Mailman 3 December 2023 - Kwant-discuss

To to separate spins, electron and hole
by Khani Hosein Oct. 11, 2024

Oct. 11, 2024

Dear all, I am using Kwant to study a system with both spins and electron and hole, so the hopping matrix is 4X4. Now I want to know how to separate the spins, electron and hole. I study this through the "2.6. Superconductors: orbital degrees of freedom, conservation laws and symmetries" smatrix = kwant.smatrix(syst, energy) data.append(smatrix.submatrix((0, 0), (0, 0)).shape[0] -smatrix.transmission((0, 0), (0, 0)) +smatrix.transmission((0, 1), (0, 0))) I do not find more information about this for kwant. For my system, if I have 3 leads, and the hopping and onsite energy is set in this order: (e↑,0,0,0)- spin up electron,first row of the 4X4matrix (0,e↓,0,0)- spin down electron,second row of the 4X4matrix (0,0, h↑ ,0)- spin up hole,third row of the 4X4matrix (0,0, 0, h ↓ )- spin down hole,fourth row of the 4X4matrix I want to obtain the transmissions from 0 →2. smatrix = kwant.smatrix(syst, energy) The transmission from h↑ to e↑ is: smatrix.transmission((2, 1), (0, 2)) The transmission from h ↓ to e↑ is: smatrix.transmission((2, 1), (0, 3)) Is my understanding correct? Thanks very much in advance! Hosein Khani

4 5

3d structure model and add 3d leads
by araya0sun＠gmail.com Jan. 2, 2024

Jan. 2, 2024

Dear kwant users, Hello, I am a new user of kwant, I want to build a 3d structure model, and add leads, I refer to a similar code, but I keep getting errors during the process, the program says "RuntimeError: All sites of this builder have been deleted because an exception occurred during the execution of fill(): see above. ", I feel that it may be the position of the lead, but I do not know how to modify it, can you give me some suggestions to modify it? Thank you very much! *This is the code I have errors in: ---------------------------------------- import kwant import numpy as np from matplotlib import pyplot #3d test def syst_3d(a=16, b=16, c=10,t=1): lat = kwant.lattice.general([(0, 0.5, 0.5), (0.5, 0, 0.5), (0.5, 0.5, 0)]) # [(0,0,0),(0.25, 0.25, 0.25)]) # a,b= lat.sublattices syst = kwant.Builder() def cuboid_shape(pos): x, y, z = pos return 0 <= x < a and 0 <= y < b and 0 <= z < c syst[lat.shape(cuboid_shape, (0, 0, 0))] = 4 * t syst[lat.neighbors()] = -t sym_lead0 = kwant.TranslationalSymmetry(lat.vec((1, 0, 0))) lead0 = kwant.Builder(sym_lead0) lead_shape = lambda pos: (-b / 2 <= pos[1] < b / 2) and abs(pos[2]) < c lead0[lat.shape(lead_shape, (-1, 0, 0))] = 4 * t lead0[lat.neighbors()] = -t lead1 = lead0.reversed() syst.attach_lead(lead0) syst.attach_lead(lead1) return syst def main(): syst = syst_3d() kwant.plot(syst) if __name__ == '__main__': main() --------------------------------------------------- *This is the code I refer to, as if this works correctly: ------------------------------------------------------- import kwant import numpy as np from matplotlib import pyplot def syst_3d(W=3, r1=2, r2=4, a=1, t=1.0): lat = kwant.lattice.general(((a, 0, 0), (0, a, 0), (0, 0, a))) syst = kwant.Builder() def ring(pos): (x, y, z) = pos rsq = x**2 + y**2 return (r1**2 < rsq < r2**2) and abs(z) < 2 syst[lat.shape(ring, (0, -r2 + 1, 0))] = 4 * t syst[lat.neighbors()] = -t sym_lead0 = kwant.TranslationalSymmetry(lat.vec((-1, 0, 0))) lead0 = kwant.Builder(sym_lead0) lead_shape = lambda pos: (-W / 2 < pos[1] < W / 2) and abs(pos[2]) < 2 lead0[lat.shape(lead_shape, (0, 0, 0))] = 4 * t lead0[lat.neighbors()] = -t lead1 = lead0.reversed() syst.attach_lead(lead0) syst.attach_lead(lead1) return syst def main(): syst = syst_3d() kwant.plot(syst) if __name__ == '__main__': main() Sincerely, Yue Xiang

3 6

kwant.continuum.discretize scale factors?
by Chagaan Baatar Dec. 28, 2023

Dec. 28, 2023

Hello, Happy holidays to the happy Kwanters! Due to the holiday break, I finally found some time and trying to go over the 2020 quantum transport mini-workshop materials available at https://virtualscienceforum.org/quantum-transport-workshop/ <https://virtualscienceforum.org/quantum-transport-workshop/>. I noticed that one of the energy band plots for the Majorana wire (in Anton’s lecture) differs in the continuum version from that of the discretized version, by some scale factors in both x- and y- axes. I have attached the notebook (grabbed from above web site) here. Before executing any cells in the notebook, I would’ve expected the plots in cells #5 and #7 to look identical? Am I wrong? Does kwant.continuum.discretize introduce any additional scale factors, e.g. k_x ==> 2*k_x, intentionally or otherwise? I suppose I could go into the code and examine it myself, but I thought I should ask folks here first, as someone may have figured it out already. Thanks! Chagaan Baatar

2 1

[kwant] Introducing KPM Tools: Advanced KPM Expansions for Kwant
by pablo.perez.piskunow＠gmail.com Dec. 22, 2023

Dec. 22, 2023

Dear Kwant Community, I'm pleased to announce the release of "KPM Tools," an open-source Python package specifically designed to extend the Kernel Polynomial Method (KPM) functionalities within Kwant, focusing on closed tight-binding systems. ## Acknowledgment to Kwant: KPM Tools builds upon the solid foundation of Kwant. The package aims to complement and enhance Kwant's existing KPM features, adhering to the high-quality standards established by the Kwant project. See the original KPM implementation in Kwant: https://kwant-project.org/doc/1/tutorial/kpm https://kwant-project.org/doc/1/reference/kwant.kpm ## About KPM Tools: KPM Tools expands the KPM capabilities in Kwant, offering advanced expansions of spectral functions like Density of States, Green's Functions, Kubo Conductivity, and Chern Markers. We introduce enhanced tools systems with periodic boundaries, including new KPM vector factories and adapted velocity and distance operators. Last but not least, I include an extremely efficient time evolution operator expansion. All the features are exemplified in the tutorials: https://kpm-tools.readthedocs.io/en/latest/tutorials.html KPM Tools is available for installation via pip: `` $ pip install kpm-tools ``` You can find more details in the `kpm-tools` repository: https://github.com/piskunow/kpm-tools and the documentation: https://kpm-tools.readthedocs.io https://kpm-tools.readthedocs.io/en/latest/api.html ## Contributions Welcome: I invite contributions, particularly in improving documentation and the 'concatenator' function/module. The documentation consists mainly of Jupyter Notebooks, allowing for easy local testing and updates. As my time to dedicate to further development is limited, your contributions, whether in code, documentation, or ideas, are not just welcome but crucial for the growth of KPM Tools. Pull requests and collaborative efforts will significantly enhance the utility and reach of this package. Looking forward to your insights, feedback, active participation in improving KPM Tools, and seeing how KPM Tools can contribute to your research and projects. Best regards, Pablo Piskunow

4 3

Plotting Andreev Spectrum of a 4 \pi Josephson Junction
by Subhadeep Chakraborty Dec. 15, 2023

Dec. 15, 2023

Hi Kwant users ! I was trying to plot the 4 \pi periodic Andreev spectrum of a topological Josephson junction. I was using a finite TSC-QSH-TSC junction and trying to calculate the spectrum as suggested in ( https://mail.python.org/archives/list/kwant-discuss@python.org/message/BYVQ… ). I have attached my code and the plot I got from the simulation below. *Am I doing something wrong?* __________________________________________________________________________________________________ # InAs Sample # TSC-QSH-TSC Josephson Junction # 4 \pi periodicity of Andreev Spectrum import kwant import numpy as np import math ## import matplotlib matplotlib.use('Agg') ## # For plotting from matplotlib import pyplot from matplotlib import cm import scipy.sparse.linalg as sla # For matrix support import tinyarray tau_z = tinyarray.array([[1,0], [0,-1]]) tau_x = tinyarray.array([[0,1], [1,0]]) tau_y = tinyarray.array([[0,-1j], [1j,0]]) I4 = tinyarray.array([[1,0,0,0], [0,1,0,0],[0,0,1,0],[0,0,0,1]]) SzSz = tinyarray.array([[1,0,0,0], [0,-1,0,0],[0,0,-1,0],[0,0,0,1]]) SxSx = tinyarray.array([[0,0,0,1], [0,0,1,0],[0,1,0,0],[1,0,0,0]]) SySy = tinyarray.array([[0,0,0,-1], [0,0,1,0],[0,1,0,0],[-1,0,0,0]]) S2Sx = tinyarray.array([[0,0,0,1], [0,0,1,0],[0,1,0,0],[1,0,0,0]]) SySx = tinyarray.array([[0,0,0,-1j], [0,0,-1j,0],[0,1j,0,0],[1j,0,0,0]]) S3Sx = tinyarray.array([[0,0,0,-1j], [0,0,-1j,0],[0,1j,0,0],[1j,0,0,0]]) SzI = tinyarray.array([[1,0,0,0], [0,1,0,0],[0,0,-1,0],[0,0,0,-1]]) ISz = tinyarray.array([[1,0,0,0], [0,-1,0,0],[0,0,1,0],[0,0,0,-1]]) SzSx = tinyarray.array([[0,1,0,0], [1,0,0,0],[0,0,0,-1],[0,0,-1,0]]) ISx = tinyarray.array([[0,1,0,0], [1,0,0,0],[0,0,0,1],[0,0,1,0]]) ISy = tinyarray.array([[0,-1j,0,0], [1j,0,0,0],[0,0,0,-1j],[0,0,1j,0]]) SyI = tinyarray.array([[0,0,-1j,0], [0,0,0,-1j],[1j,0,0,0],[0,1j,0,0]]) SxI = tinyarray.array([[0,0,1,0], [0,0,0,1],[1,0,0,0],[0,1,0,0]]) SySz = tinyarray.array([[0,0,-1j,0], [0,0,0,1j],[1j,0,0,0],[0,-1j,0,0]]) SzSy = tinyarray.array([[0,-1j,0,0], [1j,0,0,0],[0,0,0,1j],[0,0,-1j,0]]) SxSz = tinyarray.array([[0,0,1,0], [0,0,0,-1],[1,0,0,0],[0,-1,0,0]]) SxSy = tinyarray.array([[0,0,0,-1j], [0,0,1j,0],[0,-1j,0,0],[1j,0,0,0]]) # Define the tight-binding system def make_system(Bfields, W=100, L1 = 50 ; L2=100 ; L=150 ; Delta = 1.0): # Define InAs parameters A=37.0 ; B=-660.0 ; D= 0.0 ; M=-7.8 ; theta=Bfields*np.pi ; # superconducting phase bias syst = kwant.Builder() # Here, we are only working with square lattices a = 10 lat = kwant.lattice.square(a,norbs=8) # Define the scattering region #----------------------------------------------------------------------------------------------- #========================================================================================================= # Define left topological superconductor for j in range(0,W): for i in range(0, L1): # On-site Hamiltonian syst[lat(i, j)] = -4*D*np.kron(np.eye(4),tau_z)/a**2 - 4*B*np.kron(ISz,tau_z)/a**2 + M*np.kron(ISz,tau_z) + Delta*(np.cos(theta))*np.kron(np.eye(4), tau_x) + Delta*(np.sin(theta))*np.kron(np.eye(4), tau_y) if i > 0: syst[lat(i, j), lat(i - 1, j)] = D*np.kron(np.eye(4),tau_z)/a**2 + B*np.kron(ISz,tau_z)/a**2 + A*np.kron(SzSx,tau_z)/(2*1j*a) if j > 0: syst[lat(i, j), lat(i, j - 1)] = D*np.kron(np.eye(4),tau_z)/a**2 + B*np.kron(ISz,tau_z)/a**2 + A*1j*np.kron(ISy,tau_z)/(2*a) #--------------------------------------------------------------------------------------------------------------------- # Define Middle quantum spin-Hall system for i in range(L1, L2): syst[lat(i, j)] = -4*D*np.kron(np.eye(4),tau_z)/a**2 - 4*B*np.kron(ISz,tau_z)/a**2 + M*np.kron(ISz,tau_z) if i > 0: syst[lat(i, j), lat(i - 1, j)] = D*np.kron(np.eye(4),tau_z)/a**2 + B*np.kron(ISz,tau_z)/a**2 + A*np.kron(SzSx,tau_z)/(2*1j*a) if j > 0: syst[lat(i, j), lat(i, j - 1)] = D*np.kron(np.eye(4),tau_z)/a**2 + B*np.kron(ISz,tau_z)/a**2 + A*1j*np.kron(ISy,tau_z)/(2*a) #------------------------------------------------------------------------------------------------------- # Define right topological superconductor for i in range(L2, L): # On-site Hamiltonian syst[lat(i, j)] = -4*D*np.kron(np.eye(4),tau_z)/a**2 - 4*B*np.kron(ISz,tau_z)/a**2 + M*np.kron(ISz,tau_z) + Delta*np.kron(np.eye(4), tau_x) if i > 0: syst[lat(i, j), lat(i - 1, j)] = D*np.kron(np.eye(4),tau_z)/a**2 + B*np.kron(ISz,tau_z)/a**2 + A*np.kron(SzSx,tau_z)/(2*1j*a) if j > 0: syst[lat(i, j), lat(i, j - 1)] = D*np.kron(np.eye(4),tau_z)/a**2 + B*np.kron(ISz,tau_z)/a**2 + A*1j*np.kron(ISy,tau_z)/(2*a) syst = syst.finalized() return syst #%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% #%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% B_min = 0.0 ; B_max = 8.0 ; npts=51 ; Bfields = np.linspace(B_min, B_max, npts) data=[]; for i in np.arange(len(Bfields)): syst = make_system(Bfields[i]) ham_mat = syst.hamiltonian_submatrix(args=[Bfields], sparse=True) # we only calculate the k lowest eigenvalues ev = sla.eigsh(ham_mat, k=4, which='SM', return_eigenvectors=False) data.append(ev) pyplot.figure() pyplot.plot(Bfields, data) pyplot.xlabel("Phase [in units of pi]") pyplot.ylabel("energy [t]") #pyplot.show() pyplot.savefig('InAs_Andreev_Spectrum_k=4.pdf') Thanks in advance.

2 2

Conda distribution -- how do you find the libraries kwant is linked to?
by poatajoseph＠gmail.com Dec. 7, 2023

Dec. 7, 2023

Hi all, After looking through old threads I came across [1], which discusses the effect LAPACK-level parallelization has on preformance. For the user that started that thread, they saw improvements by changing their environmental variables. This I understand, what is confusing me is how you figure out which library a Kwant distribution is linked to. E.g. without setting these independently and observing what effect each has on performance, how can I tell which of the following environmental variables need to be changed? OPENBLAS_NUM_THREADS OMP_NUM_THREADS MKL_DYNAMIC MKL_NUM_THREADS I used conda to install Kwant on my M1 Macbook air. Where should I be looking in the root directory of my Kwant distribution for this information? Or is there another way to check this? Thanks, Joe

2 2