.ylim([-max,max]) pyplot.xlabel("momentum [(lattice constant)^-1]") pyplot.ylabel("energy [t]") pyplot.show(block=False) def transm(sys, energy, lead1,lead2,args): print("Smatrix for energy ", energy) smatrix = delayed(kwant.smatrix)(sys, energy,args=args) return smatrix.transmission(lead1, lead2) def plot_conductance(sys, lead1,lead2, energies,args,label): # Compute transmission as a function of energy global processors data = Parallel(n_jobs=processors)(delayed(transm)(sys, energy,lead1, lead2, args=args) for energy in energies) print(data) pyplot.figure() pyplot.plot(energies, data) pyplot.xlabel("energy [t]") pyplot.ylabel("conductance [e^2/h]") pyplot.title(label) return data

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Query for Kwant Software
by Biswadeep Upadhyay March 30, 2017

March 30, 2017

Respected Sir, It's Biswadeep Upadhyay from India. I'm a engineering student recently studying in 3rd year. I'm pursuing a study of Nano Device under the guidance of my professor specialized in Electronic devices. In that regard I consistently use the Kwant software. Recently my area of focus is Carbon Nano Tubes(CNTs). I have done several simulations on 2D structures earlier with ease. But I have question can i simulate CNTs using Kwant. More precisely will I be able to solve CNT related problem using Kwant ; for example to plot the system , band structure, plot of conductance. So I request you to have a look upon my query and enlighten me in this regard. Your active operation is highly solicited. Regards, Biswadeep

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transmission through a barrier of zero height
by Jambulat Basaev March 29, 2017

March 29, 2017

Hi Everyone! I want to solve basic problem of transmission of electron through a potential barrier without taking into account any effects contacts. But the influence of leads in all the examples provided in kwant documentation definitely exists. For example, in the quantum wire case leads are set the same way as the scattering region, that why I expect the transmission should be obtained identically one (for any energy of incident electron). This means that kwant takes into account also some regions outside the leads e.g. bulk metal contacts. Also I modified the quantum well example like this: def plot_transmission(syst, energies, welldepth): data = [] for energy in energies: smatrix = kwant.smatrix(syst, energy, args=[-welldepth]) data.append(smatrix.transmission(1, 0)) data = np.array( data ) pyplot.figure() pyplot.plot(energies, data) pyplot.xlabel("Energy [t]") pyplot.ylabel("Transmission") pyplot.show() and in the main function make a call plot_transmission(syst, [0.01 * i for i in range(1,100)], 0.0) As a result some dependence on E is obtained even for the case of zero depth of the potential whell and it is not identically one. So, is it possible to obtain in Kwant the transmission coefficient through the defined in the scattering region structures which is not affected by anything else? Sincerely, Jambulat Basaev

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Using args in hamiltonian-function
by Camilla Espedal March 27, 2017

March 27, 2017

Dear Kwant team, (am using the development version, 1.3) I am trying to plot the potential of my system and I want to use the hamiltonian(ind,ind,*args) function, but I don't understand how to use the args. Normally, I would give a vector with the values of the args as input, but this doesn't work in the case of hamiltonian (it does with hamiltonian_submatrix). What am I doing wrong? I also have a problem using the kwant.plot(sys) after I switched to Linux, I get the error message "NameError: name 'mplot3d' is not defined", is there something I need to install? Sincerely, Camilla

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function for current density calculation
by Prof. CHAN Kwok Sum March 26, 2017

March 26, 2017

In the discussion thread about calculation of current density, it is mentioned for the function defined for current as follows only work for 1 orbital per site. Does the expression work for system with spin? I guess the Hamiltonian matrix element for sites I and j will be a matrix for a system with spin and the wavefunction for a site is a vector. If this is the case, the function still works for systems with spin degree of freedom (or other internal degree of freedom) Ks chan def current(psi): H_ij = sys.hamiltonian(i, j, args=(B,)) return -2 * (psi[i].conjugate() * H_ij * psi[j]).imag Disclaimer: This email (including any attachments) is for the use of the intended recipient only and may contain confidential information and/or copyright material. If you are not the intended recipient, please notify the sender immediately and delete this email and all copies from your system. Any unauthorized use, disclosure, reproduction, copying, distribution, or other form of unauthorized dissemination of the contents is expressly prohibited.

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transmission though a barrier of zero height
by Вячеслав Семененко March 23, 2017

March 23, 2017

Hi Everyone! I want to solve basic problem of transmission of the electron through a potential barrier without taking into account any effects contacts. But the influence of leads in all the examples provided in kwant documentation definitely exists. For example, in the quantum wire case leads are set the same way as the scattering region, that why I expect the transmission should be obtained identically zero. This means that kwant takes into account also some regions outside the leads e.g. bulk metal contacts. Also I modified the quantum well example like this: def plot_transmission(syst, energies, welldepth): data = [] for energy in energies: smatrix = kwant.smatrix(syst, energy, args=[-welldepth]) data.append(smatrix.transmission(1, 0)) data = np.array( data ) pyplot.figure() pyplot.plot(energies, data) pyplot.xlabel("Energy [t]") pyplot.ylabel("Transmission") pyplot.show() and in the main function make a call plot_transmission(syst, [0.01 * i for i in range(1,100)], 0.0) As a result some dependence on E is obtained even for the case of zero depth of the potential whell and it is not identically zero. So, is it possible to obtain in Kwant the transmission coefficients through the defined in the scattering region structures which is not affected by anything else? Sincerely, Jambulat

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