Mailman 3 March 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))

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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

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Kwant for bulk system
by Weiyuan Tong 08 Jun '16

08 Jun '16

Dear all, I want to calculate the conductance and the band structure of a bulk graphene system.(infinite in y direction) I have checked the source code for the calculation of band structure. https://github.com/kwantproject/kwant/blob/7c55b0cb2d0dec163e5483dea8ffdbc8… It seems that we can get the sys.cell_hamiltonian and hopping between the sys.cell_hamiltonian in kwant. In y direction, we can also have sys.cell_hamiltonian and hopping, then it can be extended to infinite in y direction: V^\dagger e^{iky} + H + Ve^{-iky}. I am not familiar with kwant coding. Can anyone help me to write some code lines to do these calculations? Or you can also change the Tutorial 2.2.3 as an example. Thanks in advance! Best wishes Weiyuan Tong

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MUMPS parallel support
by Abdulkareem Afandi 31 Mar '16

31 Mar '16

Dear Kwant community, Is there a particular reason why kwant is configured to work with sequential MUMPS instead of parallel? I am working with very large systems (~10^8 sites) on a well equipped computer cluster, and was wondering if I could easily extend MUMPS support to parallel instead of just sequential? Best regards, Abdul

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Spin LDOS
by Hamzah Fauzi 25 Mar '16

25 Mar '16

Hello, I am trying to plot spin-up and spin-down LDOS in quantum Hall, but always got the following error message: Traceback (most recent call last): File "C:\Python34\codes\qhe.py", line 129, in <module> kwant.plotter.map(sys, d) File "C:\Python34\lib\site-packages\kwant\plotter.py", line 1547, in map img, min, max = mask_interpolate(coords, value, a, method, oversampling) File "C:\Python34\lib\site-packages\kwant\plotter.py", line 1441, in mask_interpolate raise ValueError("The number of sites doesn't match the number of" ValueError: The number of sites doesn't match the number ofprovided values. I tried to following the solution offered by Anton and Michael here ( https://www.mail-archive.com/kwant-discuss@kwant-project.org/msg00006.html) by reshaping the array like this *def density_lead0(sys, energy, args):* * wf = kwant.wave_function(sys, energy, args)* * prob = (abs(wf(0))**2)* * return np.sum(prob.reshape(-1,2), axis=1)* unfortunately, I always got similar error message. Any advice will be greatly appreciated. Best regards, Fauzi PS. This is the full code: import math from cmath import exp import numpy import numpy as np from matplotlib import pyplot import kwant from kwant.digest import gauss # For matrix support import tinyarray # Pauli matrices 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]]) #define hopping energy t = 1 #Zeeman energy e_z = 0.015 #peierls substitution def hopping(sitei, sitej, phi, salt): xi, yi = sitei.pos xj, yj = sitej.pos return -t * exp(-0.5j * phi * (xi - xj) * (yi + yj)) * sigma_0 def onsite(site, phi, salt): return 0.05 * gauss(repr(site), salt)*sigma_0 + 4 * t *sigma_0 + e_z*sigma_z def make_system(L=40): def central_region(pos): x, y = pos return -L < x < L and \ abs(y) < L - 27.5 * math.exp(-x**2 / 20**2) lat = kwant.lattice.square() sys = kwant.Builder() sys[lat.shape(central_region, (0, 0))] = onsite sys[lat.neighbors()] = hopping sym = kwant.TranslationalSymmetry((-1, 0)) lead = kwant.Builder(sym) lead[(lat(0, y) for y in range(-L + 1, L))] = 4 * t *sigma_0 + e_z*sigma_z #disorder-free lead[lat.neighbors()] = hopping sys.attach_lead(lead) sys.attach_lead(lead.reversed()) return sys.finalized() sys = make_system() energy = 0.10 #kwant.plot(sys) # Calculate and plot QHE conductance plateaus. reciprocal_phis = numpy.linspace(4, 60, 150) conductances = [] for phi in 1 / reciprocal_phis: smatrix = kwant.smatrix(sys, energy, args=[phi, ""]) conductances.append(smatrix.transmission(1, 0)) pyplot.plot(reciprocal_phis, conductances) pyplot.show() # Calculate and plot a QHE edge state. def density_lead0(sys, energy, args): wf = kwant.wave_function(sys, energy, args) prob = (abs(wf(0))**2) return np.sum(prob.reshape(-1,2), axis=1) def density_lead1(sys, energy, args): wf = kwant.wave_function(sys, energy, args) prob = (abs(wf(1))**2) return np.sum(prob.reshape(-1,2), axis=1) d = density_lead0(sys, energy, [1/40.0, ""]) + density_lead1(sys, energy, [1/40.0, ""]) kwant.plotter.map(sys, d)

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2D materials other than graphene.
by Mohammed Ghadiyali 18 Mar '16

18 Mar '16

Dear All, I am currently planning to work on stanene (2D tin), it is a quantum spin Hall insulator and other topological insulator. Majority of the work in this field is done by using VASP and other DFT code based tools. I would like to know if one can build topological insulators and 2D materials other than graphene (like stanene) in KWANT and compute it's electronic properties, such as edges states, chiral current etc. If yes can you can direct me to a resource or reference. Thank You,Ghadiyali Mohammed Kader,Research Scholar,Physics Dept.University of Mumbai.

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Re: [Kwant] Quantum Hall effect in bilayer graphene
by 고운 18 Mar '16

18 Mar '16

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Quantum Hall effect in bilayer graphene
by 고운 17 Mar '16

17 Mar '16

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Table of values intight-binding calculations
by james edward hernandez 13 Mar '16

13 Mar '16

Hello. I was wondering if there is any way to view a table of values corresponding to the plots of the electronic properties such as band structure, and conductance versus magnetic field for Hall effect systems. Regards, James

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Re: [Kwant] Starting with a sample
by Sumit Ghosh 13 Mar '16

13 Mar '16

Hi Ravish, This is where you are supposed to start. http://kwant-project.org/doc/1/tutorial/ And of course this paper http://downloads.kwant-project.org/doc/kwant-paper.pdf This section will give you an idea how to 'tell' KWANT your Hamiltonian. http://kwant-project.org/doc/1/tutorial/tutorial1 Now you must realise KWANT is not DFT, so optimisation or relaxation does not appear in the picture. It is the geometry rather than the coordinate that really matters. I would suggest to go through some basic tight binding text before you jump into KWANT. And remember, the most essential part of tight binding model is the Hamiltonian. -- Sumit Ghosh Spintronics Theory Group PSE Division KAUST -- ------------------------------ This message and its contents, including attachments are intended solely for the original recipient. If you are not the intended recipient or have received this message in error, please notify me immediately and delete this message from your computer system. Any unauthorized use or distribution is prohibited. Please consider the environment before printing this email.

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Starting with a sample
by Ravish Jamnal 12 Mar '16

12 Mar '16

Dear All, I am new to kwant and wanted to know if there is any need of knowing the Hamiltonian of the sample? Or what all I need other than the coordinates of the atoms, to get started? Regards

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Using Graphene in kwant
by Ravish Jamnal 11 Mar '16

11 Mar '16

Dear All, Hello, I wanted to know if I need to stabilize or optimize Graphene before using in kwant. After that, how can I calculate the Hamiltonian for Graphene. Best Regards Ravish

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QHE edge state
by Hamzah Fauzi 10 Mar '16

10 Mar '16

Hello, In a 2D map of QHE edge state calculated using the example code below, why there is no transmitted mode appeared in the upper arm? If my understanding is correct, the mode should be propagated to the upper arm as well (Buttiker picture). Do I need to attach 2 or 3 more leads (a 4-probe configuration) to resolve the above mentioned issue? Best regards, Fauzi import math from cmath import exp import numpy from matplotlib import pyplot import kwant from kwant.digest import gauss def hopping(sitei, sitej, phi, salt): xi, yi = sitei.pos xj, yj = sitej.pos return -exp(-0.5j * phi * (xi - xj) * (yi + yj)) def onsite(site, phi, salt): return 0.05 * gauss(repr(site), salt) + 4 def make_system(L=75): def central_region(pos): x, y = pos return -L < x < L and \ abs(y) < L - 70 * math.exp(-x**2 / 20**2) lat = kwant.lattice.square() sys = kwant.Builder() sys[lat.shape(central_region, (0, 0))] = onsite sys[lat.neighbors()] = hopping sym = kwant.TranslationalSymmetry((-1, 0)) lead = kwant.Builder(sym) lead[(lat(0, y) for y in range(-L + 1, L))] = 4 lead[lat.neighbors()] = hopping sys.attach_lead(lead) sys.attach_lead(lead.reversed()) return sys.finalized() sys = make_system() energy = 0.15 kwant.plot(sys) # Calculate and plot QHE conductance plateaus. reciprocal_phis = numpy.linspace(4, 100, 200) conductances = [] for phi in 1 / reciprocal_phis: smatrix = kwant.smatrix(sys, energy, args=[phi, ""]) conductances.append(smatrix.transmission(1, 0)) pyplot.plot(reciprocal_phis, conductances) pyplot.show() # Calculate and plot a QHE edge state. def density(sys, energy, args, lead_nr): wf = kwant.wave_function(sys, energy, args) return (abs(wf(lead_nr))**2).sum(axis=0) d = density(sys, energy, [1/40.0, ""], 0) kwant.plotter.map(sys, d)

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Problem with kwant.plotter.map
by Sudin Ganguly 03 Mar '16

03 Mar '16

Dear Sir, Recently I'm studying LDOS in presence of Rashba. For that I'm using kwant.plotter.map. It works fine if I create a system without spin. But it doesn't work if I include two types of spin. I understand that, in presence of Rashba, each lattice site has 2 degrees of freedom due to spin up and spin down. As a result when I use the following code, "ham_mat = sys.hamiltonian_submatrix(sparse=True) evecs = sla.eigsh(ham_mat, k=100, which='SM')[1]" I'll have eigen vectors twice the number of lattice sites, present in the system. Regarding this I have two questions. 1. How do I know the position of the lattice sites when I'm going to plot LDOS on my own. 2. Since kwant.plotter.map is a very nice tool to plot LDOS, can I use this to plot LDOS in my Rashba case. with Regards, Sudin

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