Kwant-discuss June 2021

kwant-discuss@python.org

14 participants
13 discussions

current-voltage diagram
by loojoo026＠gmail.com 08 Apr '22

08 Apr '22

dear all I have done my project using Kwant and I have drawn a conductance-energy diagram for the system. The question I have is how can I get the current-voltage diagram? thanks Leo

4 4

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

Graphene Conductor-Superconductor Conductance above Gap
by Henry Axt 21 Feb '22

21 Feb '22

Hello, I set up a graphene lattice with periodic boundary conditions that is connected to a superconductor (simulated with an electron and hole lattice). When observing the transmission between the electron and hole lattice, I see a small amount conductance above the superconducting gap. I do not see this with something like a square lattice. What could explain this?

2 1

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

module 'kwant.linalg._mumps' has no attribute 'dmumps' ERROR
by BHAVYA BHARDWAJ 02 Sep '21

02 Sep '21

Repected Members, I am a B.Tech Student using Kwant for simulations.Python Version: 3.7.8 Kwant Version: 1.4.2Ubuntu 20The Error I faced is given below. AttributeError Traceback (most recent call last) <ipython-input-6-c80da766c4bb> in <module> 17 pyplot.ylabel("conductance [e^2/h]") 18 pyplot.show() ---> 19 solving(model.tokwant()) <ipython-input-6-c80da766c4bb> in solving(sys) 7 energy = ie * 0.01 8 # compute the scattering matrix at a given energy ----> 9 smatrix = kwant.greens_function(sys, energy,check_hermiticity=False) 10 # compute the transmission probability from lead 0 to 11 # lead 1 ~/Downloads/112358/lib/python3.7/site-packages/kwant/_common.py in inner(*args, **kwargs) 70 if sig.bind(*args, **kwargs).arguments.get(parameter_name): 71 warn() ---> 72 return f(*args, **kwargs) 73 74 return inner ~/Downloads/112358/lib/python3.7/site-packages/kwant/solvers/common.py in greens_function(self, sys, energy, args, out_leads, in_leads, check_hermiticity, params) 485 rhs = sp.bmat([[i for i in linsys.rhs if i.shape[1]]], 486 format=self.rhsformat) --> 487 flhs = self._factorized(linsys.lhs) 488 data = self._solve_linear_sys(flhs, rhs, kept_vars) 489 ~/Downloads/112358/lib/python3.7/site-packages/kwant/solvers/mumps.py in _factorized(self, a) 102 def _factorized(self, a): 103 inst = mumps.MUMPSContext() --> 104 inst.factor(a, ordering=self.ordering) 105 return inst 106 ~/Downloads/112358/lib/python3.7/site-packages/kwant/linalg/mumps.py in factor(self, a, ordering, ooc, pivot_tol, reuse_analysis, overwrite_a) 318 row, col, data) 319 else: --> 320 self.analyze(a, ordering=ordering, overwrite_a=overwrite_a) 321 322 self.mumps_instance.icntl[22] = 1 if ooc else 0 ~/Downloads/112358/lib/python3.7/site-packages/kwant/linalg/mumps.py in analyze(self, a, ordering, overwrite_a) 227 228 if dtype != self.dtype: --> 229 self.mumps_instance = getattr(_mumps, dtype+"mumps")(self.verbose) 230 self.dtype = dtype 231 AttributeError: module 'kwant.linalg._mumps' has no attribute 'dmumps' Kindly guide me so I can overcome this error. Thank You, Regards, Bhavya Bhardwaj

2 4

3D structure
by tavakkolidjawad 19 Jul '21

19 Jul '21

Dear all In the following code I have defined a three-dimensional structure. The geometry of the lead and the scattering region are the same, but the lead is not ploted as I expected. I expected the lead to have a cubic structure. What is the problem with my code? Thanks Javad tavakoli ############################################################################ ############################################################################ import kwant lat = kwant.lattice.general([(0, 0.5, 0.5), (0.5, 0, 0.5), (0.5, 0.5, 0)], [(0, 0, 10), (0.25, 0.25, 10.25)], name=['a1', 'a2']) a1, a2 = lat.sublattices def make_system(a=10, b=10, c=30): syst = kwant.Builder() def cuboid_shape(pos): x, y, z = pos return 0 <= x < a and 0 <= y < b and 0 <= z < 10 syst[a1.shape(cuboid_shape, (0, 0, 0))] = 1 syst[a2.shape(cuboid_shape, (0, 0, 0))] = 1 syst[lat.neighbors()] = 1 def lead_shape(pos): x,y,z = pos return 0 <= x < a and 0 <= y < b and 10 <= z < 25 lead = kwant.Builder(kwant.TranslationalSymmetry((0,0,1))) lead[a1.shape(lead_shape, (0, 0, 10))] = 1 lead[a2.shape(lead_shape, (0, 0, 10))] = 1 lead[lat.neighbors()] = 1 syst.attach_lead(lead) syst.attach_lead(lead.reversed()) return syst , lead def main(): syst,lead= make_system() kwant.plot(syst) syst,lead = make_system(a=1.1, b=1.1, c=1.1) syst.attach_lead(lead) if __name__ == '__main__': main() ###########################################################################

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Inquiry about Kwant boundstate algorithm (unphysical spectra at some sets of parameters)
by Zhang, Chi 25 Jun '21

25 Jun '21

Dear Colleagues, Hi, we are 2 students at Imperial College looking to incorporate your boundstate algorithm (https://scipost.org/submissions/1711.08250v1<https://scipost.org/submissions/1711.08250v1/>) in the context of a lateral Josephson junction. The code we used was copied and pasted from here: ( https://gitlab.kwant-project.org/jbweston/kwant/-/blob/feature/boundstate/k…) As an exercise we are trying to reproduce fig. 9 in this paper. Implementing the same parameters, we managed to obtain similar graphs shown below for a value of t=0.7. [cid:d6350847-a84d-413c-966e-9f76a7e16b14] However, we notice that at some values of t, the boundstate algorithm starts yielding non-physical results. Examples include: 1. 1. At t=-1 (which is what we assumed t to be initially from the captions in fig. 7), the algorithm returned energies above the band gap in the JJ in topological regime for some values of phi, the phase difference, and returned true values for some values of phi but not for others in the trivial regime. 2. [cid:ab6b6f7d-c949-4867-a1de-fc904e9d617f] 1. In the B scan for t=-1 boundstates start disappearing from B=0.325 onwards, well before crossing the degeneracy point, and in the topological regime they do not line up with the band edge. 2. [cid:1390ff07-aa3a-4545-ae1b-11b041706548] 1. We also noticed that the algorithm results are dependent on the system setup. To be able to independently replicate fig. 9 my partner and I set up a 2-site (left lead - super - normal - right lead) and 3-site (left lead - super - normal - super - right lead) system respectively to implement the phase from crossing the S-N interface. A schematic of this is shown below. 2. [cid:ccd40751-9e75-4c9f-9dc1-66343648e586] 3. While most standard kwant functionalities seem to recognise the 2 systems are equivalent to each other, we obtained drastically different results from the boundstate algorithm. Examples include a t-scan at B=1 to uncover possible t values where physical ABS spectra could be returned. 4. [cid:d9ca0c7e-5d9f-4546-aadb-091d36aa3542] 5. 2 site 3 site 6. (We checked that the thing causing the drastically different behaviour is the number of sites in the system. We were able to replicate each other's results only by changing the number of sites in the scattering region.) 1. We plotted f(E) in the find_boundstate function for t=-1, B=0.3 (where the algorithm succeeds in detecting the bound state) and B=0.35 (where the algorithm fails to do so), respectively. We noticed that the 2 roots from B=0.3 which are validated to be the true bound states are omitted in B=0.35, not because the validation operator rejects them, but because min_eigenvalue() (or lowest value of sparse_diag()) at these 2 energies indeed returned a value much larger than tol=1e-8 (0.003). We incremented the B field to see when the boundstate to no-boundstate transition occurs and it's at B=0.325 that the min_eigenvalue suddenly shoots up to 1e-4 (for B=0.324 we have 1e-9). We do not understand how this comes to be. 2. [cid:b7e35a85-363c-47d1-b756-52827f73d3f5] 3. The above disappearance of boundstates past B=0.325 is encountered when we set sparse=False too. We would like to know if similar problems with the boundstate algorithm have been encountered before, and if so, what do these signatures tell us is wrong, or does this indeed suggest something is incomplete in the implementation? Finally, we would also like to ask about your specific system setup in Kwant to obtain figure 9, as well as the parameter t that was used, as this was not specified explicitly. Many thanks in advance for answering our query! Sincerely, Chi Zhang & Ryan Tiew Blackett Laboratory Imperial College London

4 3

To to separate spins, electron and hole
by Khani Hosein 22 Jun '21

22 Jun '21

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

3 4

Plotting band structure of 2D continuum system in 1D strip with domain wall
by thauwa＠gmail.com 19 Jun '21

19 Jun '21

Hi all, I am somewhat new to Kwant and am trying to achieve the following: I have a 2D 3-band continuum model that I want to see edge states of using band and density diagrams via a 1D real-space strip. I make the system finite in the x direction (implying translational symmetry in the y direction, making k_y a good quantum number and so constant). I setup the domain wall by choosing between two values for a potential, dependent on whether the site is before length/2 or after. I use kwant.continuum.discretize() for builder(). However, I am having trouble with the setup in general. For one, I cannot seem to apply translational symmetry to builder() because I am not sure what vector to use (I tried (0,1) and (1,0)), but to no avail. Second, if I proceed without translational symmetry, kwant.plotter.bands(syst, show=False) gives me "TypeError: Expecting an instance of InfiniteSystem." When I browsed the email archives, people suggested syst.leads[0], etc: but the issue is that I don't have these leads explicitly and that gives me an error. My understanding is that I can get a proper band diagram showing edge states if I plot eigenvalues from looping through different values of k_y that I fixed earlier. However, I don't think I saw examples of the Kwant examples doing it this way. So, it seems as if I have confused some basic applications in Kwant. Would someone mind clarifying my confusions for me? All I want to see is the a typical band structure diagram for this 3-band continuum model in a domain wall setup. Following is my code (I know that the given Hamiltonian will not give edge states, but I just want to get the code working for starters). Thank you for your time! # Minimal example import kwant.continuum import kwant import numpy as np import matplotlib.pyplot as plt import tinyarray import scipy lat_const = 3.19 # lattice constant hami = """ [[2* t0 * ((1-(2*((1/2)*k_x*a))**2/2)+2*(1-(((1/2)*k_x*a))**2/2)*(1-((momentumY*a*sqrt(3)/2))**2/2))+e1, M1(x,y)-2*sqrt(3)*t2*(((1/2)*k_x*a))*((momentumY*a*sqrt(3)/2)) + 2*1j*t1*((2*((1/2)*k_x*a)) + (((1/2)*k_x*a))*(1-((momentumY*a*sqrt(3)/2))**2/2)), 2*t2*((1-(2*((1/2)*k_x*a))**2/2) - (1-(((1/2)*k_x*a))**2/2)*(1-((momentumY*a*sqrt(3)/2))**2/2)) + 2*sqrt(3)*1j*t1*(1-(((1/2)*k_x*a))**2/2)*((momentumY*a*sqrt(3)/2))], [-M1(x,y)-2*sqrt(3)*t2*(((1/2)*k_x*a))*((momentumY*a*sqrt(3)/2)) - 2*1j*t1*((2*((1/2)*k_x*a)) + (((1/2)*k_x*a))*(1-((momentumY*a*sqrt(3)/2))**2/2)), 2*t11*(1-(2*((1/2)*k_x*a))**2/2) + (t11+3*t22)*(1-(((1/2)*k_x*a))**2/2)*(1-((momentumY*a*sqrt(3)/2))**2/2)+e2, -M2(x,y)+sqrt(3)*(t22-t11)*(((1/2)*k_x*a))*((momentumY*a*sqrt(3)/2))+4*1j*t12*(((1/2)*k_x*a))*((1-(((1/2)*k_x*a))**2/2)-(1-((momentumY*a*sqrt(3)/2))**2/2))], [2*t2*((1-(2*((1/2)*k_x*a))**2/2) - (1-(((1/2)*k_x*a))**2/2)*(1-((momentumY*a*sqrt(3)/2))**2/2)) - 2*sqrt(3)*1j*t1*(1-(((1/2)*k_x*a))**2/2)*((momentumY*a*sqrt(3)/2)), M2(x,y)+sqrt(3)*(t22-t11)*(((1/2)*k_x*a))*((momentumY*a*sqrt(3)/2))-4*1j*t12*(((1/2)*k_x*a))*((1-(((1/2)*k_x*a))**2/2)-(1-((momentumY*a*sqrt(3)/2))**2/2)), 2*t22*(1-(2*((1/2)*k_x*a))**2/2) + (3*t11+ t22)*(1-(((1/2)*k_x*a))**2/2)*(1-((momentumY*a*sqrt(3)/2))**2/2)+e2]] """ template = kwant.continuum.discretize(hami, grid = lat_const) #print(template) L = 100 def wire_shape(site): (x, ) = site.pos return (0<=x<L) val1 = 10.07822923*1j val2 = 12.42088476*1j def pot1(x,y=0): return[0,val1][x<L/2] def pot2(x,y=0): return[0,val2][x<L/2] syst = kwant.Builder(); syst.fill(template, wire_shape,(0,)); syst = syst.finalized(); def get_ham(momY): ham = syst.hamiltonian_submatrix(params=dict(M1=pot1,M2=pot2, momentumY = momY, y=0, a = 3.19, e1 = 1.046, e2 = 2.104, t0 = -0.184, t1 = 0.401, t2 = 0.507, t11 = 0.218, t12 = 0.338, t22 = 0.057),sparse = False) return ham #plt.spy(ham) #block off-diagonal #plt.show() # Band structure diagram??? # different momentumY's to iterate over v1=-2*np.pi; v2=2*np.pi; v_segs=10; vary_range = np.linspace(v1, v2, num=v_segs) # np.linspace(kx0_1, kx0_2, num=kx_segs, retstep=True) plt.figure() for i in range(v_segs): ham = get_ham(vary_range[i]) ev,evecs = scipy.linalg.eigh(ham) plt.plot(ev) # plot eigenvalues plt.show() # Wavefunction density diagram??? Should show peak at edge states, if there are any. plt.figure() for i in range(v_segs): ham = get_ham(vary_range[i]) ev,evecs = scipy.linalg.eigh(ham) wavefunction = evecs[:, len(ham)-1] up,middle,down = wavefunction[::3],wavefunction[1::3],wavefunction[2::3] density = np.abs(up)**2 + np.abs(middle)**2 + np.abs(down)**2 plt.plot(density) ##kwant.plotter.map(syst, density, show=False) plt.show() Best, Tharindu

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Kwant-discuss June 2021