Mailman 3 December 2016 - Kwant-discuss

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

Using Kwant for finding tunneling probability from metal to vacuum
by Kristjan Eimre 14 Feb '17

14 Feb '17

Hello Kwant experts, I have studied Kwant a bit, but before I delve deeper into it, I want to know if it can be applied to my problem. I have a 3d electron potential landscape for a metal-vacuum surface calculated with DFT. (More detailed info and pictures in [1]). Can I use Kwant to calculate the transmission probability of electrons incident on the surface? And if kwant is not suitable for this problem, perhaps you know of any other numerical software or method that would allow this calculation? [1] - http://physics.stackexchange.com/questions/295329/quantum-tunneling-probabi… Best regards, Kristjan

5 9

How to attach the leads manually?
by Татьяна Григоренко 20 Dec '16

20 Dec '16

Hi! How to attach the leads manually, if I have the coordinates. I use class kwant.builder.Lead and I have an error: "TypeError: Can't instantiate abstract class Lead with abstract methods finalized". What does it mean? For example, for two atoms: left_lead = kwant.builder.Lead() #add site left_lead[lat(-90.26501, 13.2107)] = 4 left_lead[lat(-91.60269, 12.67463)] = 4 #add hopping left_lead[lat(-90.26501, 13.2107), lat(-91.60269, 12.67463)] = 1 sys.attach_lead(left_lead) С уважением, Татьяна Григоренко grigorenochka(a)mail.ru

3 3

How do I get the index for a given site?
by Eric Mascot 17 Dec '16

17 Dec '16

I'm doing a self consistent calculation and I need the matrix element for a site when setting the coupling. I got it working but I wanted to know if there was a correct way. Here is my code which uses scipy.spatial. def onsite(site, Delta=None, coords=None): if (Delta is None and coords is None): Delta_r = Delta_0 else: _, i = spatial.KDTree(coords).query(site.pos) Delta_r = Delta[i] return -mu * tau_z + Delta_r * tau_x where coords is obtained by sites = kwant.plotter.sys_leads_sites(syst, 0)[0] coords = kwant.plotter.sys_leads_pos(syst, sites) I feel like this may be a roundabout solution but it is working. Any help would be appreciated. Thanks, Eric

2 2

How can I use kwant.plotter.map when using an orbital description
by Eric Mascot 15 Dec '16

15 Dec '16

I am going through the tutorials and I wanted to combine two of the lessons. 2.4. Beyond transport: Band structure and closed systems 2.6. Superconductors: orbital vs. lattice degrees of freedom In 2.4, they plot the wavefunction using kwant.plotter.map In 2.6, the system uses tinyarrays Can I combine these and plot the wavefunction using map? Here is my code import kwant import numpy as np import matplotlib.pyplot as plt import tinyarray as ta s_0 = ta.array([[1, 0], [0, 1]]) s_x = ta.array([[0, 1], [1, 0]]) s_y = ta.array([[0, -1j], [1j, 0]]) s_z = ta.array([[1, 0], [0, -1]]) def make_system(a=1, L=21, W=21, t=1.0, mu=-3.618, Delta=0.1, leads=True): lat = kwant.lattice.square(a) syst = kwant.Builder() syst[(lat(x,y) for x in range(L) for y in range(W))] = -mu * s_z + Delta * s_x syst[lat.neighbors()] = -t * s_z if (leads): lead = kwant.Builder(kwant.TranslationalSymmetry((-a, 0))) lead[(lat(0, j) for j in range(W))] = -mu * s_z lead[lat.neighbors()] = -t * s_z syst.attach_lead(lead) syst.attach_lead(lead.reversed()) return syst def plot_conductance(syst, energies): data = [] for energy in energies: smatrix = kwant.smatrix(syst, energy) # Conductance is N - R_ee + R_he data.append(smatrix.submatrix(0, 0).shape[0] - smatrix.transmission(0, 0) + smatrix.transmission(1, 0)) plt.figure() plt.plot(energies, data) plt.xlabel("energy [t]") plt.ylabel("conductance [e^2/h]") plt.show() def plot_wave_function(sys): # Calculate the wave functions in the system. ham_mat = sys.hamiltonian_submatrix(sparse=True) evecs = sla.eigsh(ham_mat, k=20, which='SM')[1] # Plot the probability density of the 10th eigenmode. kwant.plotter.map(sys, np.abs(evecs[:, 9])**2, colorbar=False, oversampling=1) syst = make_system() kwant.plot(syst) syst = syst.finalized() plot_conductance(syst, energies=[-0.25 + 0.005 * i for i in range(100)]) plot_wave_function(syst) Currently, I get the error "The number of sites doesn't match the number of provided values." Thanks, Eric

2 2

Curved Quantum Wire
by Oliver Generalao 10 Dec '16

10 Dec '16

HI, I was trying to implement the paper http://link.springer.com/article/10.1134%2FS0021364006080042 in kwant, however I have trouble creating the geometry of the wire. I tried some tutorials, I got confused since I am a novice to kwant. It is a 3D setup with the wire(ideally close to a 1-D quantum wire) on xy-plane and the external field's direction is upward(in the direction of positive z-axis). The lead input is from x=-infinity to x=0(in the negative y-axis) ,then from x=0 the wire starts to curve(in a perfect semicircle manner) with radius R towards the positive y-axis, and the output lead starts from x=0 to x=-infinity. Herein is the figure attached as well. Any guidance and help in creating the code will be greatly appreciated. Thank you. -- Oliver B. Generalao M.S. Physics student Structure and Dynamics Group National Institue of Physics University of the Philippines Diliman, Quezon City Trunkline: +63-2-981-8500 Mobile: +63-927-4033966

2 2

A question regarding the conductance formula in Kwant paper
by Camilla Espedal 07 Dec '16

07 Dec '16

Hi, I have a question regarding the equation you use to calculate the conductance (Eq. (10)) in the Kwant paper, and how it relates to Eq. (47) in this paper (https://arxiv.org/pdf/cond-mat/9910158v2.pdf) by Büttiker et al I tried to use both methods to calculate the conductance in a simple 2D two-terminal geometry. As far as I understand, you calculate the conductance assuming that the two leads only differ infinitesimally (so for low temperatures I guess it is safe to assume that the fermi-function is a delta-function around the fermi energy). My system is so that I have 2 modes in each lead. So, assume that I want the conductance in lead 0 Your formula G_00 = S_00^2 + S_01^2 S_10^2 + S_11^2 = 1.9 (the result I get from doing this is consistent with transmission(0,0)) Büttiker G_00 = - ( N_0 - S_00^2 - S_11^2) = -0.1 Where N_0 = 2 (number of modes). Now, the numerical values I got from running my program, which I include as well below. Should these results not be the same? Or is my interpretation of their meaning wrong? Before I include the script I would just like to say thank you for making Kwant, and also I am very gratefull that you take your time to answer all my questions so quickly. I really appreciate it. Thank you! Best, Camilla # Tutorial 2.2.3. Building the same system with less code # ======================================================= # # Physics background # ------------------ # Conductance of a quantum wire; subbands # # Kwant features highlighted # -------------------------- # - Using iterables and builder.HoppingKind for making systems # - introducing `reversed()` for the leads # # Note: Does the same as tutorial1a.py, but using other features of Kwant. import kwant # For plotting from matplotlib import pyplot from math import pi, sqrt, tanh import numpy as np from numpy import ndarray import scipy from scipy.constants import * def modes(energy): return 0 def plot_bandstructure(flead, momenta): bands = kwant.physics.Bands(flead) energies = [bands(k) for k in momenta] pyplot.figure() pyplot.plot(momenta, energies) pyplot.xlabel("momentum [(lattice constant)^-1]") pyplot.ylabel("energy [t]") pyplot.show() def make_system(a=1.0, t=1.0, W=2, L=3): # Start with an empty tight-binding system and a single square lattice. # `a` is the lattice constant (by default set to 1 for simplicity. lat = kwant.lattice.square(a) sys = kwant.Builder() #### Define the scattering region. #### sys[(lat(x, y) for x in range(L) for y in range(W))] = 4 * t + 2 sys[lat.neighbors()] = -t #### Define and attach the leads. #### # Construct the left lead. lead = kwant.Builder(kwant.TranslationalSymmetry((-a, 0))) lead[(lat(0, j) for j in range(W))] = 4 * t lead[lat.neighbors()] = -t # Attach the left lead and its reversed copy. sys.attach_lead(lead) lead2 = kwant.Builder(kwant.TranslationalSymmetry((a, 0))) lead2[(lat(L, j) for j in range(W))] = 4 * t lead2[lat.neighbors()] = -t sys.attach_lead(lead2) return sys, lead def plot_conductance(sys, energies): # Compute conductance data = [] for energy in energies: smatrix = kwant.smatrix(sys, energy) data.append(smatrix.transmission(1, 0)) pyplot.figure() pyplot.plot(energies, data) pyplot.xlabel("energy [t]") pyplot.ylabel("conductance [e^2/h]") pyplot.show() def main(): sys, lead = make_system() # Check that the system looks as intended. # kwant.plot(sys) # Finalize the system. sys = sys.finalized() en = 3 sm = kwant.smatrix(sys, en) print('transmission by kwant: ',sm.transmission(0,0)) smatrix = sm.data sdags = (smatrix.conj().T) # As from Eq. (10) in kwant paper print((sdags[0,0]*smatrix[0,0] + sdags[0,1]*smatrix[0,1] + sdags[1,1]*smatrix[1,1]+ sdags[1,0]*smatrix[1,0])) # As from Eq. (47) in buttiker print(sdags[0,0]*smatrix[0,0]+sdags[1,1]*smatrix[1,1] - 2) # Call the main function if the script gets executed (as opposed to imported). # See <http://docs.python.org/library/__main__.html>. if __name__ == '__main__': main()

2 1

Transmission in ZGNR
by Abhishek Sharan 05 Dec '16

05 Dec '16

Hi! I am new to using kwant, so some of my questions might be naive. I need to compute conductance (or transmission) and fano factor of the shot noise of zig-zag graphene nanoribbon for a particular geometry and a set gate voltage and a set fermi energy. I can calculate the conductance of ZGNR for a particular geometry as a function of energy. I need to understand two things: 1. I assume setting the gate voltage means fixing the energy of the electrons and finding the transmission at that energy (right?) 2. I do not understand how do I set the fermi level in the system? I would appreciate if someone could clarify on this. -- Regards

2 1

Kwant-discuss December 2016