Mailman 3 June 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 … [View More]

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Package announcement: Pymablock
by Anton Akhmerov Nov. 12, 2023

Nov. 12, 2023

Hello fellow Kwanters, I am happy to announce Pymablock, a Python package useful to combine with Kwant. Its main purpose is constructing effective models using perturbation theory, which may help you in different ways. Pymablock allows you to analyse the behavior of a few levels of a large Hamiltonian, or to construct a symbolic k.p model. We originally wrote the code for one of our projects, but then saw that this tool is useful almost for the entire group, so we decided to turn it into a … [View More]

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Realistic values of hopping parameters
by Yu Li Oct. 19, 2023

Oct. 19, 2023

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 … [View More]

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Scattering region and lead with different kind of lattice
by Gabriel Garcia July 11, 2023

July 11, 2023

Hi devs, I am learning kwant alone, but i have doubts. I am trying to construct a system with a diatomic chain as scattering region and the leads as a monoatomic chain. But i am doing something wrong. Someone else can help me? Bellow i will show the code: ##################################################################################################################### from matplotlib import pyplot as plt from matplotlib import backends import kwant # Defining the parameters L = 5 # range … [View More]of scattering region C = 2 # primitive vector # Definindo o parametro de Hopping t = 5 # hopping parameter lat = kwant.lattice.general([(C,0),(0,1)],[(0,0),(1,0)], norbs=1) a, b = lat.sublattices syst = kwant.Builder() # Scattering region for i in range(L): syst[a(i, 0)] = 0 syst[b(i, 0)] = 0 syst[kwant.builder.HoppingKind((0, 0), a, b)] = -t syst[kwant.builder.HoppingKind((1, 0), b, a)] = -t kwant.plot(syst) plt.show() # leaft lead (lead 1) lat_lead1 = kwant.lattice.chain(C, norbs=1) sym_lead1 = kwant.TranslationalSymmetry((-C, 0)) lead1 = kwant.Builder(sym_lead1) lead1[lat_lead(0,0)] = 4*t lead1[lat_lead1.neighbors()] = -t syst[(lat_lead1(-C, 0), a(0, 0))] = -t syst.attach_lead(lead1) kwant.plot(syst) --------------------------------------------------------------------------- ValueError Traceback (most recent call last) ~\anaconda3\lib\site-packages\kwant\builder.py in __new__(cls, family, tag, _i_know_what_i_do) 75 try: ---> 76 tag = family.normalize_tag(tag) 77 except (TypeError, ValueError) as e: ~\anaconda3\lib\site-packages\kwant\lattice.py in normalize_tag(self, tag) 475 if len(tag) != self.lattice_dim: --> 476 raise ValueError("Dimensionality mismatch.") 477 return tag ValueError: Dimensionality mismatch. During handling of the above exception, another exception occurred: ValueError Traceback (most recent call last) <ipython-input-46-3d36b05d2870> in <module> 8 lead1[lat_lead1.neighbors()] = -t 9 ---> 10 syst[(lat_lead1(-C, 0), a(0, 0))] = -t 11 12 syst.attach_lead(lead1) ~\anaconda3\lib\site-packages\kwant\builder.py in __call__(self, *tag) 195 raise ValueError('Use site_family(1, 2) instead of ' 196 'site_family((1, 2))!') --> 197 return Site(self, tag) 198 199 ~\anaconda3\lib\site-packages\kwant\builder.py in __new__(cls, family, tag, _i_know_what_i_do) 77 except (TypeError, ValueError) as e: 78 msg = 'Tag {0} is not allowed for site family {1}: {2}' ---> 79 raise type(e)(msg.format(repr(tag), repr(family), e.args[0])) 80 return tuple.__new__(cls, (family, tag)) 81 ValueError: Tag (-2, 0) is not allowed for site family kwant.lattice.Monatomic([[2.0]], [0.0], '', 1): Dimensionality mismatch. ############################################################################################# Thanks! Gabriel Garcia [View Less]

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Plotting Particle-Hole density in KWANT
by sc20rs001＠iiserkol.ac.in June 30, 2023

June 30, 2023

Hi KWANT users! I was trying to plot particle-hole density in KWANT. My system has spin, pseudospin and particle-hole so, norbs = 8. I used kwant.operator.Density(np.kron(np.eye(4), \tau_z)) to plot particle-hole density but could not obtain correct result. It would be great if someone could tell how to plot particle hole density in this case ? Thanks in advance.

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random sites
by Hossein Karbaschi June 20, 2023

June 20, 2023

Hi everybody, In the following code I want to delete few random sites from the scattering region. Please help me in this case. Best regards, Hossein import kwant from math import sqrt import matplotlib.pyplot as plt import tinyarray import numpy as np import math import matplotlib #Constants......................................................... #Parameter......................................................... a0=2.617*sqrt(3); d0=2.617; dz0=1.59047; D0=sqrt((d0)**2+(dz0)**2); #st=0;… [View More] st=-0.0; dz=1.59047+st; d=-0.3*dz+3.09; a1=-0.3*sqrt(3)*dz+5.35; D=sqrt((d)**2+(dz)**2); scale=(D/D0)**(-8); qo=[]; N=dz/D; delta1=0j; delta2=0; R=(2*a1)**2; #on-site energy................................................... Es=-10.906; Ep=-0.486; Ep1=-0.486; Ep2=-0.486; #nearest neighbor................................................ sssigma=-0.608*scale; spsigma=1.32*scale; ppsigma=1.854*scale; pppay=-0.6*scale; #next nearest neighbor......................................... ppsigma2=0.156*scale; pppay2=0; sssigma2=0; spsigma2=0; #onsite potentials ........................................... pot_a=10; pot_b=0; #nearest neighbors............................................................. l1=(math.cos(math.pi/6))*(d/D); m1=(math.sin(math.pi/6))*(d/D); N1=dz/D; #second neighbors.............................................................. l2=(math.cos(math.pi/3)) m2=(math.sin(math.pi/3)) latt = kwant.lattice.general([(a1,0),(a1*0.5,a1*math.sqrt(3)/2)], [(a1/2,-d/2),(a1/2,d/2)]) a,b = latt.sublattices syst= kwant.Builder() # Onsite matrice energt Onsite_a=tinyarray.array([[Es,0,0,0],[0,Ep,delta1,0],[0,-delta1,Ep,0], [0,0,0,Ep1]]) Onsite_b=tinyarray.array([[Es,0,0,0],[0,Ep,delta1,0],[0,-delta1,Ep,0], [0,0,0,Ep2]]) pot_edge_a=tinyarray.array([[Es+pot_a,0,0,0],[0,Ep+pot_a,delta1,0],[0,-delta1,Ep+pot_a,0], [0,0,0,Ep1+pot_a]]) pot_edge_b=tinyarray.array([[Es+pot_b,0,0,0],[0,Ep+pot_b,delta1,0],[0,-delta1,Ep+pot_b,0], [0,0,0,Ep2+pot_b]]) #nearest neighbors............................................................. first_up=tinyarray.array([[sssigma, l1*spsigma,m1*spsigma,N1*spsigma], [-l1*spsigma, l1**2*ppsigma+(1-l1**2)*pppay,l1*m1*(ppsigma-pppay),l1*N1*(ppsigma-pppay)], [-m1*spsigma ,l1*m1*(ppsigma-pppay), m1**2*ppsigma+(1-m1**2)*pppay,N1*m1*(ppsigma-pppay)], [-N1*spsigma,l1*N1*(ppsigma-pppay),N1*m1*(ppsigma-pppay),N1**2*ppsigma+(1-N1**2)*pppay]]) first_left_up=tinyarray.array([[sssigma,-l1*spsigma,m1*spsigma,N1*spsigma], [l1*spsigma, l1**2*ppsigma+(1-l1**2)*pppay,- l1*m1*(ppsigma-pppay),-l1*N1*(ppsigma-pppay)], [-m1*spsigma ,-l1*m1*(ppsigma-pppay), m1**2*ppsigma+(1-m1**2)*pppay,N1*m1*(ppsigma-pppay)], [-N1*spsigma,-l1*N1*(ppsigma-pppay),N1*m1*(ppsigma-pppay),N1**2*ppsigma+(1-N1**2)*pppay]]) first=tinyarray.array([[sssigma,0,-(d/D)*spsigma,N1*spsigma], [0,pppay,0,0], [(d/D)*spsigma ,0, (d/D)**2*ppsigma+(1-(d/D)**2)*pppay,-N1*(d/D)*(ppsigma-pppay)], [-N1*spsigma,0,-N1*(d/D)*(ppsigma-pppay),N1**2*ppsigma+(1-N1**2)*pppay]]) #second neighbors.............................................................. second_up=tinyarray.array([[sssigma2,l2*spsigma2,m2*spsigma2,0], [-l2*spsigma2,l2**2*ppsigma2+(1-l2**2)*pppay2,l2*m2*(ppsigma2-pppay2),0], [-m2*spsigma2 ,l2*m2*(ppsigma2-pppay2),m2**2*ppsigma2+(1-m2**2)*pppay2,0], [0,0,0,pppay2]]) second_left_up=tinyarray.array([[sssigma2,-l2*spsigma2,m2*spsigma2,0], [l2*spsigma2,l2**2*ppsigma2+(1-l2**2)*pppay2,-l2*m2*(ppsigma2-pppay2),0], [-m2*spsigma2 ,-l2*m2*(ppsigma2-pppay2),m2**2*ppsigma2+(1-m2**2)*pppay2,0], [0,0,0,pppay2]]) second_right_down=tinyarray.array([[sssigma2,l2*spsigma2,-m2*spsigma2,0], [-l2*spsigma2,l2**2*ppsigma2+(1-l2**2)*pppay2,-l2*m2*(ppsigma2-pppay2),0], [m2*spsigma2,-l2*m2*(ppsigma2-pppay2),m2**2*ppsigma2+(1-m2**2)*pppay2,0], [0,0,0,pppay2]]) second_down=tinyarray.array([[sssigma2,-l2*spsigma2,-m2*spsigma2,0], [l2*spsigma2,l2**2*ppsigma2+(1-l2**2)*pppay2,l2*m2*(ppsigma2-pppay2),0], [m2*spsigma2 ,l2*m2*(ppsigma2-pppay2),m2**2*ppsigma2+(1-m2**2)*pppay2,0], [0,0,0,pppay2]]) second_right=tinyarray.array([[sssigma2,spsigma2,0,0], [-spsigma2,ppsigma2,0,0],[0 ,0,pppay2,0], [0,0,0,pppay2]]) second_left=tinyarray.array([[sssigma2,-spsigma2,0,0], [spsigma2,ppsigma2,0,0],[0 ,0,pppay2,0], [0,0,0,pppay2]]) #................................................................................... def rectangle(pos): x, y = pos # z=x**2+y**2 return -9.2*a1<x<9.2*a1 and -12*d<=y<12*d syst[a.shape(rectangle, (1,1))] = Onsite_a syst[b.shape(rectangle, (1,1))] = Onsite_b #nearest neighbors............................................................. syst[[kwant.builder.HoppingKind((0,0),a,b)]] = first syst[[kwant.builder.HoppingKind((0,1),a,b)]] = first_up syst[[kwant.builder.HoppingKind((-1,1),a,b)]] = first_left_up #second neighbors.............................................................. syst[[kwant.builder.HoppingKind((0,1),a,a)]]=second_up syst[[kwant.builder.HoppingKind((-1,1),a,a)]]=second_left_up syst[[kwant.builder.HoppingKind((1,-1),a,a)]]=second_right_down syst[[kwant.builder.HoppingKind((0,-1),a,a)]]=second_down syst[[kwant.builder.HoppingKind((1,0),a,a)]]=second_right syst[[kwant.builder.HoppingKind((-1,0),a,a)]]=second_left syst[[kwant.builder.HoppingKind((0,1),b,b)]]=second_up syst[[kwant.builder.HoppingKind((-1,1),b,b)]]=second_left_up syst[[kwant.builder.HoppingKind((1,-1),b,b)]]=second_right_down syst[[kwant.builder.HoppingKind((0,-1),b,b)]]=second_down syst[[kwant.builder.HoppingKind((1,0),b,b)]]=second_right syst[[kwant.builder.HoppingKind((-1,0),b,b)]]=second_left 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) # ---- random impurity # --- leads def lead_shape(pos): x, y = pos return -12*d<=y<12*d and -5.2*a1<x<5.2*a1 lead[a.shape(lead_shape, (1,1))] = Onsite_a lead[b.shape(lead_shape, (1,1))] = Onsite_b lead[[kwant.builder.HoppingKind((0,0),a,b)]] =first lead[[kwant.builder.HoppingKind((0,1),a,b)]] =first_up lead[[kwant.builder.HoppingKind((-1,1),a,b)]] =first_left_up lead[[kwant.builder.HoppingKind((0,1),a,a)]]=second_up lead[[kwant.builder.HoppingKind((-1,1),a,a)]]=second_left_up lead[[kwant.builder.HoppingKind((1,-1),a,a)]]=second_right_down lead[[kwant.builder.HoppingKind((0,-1),a,a)]]=second_down lead[[kwant.builder.HoppingKind((1,0),a,a)]]=second_right lead[[kwant.builder.HoppingKind((-1,0),a,a)]]=second_left lead[[kwant.builder.HoppingKind((0,1),b,b)]]=second_up lead[[kwant.builder.HoppingKind((-1,1),b,b)]]=second_left_up lead[[kwant.builder.HoppingKind((1,-1),b,b)]]=second_right_down lead[[kwant.builder.HoppingKind((0,-1),b,b)]]=second_down lead[[kwant.builder.HoppingKind((1,0),b,b)]]=second_right lead[[kwant.builder.HoppingKind((-1,0),b,b)]]=second_left syst.attach_lead(lead,add_cells=0) syst.attach_lead(lead.reversed(),add_cells=0) fsys = syst.finalized() def family_color(site): #print(sys[site]) if syst[site]==Onsite_a: return 'black' elif syst[site]==Onsite_b: return 'green' elif syst[site]==pot_edge_a: return 'yellow' else: return 'blue' ax=kwant.plot(syst,site_color=family_color); ax.savefig('syst.pdf') [View Less]

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Regarding Conductance in Graphene ( Andreev Reflection)
by Sarbajit Mazumdar June 15, 2023

June 15, 2023

Hi All, I am trying to reproduce Fig. 4 in PRL 97, 067007 (2006) - Specular Andreev Reflection in Graphene. This had been done in KWANT in the PhD thesis of Tibor Sekera - "Quantum transport of fermions in honeycomb lattices and cold atomic systems", chapter 4. My code is the following. Can Anyone help me? I am not getting same result. I am trying the same code this question has been asked before here (https://mail.python.org/archives/list/kwant-discuss@python.org/thread/3JH5W…), but no … [View More]fruitful outcome was gained. I shall be highly grateful if anyone can help me. ################################################################ import kwant, tinyarray from math import pi, sqrt from matplotlib import pyplot as plt import numpy as np plt.rcParams['figure.dpi']=150 ####___Fundamental Constants___#### e = 1.60217662 * (10**-19) hbar = 1.0545718 * (10**-34) h = 6.62607004 * (10**-34) e_hb = e / hbar ################################### # Specifying 2x2 Pauli matrices acting on spin s_x = tinyarray.array([[0, 1], [1, 0]]) s_y = tinyarray.array([[0, -1j], [1j, 0]]) s_z = tinyarray.array([[1, 0], [0, -1]]) s_0 = tinyarray.array([[1, 0], [0, 1]]) # Specifying 2x2 Pauli matrices acting on particle-hole tau_0 = tinyarray.array([[1, 0], [0, 1]]) tau_x = tinyarray.array([[0, 1], [1, 0]]) tau_y = tinyarray.array([[0, -1j], [1j, 0]]) tau_z = tinyarray.array([[1, 0], [0, -1]]) #Fix hopping, Fermi energy, and superconducting gap t = 1 # Ef = 0 Ef_S=2 Delta= 2 a=1 V0=0.5 #Length and Width of scattering region (the superconductor) L = 20 W = 10 def make_system(): lat = kwant.lattice.general([(sqrt(3)*0.5,0.5),(0,1)],[(0,0),(1/(2*sqrt(3)),1/2)],norbs = 4) a, b = lat.sublattices def channel(pos): x, y = pos return -W <= y <= W and -L <= x <= L syst = kwant.Builder() syst[lat.shape(channel, (0, 0))] = Ef_S * -1 * np.kron(tau_z, s_0) syst[lat.neighbors()] = t * -1 * np.kron(tau_z, s_0) syst.eradicate_dangling() def lead0_shape(pos): # left lead x, y = pos return -W <=y <=W sym_up = kwant.TranslationalSymmetry(lat.vec((-2,1))) # Symmetry along the x-axis # Normal graphene lead-0 lead0 = kwant.Builder(sym_up, conservation_law=np.kron(tau_z, s_0), particle_hole=np.kron(tau_x, s_0)) lead0[lat.shape(lead0_shape, (0, 0))] = Ef_S * -1 * np.kron(tau_z, s_0) lead0[lat.neighbors()] = t * -1 * np.kron(tau_z, s_0) ######################################################################################################################## def lead1_shape(pos): # right x, y = pos return -W <=y <=W sym_down = kwant.TranslationalSymmetry(lat.vec((2, -1))) # Superconducting graphene lead-1 lead1 = kwant.Builder(sym_down) lead1[lat.shape(lead1_shape, (0, 0))] = (Ef_S + V0) * -1 * np.kron(tau_z, s_0) + Delta * np.kron(tau_z, s_0) lead1[lat.neighbors()] = t * -1 * np.kron(tau_z, s_0) return syst, [lead0, lead1] def plot_conductance(syst, energies): # Compute conductance data = [] for energy in energies: smatrix = kwant.smatrix(syst, energy) # Conductance is N - R_ee + R_he data.append(smatrix.submatrix((0, 0), (0, 0)).shape[0] - smatrix.transmission((0, 0), (0, 0)) + smatrix.transmission((0, 1), (0, 0))) plt.figure() plt.plot(energies, data,'*-r') plt.xlabel("energy [t]") plt.ylabel("conductance [e^2/h]") plt.show() #Plot the band in the lead #Make my system and attach the leads def main(): system, leads = make_system() # plot_system(system, a) # Attach the leads to the system. for lead in leads: system.attach_lead(lead) # # Plot system with leads # def family_colors(site): # return 0 if site.family == a else 1 # # kwant.plot(system, site_color=family_colors, site_lw=0.1, lead_site_lw=0, colorbar=False) # Finalize the system. kwant.plot(system,fig_size=(5,5)) system = system.finalized() # #Evaluate the band in the lead L_1 = leads[0].finalized() # bands = kwant.physics.Bands(L_1) # #Plot the band in the lead # ks = np.linspace(-pi,pi,num=101) # energies=[bands(k) for k in ks] # f, ax = plt.subplots() # ax.plot(ks,energies) # plt.show() plot_conductance(system, energies=[0.01 * i+0.00001 for i in range(200)]) main() [View Less]

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Methods for calculating Josephson Current ?
by guilhermewells＠gmail.com June 6, 2023

June 6, 2023

Hi, I'm new to Kwant and I've been looking for calculating Josephson Current with it. The past three weeks I've been reading a lot the tutorials, the mailing list and some online courses. The problem is that I can't get a straight answer on where it is possible to calculate Josephson current reallistically. The most complete answer was given by J. Weston here [1], the problem is that the methods suggested are also not so clear, since I coundn't find tutorials using properly Self-Energy and … [View More]

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modelling chiral channels
by Sergey Slizovskiy June 5, 2023

June 5, 2023

Hi, I am thinking if it's possible to use Kwant to compute the conductance matrix for a network of chiral 1D channels? Looks very similar to what kwant normally does, I suppose, but kwant does not allow for non-symmetric hoppings. Any ideas? Thank you, Sergey

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