Hall conductivity from kwant.kpm.conductivity scaled?
Hello, I was calculating the Hall conductivity for the QWZ model of the Chern insulator using kwant.kpm.conductivity as shown in the tutorial and the result shows that the Hall conductivity within the energy gap is 0.5 when it should have been 1 if it was scaled by the conductance quantum. Is the result scaled by some other factor? I am providing my code below, L = 21; W = 21 M = -1.0 def ChernIns(L,W,M): lat = kwant.lattice.square(norbs=2) sys = kwant.Builder() for i in range(L): for j in range(W): sys[lat(i,j)] = (2+M)*sz if i>0: sys[lat(i,j),lat(i-1,j)] = -0.5*sz+0.5j*sx if j>0: sys[lat(i,j),lat(i,j-1)] = -0.5*sz+0.5j*sy return lat, sys.finalized() where = lambda s: np.linalg.norm(s.pos-np.array([L/2,W/2]))<2 lat, syst_topo = ChernIns(L,W,M) s_factory = kwant.kpm.LocalVectors(syst_topo,where) cond_xy = kwant.kpm.conductivity(syst_topo, alpha='y',beta='x',mean=True,num_vectors=None,vector_factory=s_factory,rng=0)#,mean=True,num_vectors=None,vector_factory=s_factory,rng=0) energies = cond_xy.energies Sigma_xy = np.array([cond_xy(mu=e,temperature=0.01).real for e in energies]) area_per_site = np.linalg.norm(np.cross(*lat.prim_vecs))/len(lat.sublattices) Sigma_xy = Sigma_xy/area_per_site fig = plt.figure(dpi=150) plt.plot(energies,Sigma_xy,'-k') plt.xlabel('Energy') plt.ylabel(r'$\sigma_{xy}$') plt.show() Any help is appreciated. Best, Adipta.
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adiptapal7@gmail.com