Dear all, Using the Kwant package to calculate the spin-resolved density of states in a graphene nanoribbon system, where the central device region contains Rashba spin-orbit coupling (RSOC) in its Hamiltonian while the leads are free of spin-orbit coupling. We aim to obtain the total spin-up density of states distribution in the device region as the electron energy varies from 0 to 1.The attached files contain our program code. We found that when the wire contains a suspended key, we can run the result, but we don't know if the result is correct. When the wire does not have a hovering key, a strange value appears when executing, and an error is reported. We seek advice on the necessary modifications to correct these errors. For reference and convenience, I attach the code I'm using at the end of this message. Any help and guidance would be appreciated! Best regards, Rease ############################################ import numpy as np import tinyarray as ta import kwant import matplotlib.pyplot as plt sigma_0 = ta.array([[1, 0], [0, 1]]) sigma_x = ta.array([[0, 1], [1, 0]]) sigma_y = ta.array([[0, -1j], [1j, 0]]) sigma_z = ta.array([[1, 0], [0, -1]]) lat = kwant.lattice.honeycomb(norbs=2) def make_system(t=1.0, lambda_rsoc=0.1): syst = kwant.Builder() def onsite(site): return sigma_0 def hopping(site1, site2): dx, dy = site2.pos - site1.pos rsoc = 1j * lambda_rsoc * (sigma_x * dy - sigma_y * dx) return -t * sigma_0 + rsoc def rectangle(pos): x, y = pos return 0 <= x < 10 and 0.5 <= y < 10 syst[lat.shape(rectangle, (0, 0))] = onsite syst[lat.neighbors()] = hopping def lead_onsite(site): return sigma_0 def lead_hopping(site1, site2): return -t * sigma_0 sym_left = kwant.TranslationalSymmetry((-1, 0)) lead_left = kwant.Builder(sym_left, conservation_law=-sigma_z) lead_left[lat.shape(rectangle, (0, 0))] = lead_onsite lead_left[lat.neighbors()] = lead_hopping syst.attach_lead(lead_left) sym_right = kwant.TranslationalSymmetry((1, 0)) lead_right = kwant.Builder(sym_right, conservation_law=-sigma_z) lead_right[lat.shape(rectangle, (0, 0))] = lead_onsite lead_right[lat.neighbors()] = lead_hopping syst.attach_lead(lead_right) return syst syst = make_system().finalized() def spin_up_dos(syst): spin_up = 0.5 * (sigma_0 + sigma_z) return kwant.operator.Density(syst, spin_up, sum=True) energies = np.linspace(0, 1, 100) dos = [] for energy in energies: ldos = kwant.ldos(syst, energy) dos.append(np.sum(ldos[::2])) plt.figure(figsize=(8, 6)) plt.plot(energies, dos, label="Spin-Up DOS") plt.xlabel("Energy [t]") plt.ylabel("Density of States") plt.title("Spin-Up Density of States in Graphene Nanoribbon") plt.legend() plt.grid(True) plt.show()