Mailman 3 January 2015 - 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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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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Unable to update to Tinyarray 1.0.5
by Bas Nijholt Jan. 30, 2015

Jan. 30, 2015

Hi, I’ve installed kwant through Homebrew, Michaels provided method. Now I’m trying to update Tinyarray through pip and get the following message: Bass-MacBook-Pro:Desktop basnijholt$ pip install tinyarray Requirement already satisfied (use --upgrade to upgrade): tinyarray in /usr/local/lib/python2.7/site-packages Bass-MacBook-Pro:Desktop basnijholt$ pip install tinyarray --upgrade Collecting tinyarray from https://pypi.python.org/packages/source/t/tinyarray/tinyarray-1.0.5.tar.gz#… Using cached tinyarray-1.0.5.tar.gz Installing collected packages: tinyarray Found existing installation: tinyarray 1.0.2 Can't uninstall 'tinyarray'. No files were found to uninstall. Running setup.py install for tinyarray building 'tinyarray' extension clang -fno-strict-aliasing -fno-common -dynamic -I/usr/local/include -I/usr/local/opt/sqlite/include -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.10.sdk -I/Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.10.sdk/System/Library/Frameworks/Tk.framework/Versions/8.5/Headers -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -I/usr/local/Cellar/python/2.7.9/Frameworks/Python.framework/Versions/2.7/include/python2.7 -c src/arithmetic.cc -o build/temp.macosx-10.10-x86_64-2.7/src/arithmetic.o clang -fno-strict-aliasing -fno-common -dynamic -I/usr/local/include -I/usr/local/opt/sqlite/include -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.10.sdk -I/Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.10.sdk/System/Library/Frameworks/Tk.framework/Versions/8.5/Headers -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -I/usr/local/Cellar/python/2.7.9/Frameworks/Python.framework/Versions/2.7/include/python2.7 -c src/array.cc -o build/temp.macosx-10.10-x86_64-2.7/src/array.o clang -fno-strict-aliasing -fno-common -dynamic -I/usr/local/include -I/usr/local/opt/sqlite/include -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.10.sdk -I/Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.10.sdk/System/Library/Frameworks/Tk.framework/Versions/8.5/Headers -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -I/usr/local/Cellar/python/2.7.9/Frameworks/Python.framework/Versions/2.7/include/python2.7 -c src/functions.cc -o build/temp.macosx-10.10-x86_64-2.7/src/functions.o clang++ -bundle -undefined dynamic_lookup -L/usr/local/lib -L/usr/local/opt/sqlite/lib -isysroot /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.10.sdk build/temp.macosx-10.10-x86_64-2.7/src/arithmetic.o build/temp.macosx-10.10-x86_64-2.7/src/array.o build/temp.macosx-10.10-x86_64-2.7/src/functions.o -o build/lib.macosx-10.10-x86_64-2.7/tinyarray.so Successfully installed tinyarray-1.0.2 Bass-MacBook-Pro:Desktop basnijholt$ Regards, Bas

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Re: [Kwant] Shape definition
by Lee Kwok-Long Jan. 21, 2015

Jan. 21, 2015

Dear Joe， Thanks a lot for your reply. Also, I want to tell the authors that I can not receive the reply through email. Is my email address added to mailing list? Kwok-Long Lee

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Shape definition
by Lee Kwok-Long Jan. 20, 2015

Jan. 20, 2015

Dear all， I note that all the shapes of the scattering regions in the tutorials can be simply realized by using one sentence like "return x ** 2 + y ** 2 < r ** 2". I want to try a scattering region with a shape: 0<=x<=5， 0<=y<=10; 6<=x<=10，-5<=y<=15.So it is a combined two square regions. I know that it is very convenient to add and delete sites in Kwant, but is there a simple way to define this scattering region? Can anyone help me with this example? Thanks in advance. Kwok-Long Lee

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About different transport regime
by ANANT Jan. 19, 2015

Jan. 19, 2015

Hello! I have a question about the conductance formula that you have given in Kwant paper.It reads as summation over elctrodes of the scattering matrix.My question is about how the calculation are being done in different regimes as transmission formula gets changed in different regimes.In diffusive regime its no of modes multiplied lambda/l+lambda i.e.(M*l/L+l).How kwant deals with it?And also what about the (-del F/del E ) i.e differene in energy levels in both the leads(say we have only 2).My apology if it's more of a physics question,but I want to calculate with hands.Any intuition is appreciated.

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About LDOS map for 3 d system's surface
by ANANT Jan. 4, 2015

Jan. 4, 2015

Hello ! I am trying to plot the surface LDOS of a 3d cubic lattice .But I am having an error .Please have a look at the code this code is for topological insulator on a cubic lattice.It generates the correct band structure but not LDOS and conductance:I am not mentioning the libraries to keep it small.I have tried using the 3rd dimension zero it still not working lat = kwant.lattice.general([(1,0,0),(0,1,0),(0,0,1)]) # All pauli matrices to define pseuospin and spin degree of freedom. s_0=np.identity(2) s_z =np.array([[1, 0], [0, -1]]) s_x = np.array([[0, 1], [1, 0]]) s_y = np.array([[0, -1j], [1j, 0]]) # 4x4 matrices g1= tinyarray.array(np.kron(s_x,s_x)) g2= tinyarray.array(np.kron(s_y,s_x)) g3 = tinyarray.array(np.kron(s_z,s_x)) g4= tinyarray.array(np.kron(s_0,s_y)) g5 = tinyarray.array(np.kron(s_0,s_z)) def make(a = 14 ,b = 5, c= 0,t=1,delta =.4,m =2): sym = kwant.TranslationalSymmetry((1,0,0)) sys = kwant.Builder() def cube(pos): x,y,z = pos return 0<=x<=a and 0<=y<=b and 0<=z<=c #Onsite energy sys[lat.shape(cube,(0,0,0))] = m*tau_0z #hopping in x direction sys[kwant.builder.HoppingKind((1, 0,0), lat,lat)] = -t*tau_0z - 1j*delta*tau_zx #hopping in y direction sys[kwant.builder.HoppingKind((0,1,0), lat,lat)] = -t*tau_0z + 1j*delta*tau_0y #hopping in z direction sys[kwant.builder.HoppingKind((0,0,1), lat,lat)] = -t*tau_0z - 1j*delta*tau_xx #leads lead = kwant.Builder(sym) def cube1(pos): x,y,z = pos return 0<=y<=b and 0<=z<=c #Onsite energy lead[lat.shape(cube,(0,0,0))] = m*tau_0z #hopping in x direction lead[kwant.builder.HoppingKind((1, 0,0), lat,lat)] = -t*tau_0z - 1j*delta*tau_zx #hopping in y direction lead[kwant.builder.HoppingKind((0,1,0), lat,lat)] = -t*tau_0z + 1j*delta*tau_0y #hopping in z direction sys[kwant.builder.HoppingKind((0,0,1), lat,lat)] = -t*tau_0z - 1j*delta*tau_xx sys.attach_lead(lead) sys.attach_lead(lead.reversed()) return sys.finalized() return sys energy =.5 def density(sys, energy, args, lead_nr): wf = kwant.wave_function(sys, energy, args) return(abs(wf(lead_nr))**2).sum(axis=0) def lds(sys, energy, args, lead_nr): dos = kwant.ldos(sys, energy, args) return dos #main funcation call def main(): sys = make() kwant.plot(sys, site_size=0.19, site_lw=0.01, hop_lw=0.03,site_color = 'c') d = density(sys, energy, [.0, "" ], 0) kwant.plotter.map(sys,d) s = lds(sys,energy,[.0, "" ], 0) kwant.plotter.map(sys,s) if __name__ == '__main__': main() the error is : ValueError: Only 2D systems can be plotted this way.

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