Dear kwant users and developers, I am trying to calculate the up and down conductance in the following system, separately, to calculate spin polarization. I followed some of the steps suggested in the mailing list before (wavefuncation or current operator). I know for this system I should get the same conductance for up and down spins. I first calculate the total conductance But then 1- The wave function approach does not give the the up/down conductance similar to total. 2- the current-operator approach gives the error 'kwant.graph.core.EdgeDoesNotExistError'.
I have attached the code in the following. If one runs the code it plot the system with leads correctly the first conductance plot is what one expects (if trans:) then the second plot is incorrect (if strans1:) and then gives the error (if strans:). I appreciate any help Patrik ----------------------------------------------------------------- from mpl_toolkits.mplot3d import Axes3D from scipy.spatial import * from matplotlib import rcParams from numpy import * from numpy.linalg import * import pickle import sys import os import string import heapq import kwant import tinyarray from matplotlib import pyplot chiral=True if chiral: p = pi/5 #phi t = 0.66 #theta a = 0.34 x = 1.4 e1 = 0 e2 = 0.3 t2=0.1 t1=-x*t2 t0 = 2 lam=-0.08 t_so1 = 0.01 #spin-orbit coupling param t_so2 = x*t_so1 #spin-orbit coupling param tl=tr=0.3 N = 30 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]]) no=2 #number of orbitals def sigma_v1(ap): # pauli metrix along the vertical axis value=sigma_z*cos(t)+sin(t)*(sigma_x*sin(ap)-sigma_y*cos(ap)) return value def sigma_v2(ap): # pauli metrix along the vertical axis value=sigma_z*cos(t)-sin(t)*(sigma_x*sin(ap)-sigma_y*cos(ap)) return value def family_color(sites): return 'black' #if site.family == sites def hopping_lw(site1, site2): return 0.08 class Amorphous(kwant.builder.SiteFamily): def __init__(self, coords): self.coords = coords super(Amorphous, self).__init__("amorphous", "",no) def normalize_tag(self, tag): try: tag = int(tag[0]) except: raise KeyError if 0 <= tag < len(coords): return tag else: raise KeyError def pos(self, tag): return self.coords[tag] coords=[(0.0000000000, 0.0000000000, 0.0000000000), (-0.1336881039, 0.4114496766, 0.3400000000), (-0.4836881039, 0.6657395614, 0.6800000000), (-0.9163118961, 0.6657395614, 1.0200000000), (-1.2663118961, 0.4114496766, 1.3600000000), (-1.4000000000, 0.0000000000, 1.7000000000), (-1.2663118961, -0.4114496766, 2.0400000000), (-0.9163118961, -0.6657395614, 2.3800000000), (-0.4836881039, -0.6657395614, 2.7200000000), (-0.1336881039, -0.4114496766, 3.0600000000), (0.0000000000, -0.0000000000, 3.4000000000), (-0.1336881039, 0.4114496766, 3.7400000000), (-0.4836881039, 0.6657395614, 4.0800000000), (-0.9163118961, 0.6657395614, 4.4200000000), (-1.2663118961, 0.4114496766, 4.7600000000), (-1.4000000000, 0.0000000000, 5.1000000000), (-1.2663118961, -0.4114496766, 5.4400000000), (-0.9163118961, -0.6657395614, 5.7800000000), (-0.4836881039, -0.6657395614, 6.1200000000), (-0.1336881039, -0.4114496766, 6.4600000000), (0.0000000000, -0.0000000000, 6.8000000000), (-0.1336881039, 0.4114496766, 7.1400000000), (-0.4836881039, 0.6657395614, 7.4800000000), (-0.9163118961, 0.6657395614, 7.8200000000), (-1.2663118961, 0.4114496766, 8.1600000000), (-1.4000000000, 0.0000000000, 8.5000000000), (-1.2663118961, -0.4114496766, 8.8400000000), (-0.9163118961, -0.6657395614, 9.1800000000), (-0.4836881039, -0.6657395614, 9.5200000000), (-0.1336881039, -0.4114496766, 9.8600000000), (-1.4000000000, 0.0000000000, 0.0000000000), (-1.2663118961, -0.4114496766, 0.3400000000), (-0.9163118961, -0.6657395614, 0.6800000000), (-0.4836881039, -0.6657395614, 1.0200000000), (-0.1336881039, -0.4114496766, 1.3600000000), (0.0000000000, -0.0000000000, 1.7000000000), (-0.1336881039, 0.4114496766, 2.0400000000), (-0.4836881039, 0.6657395614, 2.3800000000), (-0.9163118961, 0.6657395614, 2.7200000000), (-1.2663118961, 0.4114496766, 3.0600000000), (-1.4000000000, 0.0000000000, 3.4000000000), (-1.2663118961, -0.4114496766, 3.7400000000), (-0.9163118961, -0.6657395614, 4.0800000000), (-0.4836881039, -0.6657395614, 4.4200000000), (-0.1336881039, -0.4114496766, 4.7600000000), (0.0000000000, -0.0000000000, 5.1000000000), (-0.1336881039, 0.4114496766, 5.4400000000), (-0.4836881039, 0.6657395614, 5.7800000000), (-0.9163118961, 0.6657395614, 6.1200000000), (-1.2663118961, 0.4114496766, 6.4600000000), (-1.4000000000, 0.0000000000, 6.8000000000), (-1.2663118961, -0.4114496766, 7.1400000000), (-0.9163118961, -0.6657395614, 7.4800000000), (-0.4836881039, -0.6657395614, 7.8200000000), (-0.1336881039, -0.4114496766, 8.1600000000), (0.0000000000, -0.0000000000, 8.5000000000), (-0.1336881039, 0.4114496766, 8.8400000000), (-0.4836881039, 0.6657395614, 9.1800000000), (-0.9163118961, 0.6657395614, 9.5200000000), (-1.2663118961, 0.4114496766, 9.8600000000)] amorphous_lat = Amorphous(coords) syst = kwant.Builder() #adding the onsite and hopping to the system for i in range(N): syst[amorphous_lat(i)] = e1*sigma_0 syst[amorphous_lat(N+i)] = e2*sigma_0 syst[amorphous_lat(i), amorphous_lat(N+i)] = lam*sigma_0 if i > 0: syst[amorphous_lat(i), amorphous_lat(i-1)] = t1*sigma_0 + 1j*t_so1*(sigma_v1(i*p)+sigma_v1((i-1)*p)) syst[amorphous_lat(N+i),amorphous_lat(N+i-1)] = t2*sigma_0 + 1j*t_so2*(sigma_v2(i*p)+sigma_v2((i-1)*p)) # If we want to attach to vertical 1D chains to the system # we first add a site of the down lead to the scattering region lat=kwant.lattice.cubic(a, norbs=no) syst[lat(0, 0, -1)] = e1*sigma_0 syst[amorphous_lat(0), lat(0, 0, -1)] = tl*sigma_0 # We make a regular down lead and attach it to the system dn_lead = kwant.Builder(kwant.TranslationalSymmetry((0, 0, -a))) dn_lead[lat(0, 0, -2)] = e1*sigma_0 dn_lead[lat.neighbors()] = t0*sigma_0 syst.attach_lead(dn_lead) prim_vecs=tinyarray.array([(a,0.,0.),(0.,a,0.),(0.,0.,a)]) offset=tinyarray.array((-1.2663118961, 0.4114496766,0.0)) lat2=kwant.lattice.Monatomic(prim_vecs, offset, norbs=no) syst[lat2(0, 0, N)] = e1*sigma_0 syst[amorphous_lat(2*N-1), lat2(0, 0, N)] = tr*sigma_0 up_lead = kwant.Builder(kwant.TranslationalSymmetry((0, 0, a))) up_lead[lat2(0, 0, N+1)] = e1*sigma_0 up_lead[lat2.neighbors()] = t0*sigma_0 syst.attach_lead(up_lead) system=kwant.plot(syst, site_lw=0.1, site_color=family_color, hop_lw=hopping_lw) trans=True if trans: syst = syst.finalized() energies = [] data = [] for ie in range(-320,520): energy = ie * 0.001 smatrix = kwant.smatrix(syst, energy=energy) energies.append(energy) data.append(0.5*smatrix.transmission(1, 0)) fig = pyplot.figure(figsize=(6,2)) pyplot.plot(energies, data) pyplot.xlim([-0.32,0.52]) pyplot.ylim([-0.03,1.25]) pyplot.xlabel("energy [eV]") pyplot.ylabel("conductance [e^2/h]") pyplot.show() strans1=True if strans1: #syst = syst.finalized() energies = [] data = [] def oscle(ene, lead_nr): wfs=kwant.wave_function(syst, ene, check_hermiticity=True)(lead_nr) spin_current_z = 0 for psi in wfs: psi_start = psi[0 : 2] psi_end = psi[2 * 61: 2 * 61 + 2] #spin_current_z += -2 * imag(psi_end.conjugate().dot(sigma_z).dot(psi_start)) spin_current_z += abs(imag(psi_end.conjugate().dot(sigma_z).dot(psi_start))) return spin_current_z for ie in range(-320,520): energy = ie * 0.001 energies.append(energy) data.append(oscle(ene=energy, lead_nr=1)) fig = pyplot.figure(figsize=(6,2)) pyplot.plot(energies, data) pyplot.show() strans=True if strans: #syst = syst.finalized() J_spin = kwant.operator.Current(syst, sigma_z, where=[(amorphous_lat(0), amorphous_lat(N-2))], sum=True) all_wfs = kwant.wave_function(syst, energy=0.25)(1) spin_current_list = sum(J_spin(wf) for wf in all_wfs) print(spin_current_list)