Mailman 3 April 2021 - Kwant-discuss

Realistic values of hopping parameters
by Yu Li 19 Oct '23

19 Oct '23

Dear all, Now I’m studying some transport property based on multilayered system, with nonmagnetic layer/ferromagnetic layer (NM/FM) stack. May I ask when creating a tight binding system, and setting hoppings by the following function: syst[(lat(1, 0), lat(1, 1))] = t, how to associate the hopping with a realistic system? Such as hoppings between FM and FM atoms, or between FM and NM atoms? I found in many literatures people just simply put t=1, but I assume the value should depend on the type of atoms. My another question is, is it possible to define more than one type of hopping between two sites? For the tight-binding approximation of p electrons, there are two types of hopping integrals: Vppσ, and Vppπ, so I’m wondering if it’s possible to simulate the effect of both hoppings? Thanks a lot for reading my questions! Cheers, Yu Li

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Gate-defined Nanowire Quantum Dot
by Jonathan Fields 15 Sep '22

15 Sep '22

Dear Reader, I am new to KWANT and trying to figure out if it is suitable for calculating transport properties of gate-defined quantum dots made out of nanowires, along the lines of the structure used in https://arxiv.org/abs/cond-mat/0609463. Now, I understand that the mailing list is not a place to ask people to do my work for me, and my question is also not for someone to do this. What I am looking for is some insights into if this is possible (and not all that difficult) with the package. At first sight (and going through the tutorials as well as the APS March Meeting material) this does not seem straightforward; what I struggle with is how to define this type of dot in KWANT. Now, one way would of course be to built the entire 3D geometry of the system, but this will be computationally expensive, and probably also rather tricky to do in terms of defining everything, from the hexagonal wire itself to all of the gates and oxide layers and such. Some abstraction would be preferred, perhaps even reducing the dimensionality and making a 2D system, such as often done in the tutorial. Is this a good idea? My problem is that if one does this, then I run into the problem of how to model the 'half wrap-around' type gates typically used in these devices. In the transport through barrier section of the APS March Meeting material there is a section on how to model realistic potentials, but this would not work all that well for these wrap around type gates. On the other hand, in a way they are perhaps not so different from the QPC in that section. One could model the three gates as something like https://i.imgur.com/WZC983c.png as they do essentially form channels in the wire. Apart from if this sacrifices too much of the nanowire nature in favor of a 2DEG system, I do suppose such a system should in principle be able to be treated as a quantum dot. I haven't been able to confirm this as I am not yet sure how one can apply a source-drain voltage in KWANT; I first thought that this would probably be related to the energy of the modes, but then again I have not been able to produce Coulomb diamonds in this way. The question is getting rather lenghty, and also a bit unclear at this point. Perhaps I should finish up by stating it in a concise form; would you think that it is possible to simulate the transport of such a gate defined nanowire quantum dot device with KWANT, and if so, is the approach I am suggesting above a viable one, or would you go about it very differently? Kind regards Jonathan <http://aka.ms/weboutlook>

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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

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How the spin is positioned in the Smatrix?
by Qingtian Zhang 07 Mar '22

07 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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Spin polarized transport calculation
by L.M J 07 Mar '22

07 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

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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?

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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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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

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KPM conductivity
by Sergey Slizovskiy 27 Apr '21

27 Apr '21

Dear Kwant Developers, I am trying to use KPM conductance method and getting a low precision, complex results and overflow if I put temperature too low. Is there a way to add moments or to improve in other ways? I have tried add_moments, but it produced errors and ate almost all memory. cond = kwant.kpm.conductivity(sys,alpha=component1,beta=component2,params=params) cond.add_moments(100) return cond(mu=energy,temperature=0.002) The LDOS calculation with 10000 moments worked very well in my prior experince. Shall I also add spectrum boundaries by hands (as I did before)? Best wishes, Sergey

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access to element matrix
by Nafise Nouri 19 Apr '21

19 Apr '21

Dear all, I need to access the matrix diagonal element in the scattering region in my program. Is there any way to access the matrix diagonal element in the following program or do I have to use numpy? Best regard, import kwant import matplotlib.pyplot as plt import tinyarray import numpy as np import math from functools import partial from kwant.physics import dispersion #mport matplotlib d=1.42; a1=d*math.sqrt(3); latt = kwant.lattice.general([(a1,0),(0.5*a1,a1*math.sqrt(3)/2)], [(0,0),(0,a1/math.sqrt(3))]) a,b = latt.sublattices syst= kwant.Builder() #................................................................................... def rectangle(pos): x, y = pos z=x**2+y**2 return -4*3*a1<y<4.5*3*a1 and -4.5*d<=x<4.5*d syst[a.shape(rectangle, (2,2))] = 0 syst[b.shape(rectangle, (2,2))] = 0 #nearest neighbors............................................................. syst[[kwant.builder.HoppingKind((0,0),a,b)]] = -2.7 syst[[kwant.builder.HoppingKind((0,1),a,b)]] = -2.7 syst[[kwant.builder.HoppingKind((-1,1),a,b)]] = -2.7 ax=kwant.plot(syst); sym = kwant.TranslationalSymmetry(latt.vec((-1,0))) sym.add_site_family(latt.sublattices[0], other_vectors=[(-1, 2)]) sym.add_site_family(latt.sublattices[1], other_vectors=[(-1, 2)]) lead = kwant.Builder(sym) def lead_shape(pos): x, y = pos return -4*3*a1<y<4.5*3*a1 lead[a.shape(rectangle, (2,2))] = 0 lead[b.shape(rectangle, (2,2))] = 0 #nearest neighbors............................................................. lead[[kwant.builder.HoppingKind((0,0),a,b)]] = -2.7 lead[[kwant.builder.HoppingKind((0,1),a,b)]] = -2.7 lead[[kwant.builder.HoppingKind((-1,1),a,b)]] = -2.7 syst.attach_lead(lead) syst.attach_lead(lead.reversed()) ax=kwant.plot(syst); ###############################################################################\ fsys = syst.finalized() Sites= list(fsys.sites) #list of all the sites in the scattering region number_of_sites=len(Sites) bands = dispersion.Bands(fsys.leads[0]) momenta = np.linspace(-np.pi,np.pi, 100) energies=[bands(k) for k in momenta] np.savetxt('band1.txt',bands(-np.pi)) plt.plot(momenta,energies) plt.xlabel(r'$K$') plt.ylabel(r'$band structure (eV)$') plt.ylim((-0.5,0.5)) plt.savefig('bandsarmBiStrain.pdf') plt.show()

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Adding "norbs = 1" changes conductance calculation
by Henry Axt 16 Apr '21

16 Apr '21

Hello, I am having trouble figuring out what the cause of the change in conductance is when the only thing I do is I add the "norbs=1" command to the definition of the electron and hole lattices (is this not default?). Below is the code, I have added in "norbs = 1" in lines 70 and 71, if you take them out, you get the proper result. (sorry of the long code). import kwant from matplotlib import pyplot from math import pi, sqrt, tanh, cos, ceil from cmath import exp import numpy as np import time import textwrap as tw sin_30, cos_30, tan_30 = (1 / 2, sqrt(3) / 2, 1 / sqrt(3)) def create_system(n_length, np_transition_length, p_length, width, lattice_spacing, onsite_potential_left_lead, onsite_potential_superconducting_lead, onsite_potential_n, onsite_potential_p, hopping_parameter, Delta, boundary_hopping): saved_args = locals() padding = 0.5*lattice_spacing*tan_30 def calc_total_length(n_length, np_transition_length, p_length, lattice_spacing): total_length = n_length + np_transition_length + p_length N = total_length//lattice_spacing # Number of times a graphene hexagon fits in horizontially fully new_length = N*lattice_spacing + lattice_spacing*0.5 diff = total_length - new_length if diff != 0: n_length = n_length - diff total_length = new_length return total_length, n_length def calc_width(width,lattice_spacing, padding): stacking_width = lattice_spacing*((tan_30/2)+(1/(2*cos_30))) N = width//stacking_width if N % 2 == 0.0: # Making sure that N is odd. N = N-1 new_width = N*stacking_width + padding width = new_width return width, int(N) def rectangle(pos): x,y = pos if (0 < x <= total_length) and (-padding <= y <= width -padding): return True return False def potential_e(site): (x,y) = site.pos return onsite_potential_n + (0.5*(1+tanh((x-n_length- 0.5*np_transition_length)/np_transition_length)))*(onsite_potential_p- onsite_potential_n) def potential_h(site): (x,y) = site.pos return (-1)*(onsite_potential_n + (0.5*(1+tanh((x-n_length- 0.5*np_transition_length)/np_transition_length)))*(onsite_potential_p- onsite_potential_n)) def lead_shape(pos): x, y = pos return 0 - padding <= y <= width def tag_site_calc(x): return int(-1*(x*0.5+0.5)) total_length, n_length = calc_total_length(n_length, np_transition_length,p_length, lattice_spacing) width, N = calc_width(width, lattice_spacing, padding) ### Defining lattices ### graphene_e = kwant.lattice.honeycomb(a=lattice_spacing,name='e', norbs=1) graphene_h = kwant.lattice.honeycomb(a=lattice_spacing,name='h', norbs=1) a, b = graphene_e.sublattices c, d = graphene_h.sublattices sys = kwant.Builder() sys[graphene_e.shape(rectangle, (0.5*lattice_spacing, 0))] = potential_e sys[graphene_h.shape(rectangle, (0.5*lattice_spacing, 0))] = potential_h sys[graphene_e.neighbors()] = -hopping_parameter sys[graphene_h.neighbors()] = hopping_parameter ### Boundary conditions for scattering region for site in sys.sites(): (x,y) = site.tag if float(site.pos[1]) < 0: if str(site.family) == "<Monatomic lattice e1>": sys[b(x,y),a(int(x+tag_site_calc(N)),N)] = -boundary_hopping if str(site.family) == "<Monatomic lattice h1>": sys[d(x,y),c(int(x+tag_site_calc(N)),N)] = boundary_hopping # kwant.plot(sys) kwant.plot(sys, site_color=potential_e, site_lw=0,hop_lw=0,site_size=0.2, lead_site_lw=0, colorbar=True, cmap='jet') ### Defning leads ### # Symmetry of the left and right leads sym_l = kwant.TranslationalSymmetry((-1, 0)) sym_r = kwant.TranslationalSymmetry((1, 0)) # Redefining the shape of the unit cell so that we don't add new sites sym_l.add_site_family(graphene_e.sublattices[0], other_vectors=[(-1, 2)]) sym_l.add_site_family(graphene_e.sublattices[1], other_vectors=[(-1, 2)]) sym_r.add_site_family(graphene_e.sublattices[0], other_vectors=[(-1, 2)]) sym_r.add_site_family(graphene_e.sublattices[1], other_vectors=[(-1, 2)]) sym_l.add_site_family(graphene_h.sublattices[0], other_vectors=[(-1, 2)]) sym_l.add_site_family(graphene_h.sublattices[1], other_vectors=[(-1, 2)]) sym_r.add_site_family(graphene_h.sublattices[0], other_vectors=[(-1, 2)]) sym_r.add_site_family(graphene_h.sublattices[1], other_vectors=[(-1, 2)]) lead0 = kwant.Builder(sym_l) # Left electron lead0[graphene_e.shape(lead_shape, (1,1))] = -onsite_potential_left_lead lead0[graphene_e.neighbors()] = -hopping_parameter for site in lead0.sites(): (x,y) = site.tag if site.pos[1]<0: lead0[b(x,y),a(int(x+tag_site_calc(N)),N)] = -boundary_hopping lead1 = kwant.Builder(sym_l) # Left hole lead1[graphene_h.shape(lead_shape, (1,1))] = onsite_potential_left_lead lead1[graphene_h.neighbors()] = hopping_parameter for site in lead1.sites(): (x,y) = site.tag if site.pos[1]<0: lead1[d(x,y),c(int(x+tag_site_calc(N)),N)] = boundary_hopping lead3 = kwant.Builder(sym_r) # Right electron lead3[graphene_e.shape(lead_shape, (1,1))] = -onsite_potential_superconducting_lead lead3[graphene_e.neighbors()] = -hopping_parameter for site in lead3.sites(): (x,y) = site.tag if site.pos[1]<0: lead3[b(x,y),a(int(x+tag_site_calc(N)),N)] = -boundary_hopping lead4 = kwant.Builder(sym_r) # Right hole lead4[graphene_h.shape(lead_shape, (1,1))] = onsite_potential_superconducting_lead lead4[graphene_h.neighbors()] = hopping_parameter for site in lead4.sites(): (x,y) = site.tag if site.pos[1]<0: lead4[d(x,y),c(int(x+tag_site_calc(N)),N)] = boundary_hopping lead2 = kwant.Builder(sym_r) # Right superconducting lead2.update(lead3) lead2.update(lead4) # Hopping between electron and hole lead lattices in superconducting lead for site in lead2.sites(): (x,y) = site.tag if str(site.family) == "<Monatomic lattice e0>": lead2[c(x,y),a(x,y)] = Delta if str(site.family) == "<Monatomic lattice e1>": lead2[d(x,y),b(x,y)] = Delta # Attaching the left electron, left hole and right superconducting lead sys.attach_lead(lead0) sys.attach_lead(lead1) sys.attach_lead(lead2) return sys, [lead0, lead1, lead2], width, N, saved_args def plot_conductance(syst, energies, lead_in, lead_out, saved_args, width, geo_prop, pot_prop): """ Return conductance as a function of energy from lead_in to lead_out. """ lead_dict = { 0: "Electron Lead", 1: "Hole Lead", 2: "Superconducting Lead" } data = [] step_counter = 1 energy_size = energies.size elapsed_time_per_step_average = 0.0 for energy in energies: start = time.time() print('Step: ', step_counter, '/', energy_size) smatrix = kwant.smatrix(syst, energy) data.append(smatrix.transmission(lead_out, lead_in)) end = time.time() elapsed_time_per_step = int(end - start) print(' Time per step:', elapsed_time_per_step, ' seconds') if elapsed_time_per_step_average > 0: elapsed_time_per_step_average = (elapsed_time_per_step_average + elapsed_time_per_step)/2 else: elapsed_time_per_step_average = elapsed_time_per_step time_left = int(elapsed_time_per_step_average*(energy_size-step_counter)/60) print(' Time left: ', time_left, ' minutes') step_counter = step_counter + 1 pyplot.figure() pyplot.plot(energies, data) str1 = str(lead_dict[lead_in]) str2 = str(lead_dict[lead_out]) title_str = "From " + str1 + " to " + str2 pyplot.title(title_str) pyplot.xlabel("Energy [t]") pyplot.ylabel("Conductance [e^2/h]") ### All variables used ### # comment2_txt = "N Length = " + str(saved_args['n_length']) + ", NP Length = " + str(saved_args['np_transition_length']) + ", P Length = " + str(saved_args['p_length']) + ", Width = " + str(0.01*int(100*width)) + ", Potential Left Lead = " + str(saved_args['onsite_potential_left_lead']) + ", Potential Superconducting Lead = " + str(saved_args['onsite_potential_superconducting_lead']) + ", Potential N = " + str(saved_args['onsite_potential_n']) + ", Potential P = " + str(saved_args['onsite_potential_p']) + ", Hopping Parameter = " + str(saved_args['hopping_parameter']) + ", Delta = " + str(saved_args['Delta']) + ", Resolution = " + str(energy_size) ### Main variables: pn_transition_length, width, length_of_P ### comment2_txt = "NP Transition Length = " + str(geo_prop[1]) + ", P Length = " + str(geo_prop[2]) + ", Width = " + str(geo_prop[0]) comment1_txt = "Left Lead = " + str(pot_prop[0]) + ", N-Region: " + str(pot_prop[1]) + ", P-Region: "+str(pot_prop[2]) +", SC Lead: " + str(pot_prop[3])+", Delta: " +str(pot_prop[4]) comment0_txt = "Resoltuion: " + str(energy_size) fig_txt = tw.fill(tw.dedent(comment1_txt.rstrip() ), width=80) pyplot.figtext(0.5, -0.12, fig_txt, horizontalalignment='center', fontsize=8, multialignment='left', bbox=dict(boxstyle="round", facecolor='#D8D8D8', ec="0.5", pad=0.5, alpha=1), fontweight='bold') fig_txt = tw.fill(tw.dedent(comment2_txt.rstrip() ), width=80) pyplot.figtext(0.5, -0.05, fig_txt, horizontalalignment='center', fontsize=8, multialignment='left', bbox=dict(boxstyle="round", facecolor='#D8D8D8', ec="0.5", pad=0.5, alpha=1), fontweight='bold') fig_txt = tw.fill(tw.dedent(comment0_txt.rstrip() ), width=80) pyplot.figtext(0.81, 0.84, fig_txt, horizontalalignment='center', fontsize=6, multialignment='left', bbox=dict(boxstyle="round", facecolor='#D8D8D8', ec="0.5", pad=0.5, alpha=1), fontweight='bold') # pyplot.ylim(0,3) pyplot.xlim(0.0,2.0) pyplot.show() return data def calc_fermi_wavelength(onsite_potential): return 2*pi*(1/sqrt(3+onsite_potential)) def main(): """ GEOMETRIC PROPERTIES - IN UNITS OF FERMI WAVELENGTH """ geo_prop = np.array([8, # Width 2, # PN-Junction transition length 2]) # P-Region length """ ENERGIES - IN UNITS OF t """ pot_prop = np.array([-1.0001, # Left lead 0.3, # N-Region 0.3, # P-Region 0.3, # Superconducting lead 1.0]) # Delta # Converting property arrays from units of Fermi wavelength to #units of lattice sites. fermi_wavelength = calc_fermi_wavelength(pot_prop[2]) geo_prop2 = fermi_wavelength*geo_prop k_phase_kick = 0.0 # Phase-kick due to boundary condition ## create_system using above defined property arrays sys, leads, width, N, saved_args = create_system(n_length = ceil(2*fermi_wavelength), np_transition_length = geo_prop[1], p_length = ceil(geo_prop2[2]) # GEOMETRIC PROPERTIES , width = geo_prop2[0], lattice_spacing = 1.0, onsite_potential_left_lead = pot_prop[0], onsite_potential_superconducting_lead = pot_prop[3], # POTENTIALS onsite_potential_n = pot_prop[1], onsite_potential_p = pot_prop[2], hopping_parameter = 1.0, Delta = pot_prop[4], # HOPPING PARAMETERS boundary_hopping = 1.0*exp(-1j*k_phase_kick)) sys = sys.finalized() ### Plot Conductance ### Es = np.linspace(0.0001, 2.00, 20) data = plot_conductance(sys, Es, 0,1, saved_args, width, geo_prop, pot_prop) return #d_energies if __name__ == "__main__": main()

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Using kwant.plotter.density selectively?
by Henry Axt 14 Apr '21

14 Apr '21

Hello, I am plotting the wavefunction of my system as such: import scipy.linalg as la ham = sys.hamiltonian_submatrix(params=dict(pot=0)) evecs = la.eigh(ham)[1] wf = abs(evecs[:, 1])**2 kwant.plotter.density(sys, wf) I am wondering how/if I could give plotter.density some condition to only plot part of my system? Some region's wavefunction values don't appear as they are too small, but those are the ones I am trying to observe.

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Re: Is k a good quantum number in this infinite wire?
by Joseph Weston (Aquent LLC - Canada) 08 Apr '21

08 Apr '21

Hi Michael, > I am adding a periodic magnetic field to an infinite wire, where the periods of the lattice and magnetic field are not the same. > This would appear to be a violation of the part of Bloch's theorem where $u_k(x)=u_k(x+n.a)$. Your assessment is correct: to apply Bloch's theorem the Hamiltonian has to have (discrete) translational symmetry. To get meaningful results out you are going to have to ensure that your model is commensurate with the lattice on which you are trying to discretize. In general Kwant does not try to figure out whether your model _does_ actually possess a symmetry; it just takes your word for it. Kwant only evaluates your model on the fundamental domain of the symmetry; this is why it appears to "just work" in your case. Let us know if you need some extra clarification! Happy Kwanting, Joe

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Is k a good quantum number in this infinite wire?
by michael.hynes.18＠ucl.ac.uk 07 Apr '21

07 Apr '21

Dear all, I am adding a periodic magnetic field to an infinite wire, where the periods of the lattice and magnetic field are not the same. This would appear to be a violation of the part of Bloch's theorem where $u_k(x)=u_k(x+n.a)$. When I model this in kwant however (minimal working code below), I am able to plot the band structure just fine. I'm not totally sure how kwant is doing this, so I ask what are the implications here? Is k_x a bad quantum number as a result? Have I misunderstood what kwant is doing here? Best wishes, Michael import kwant import kwant.continuum import numpy as np import matplotlib.pyplot hamiltonian = ( "A * (k_x**2 + k_y**2) * kron(sigma_z, sigma_0)" #kinetic terms "- mu * kron(sigma_z, sigma_0)" #chemical potential "+ 0.5 * g * mu_B * M * (kron(sigma_0, sigma_x) * sin(period*x) + kron(sigma_0, sigma_y) * cos(period*x))" #periodic magnetic field "+ delta * kron(sigma_x, sigma_0)" #superconductivity ) ham_template = kwant.continuum.discretize(hamiltonian, coords="xy",grid=20) infinite_wire = kwant.wraparound.wraparound(ham_template).finalized() momenta = np.linspace(-1,1, 100) def spectrum_discrete(**params): kwant.plotter.spectrum( infinite_wire, ('k_x', momenta), params=params, ) spectrum_discrete( period=7.3, A=2.01,#eV/nm^2 g=10, mu_B=57.9e-6,#eV/T M=1,#T mu=0,#eV delta=180e-6,#eV k_y=0, cos=np.cos, sin=np.sin )

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Memory error while using tkwant
by dakshesh.kololgi17＠imperial.ac.uk 04 Apr '21

04 Apr '21

Dear users, I am a Physics Masters student and am using tkwant to simulate braiding (adiabatic exchanging) of Majorana fermions in a 2D system. Currently, even for the smallest systems, although these do work using Jupyter, I get a memory error when using my university's HPC supercomputer and MPI ranks. Also, when running simulations on Jupyter notebook (supercomputer client) any large-ish system never actually completes. More specifically, my issue seems to lie with 'wave_function.evolve' and 'wave_function.evaluate' for the time for loop. density_operator = kwant.operator.Density(syst, np.eye(8)).bind(params=params) wave_function = manybody.WaveFunction(psi_init, tasks) for time in times: wave_function.evolve(time) density = wave_function.evaluate(density_operator) densities.append(density) plt.plot(sites, density - density0, label='time={}'.format(time)) In my system, I have 4 time-dependent gates and they are supposed to turn on and off according to what time the system is in. I have used 'if' statements to specify when the gates should be on or off. If anyone can help it would be of great help. Thank you.

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