# coupling to the leads - nearest neighbor only H_scat[1, 2] = H_scat[2, 1] = H_scat[3, 4] = H_scat[4, 3] = 0.2 tcalc = TransportCalculator( h=H_scat, # Scattering Hamiltonian h1=H_lead, # Lead 1 (left) h2=H_lead, # Lead 2 (right) energies=np.arange(-3, 3, 0.02)) T_e = tcalc.get_transmission() pylab.plot(tcalc.energies, T_e) pylab.title('Transmission function') pylab.show() tcalc.set(pdos=[2, 3]) pdos_ne = tcalc.get_pdos() pylab.plot(tcalc.energies, pdos_ne[0], ':') pylab.plot(tcalc.energies, pdos_ne[1], '--') pylab.title('Projected density of states') pylab.show() h_rot, s_rot, eps_n, vec_nn = tcalc.subdiagonalize_bfs([2, 3]) tcalc.set(h=h_rot, s=s_rot) # Set the rotated matrices for n in range(2): print("eigenvalue, eigenvector:", eps_n[n], ',', vec_nn[:, n]) pdos_rot_ne = tcalc.get_pdos() pylab.plot(tcalc.energies, pdos_rot_ne[0], ':') pylab.plot(tcalc.energies, pdos_rot_ne[1], '--') pylab.title('Projected density of states (rotated)') pylab.show()
def test_transport_calculator(): H_lead = np.zeros([4, 4]) # On-site energies are zero for i in range(4): H_lead[i, i] = 0.0 # Nearest neighbor hopping is -1.0 for i in range(3): H_lead[i, i + 1] = -1.0 H_lead[i + 1, i] = -1.0 # Next-nearest neighbor hopping is 0.2 for i in range(2): H_lead[i, i + 2] = 0.2 H_lead[i + 2, i] = 0.2 H_scat = np.zeros([6, 6]) # Principal layers on either side of S H_scat[:2, :2] = H_lead[:2, :2] H_scat[-2:, -2:] = H_lead[:2, :2] # Scattering region H_scat[2, 2] = 0.0 H_scat[3, 3] = 0.0 H_scat[2, 3] = -0.8 H_scat[3, 2] = -0.8 # External coupling H_scat[1, 2] = 0.2 H_scat[2, 1] = 0.2 H_scat[3, 4] = 0.2 H_scat[4, 3] = 0.2 energies = np.arange(-3, 3, 0.02) tcalc = TransportCalculator(h=H_scat, h1=H_lead, eta=0.02, energies=energies) T = tcalc.get_transmission() tcalc.set(pdos=[2, 3]) pdos = tcalc.get_pdos() tcalc.set(dos=True) dos = tcalc.get_dos() write('T.dat', tcalc.energies, T) write('pdos0.dat', tcalc.energies, pdos[0]) write('pdos1.dat', tcalc.energies, pdos[1]) #subdiagonalize h_rot, s_rot, eps, u = tcalc.subdiagonalize_bfs([2, 3], apply=True) T_rot = tcalc.get_transmission() dos_rot = tcalc.get_dos() pdos_rot = tcalc.get_pdos() write('T_rot.dat', tcalc.energies, T_rot) write('pdos0_rot.dat', tcalc.energies, pdos_rot[0]) write('pdos1_rot.dat', tcalc.energies, pdos_rot[1]) print('Subspace eigenvalues:', eps) assert sum(abs(eps - (-0.8, 0.8))) < 2.0e-15, 'Subdiagonalization. error' print('Max deviation of T after the rotation:', np.abs(T - T_rot).max()) assert max(abs(T - T_rot)) < 2.0e-15, 'Subdiagonalization. error' #remove coupling h_cut, s_cut = tcalc.cutcoupling_bfs([2], apply=True) T_cut = tcalc.get_transmission() dos_cut = tcalc.get_dos() pdos_cut = tcalc.get_pdos() write('T_cut.dat', tcalc.energies, T_cut) write('pdos0_cut.dat', tcalc.energies, pdos_cut[0]) write('pdos1_cut.dat', tcalc.energies, pdos_cut[1])
H_scat[3, 3] = 0.0 H_scat[2, 3] = -0.8 H_scat[3, 2] = -0.8 # External coupling H_scat[1, 2] = 0.2 H_scat[2, 1] = 0.2 H_scat[3, 4] = 0.2 H_scat[4, 3] = 0.2 energies = np.arange(-3, 3, 0.02) tcalc = TransportCalculator(h=H_scat, h1=H_lead, eta=0.02, energies=energies) T = tcalc.get_transmission() tcalc.set(pdos=[2, 3]) pdos = tcalc.get_pdos() tcalc.set(dos=True) dos = tcalc.get_dos() write('T.dat', tcalc.energies, T) write('pdos0.dat', tcalc.energies, pdos[0]) write('pdos1.dat', tcalc.energies, pdos[1]) #subdiagonalize h_rot, s_rot, eps, u = tcalc.subdiagonalize_bfs([2, 3], apply=True) T_rot = tcalc.get_transmission() dos_rot = tcalc.get_dos() pdos_rot = tcalc.get_pdos() write('T_rot.dat', tcalc.energies, T_rot)
for n in range(len(eps_n)): print("bf %i corresponds to the eigenvalue %.2f eV" % (bfs[n], eps_n[n])) # Switch to the rotated basis set tcalc.set(h=h_rot, s=s_rot) # plot the transmission function tcalc.set(energies=np.arange(-8, 4, 0.1)) T = tcalc.get_transmission() pylab.plot(tcalc.energies, T) pylab.title('Transmission function') pylab.show() # ... and the projected density of states (pdos) of the H2 molecular orbitals tcalc.set(pdos=bfs) pdos_ne = tcalc.get_pdos() pylab.plot(tcalc.energies, pdos_ne[0], label='bonding') pylab.plot(tcalc.energies, pdos_ne[1], label='anti-bonding') pylab.title('Projected density of states') pylab.legend() pylab.show() # Cut the coupling to the anti-bonding orbital. print('Cutting the coupling to the renormalized molecular state at %.2f eV' % (eps_n[1])) h_rot_cut, s_rot_cut = tcalc.cutcoupling_bfs([bfs[1]]) tcalc.set(h=h_rot_cut, s=s_rot_cut) pylab.plot(tcalc.energies, tcalc.get_transmission()) pylab.title('Transmission without anti-bonding orbital') pylab.show()
# coupling to the leads - nearest neighbor only H_scat[1, 2] = H_scat[2, 1] = H_scat[3, 4] = H_scat[4, 3] = 0.2 tcalc = TransportCalculator(h=H_scat, # Scattering Hamiltonian h1=H_lead, # Lead 1 (left) h2=H_lead, # Lead 2 (right) energies=np.arange(-3, 3, 0.02)) T_e = tcalc.get_transmission() pylab.plot(tcalc.energies, T_e) pylab.title('Transmission function') pylab.show() tcalc.set(pdos=[2, 3]) pdos_ne = tcalc.get_pdos() pylab.plot(tcalc.energies, pdos_ne[0], ':') pylab.plot(tcalc.energies, pdos_ne[1], '--') pylab.title('Projected density of states') pylab.show() h_rot, s_rot, eps_n, vec_nn = tcalc.subdiagonalize_bfs([2, 3]) tcalc.set(h=h_rot, s=s_rot) # Set the rotated matrices for n in range(2): print("eigenvalue, eigenvector:", eps_n[n], ',', vec_nn[:, n]) pdos_rot_ne = tcalc.get_pdos() pylab.plot(tcalc.energies, pdos_rot_ne[0], ':') pylab.plot(tcalc.energies, pdos_rot_ne[1], '--') pylab.title('Projected density of states (rotated)') pylab.show()
# External coupling H_scat[1,2] = 0.2 H_scat[2,1] = 0.2 H_scat[3,4] = 0.2 H_scat[4,3] = 0.2 energies = np.arange(-3,3,0.02) tcalc = TransportCalculator(h=H_scat, h1=H_lead, h2=H_lead, energies=energies) T = tcalc.get_transmission() tcalc.set(pdos=[2, 3]) pdos = tcalc.get_pdos() tcalc.set(dos=True) dos = tcalc.get_dos() write('T.dat',tcalc.energies,T) write('pdos0.dat', tcalc.energies,pdos[0]) write('pdos1.dat', tcalc.energies,pdos[1]) #subdiagonalize h_rot, s_rot, eps, u = tcalc.subdiagonalize_bfs([2, 3]) tcalc.set(h=h_rot,s=s_rot) T_rot = tcalc.get_transmission() dos_rot = tcalc.get_dos() pdos_rot = tcalc.get_pdos()
for n in range(len(eps_n)): print("bf %i corresponds to the eigenvalue %.2f eV" % (bfs[n], eps_n[n])) # Switch to the rotated basis set tcalc.set(h=h_rot, s=s_rot) # plot the transmission function tcalc.set(energies=np.arange(-8, 4, 0.1)) T = tcalc.get_transmission() pylab.plot(tcalc.energies, T) pylab.title('Transmission function') pylab.show() # ... and the projected density of states (pdos) of the H2 molecular orbitals tcalc.set(pdos=bfs) pdos_ne = tcalc.get_pdos() pylab.plot(tcalc.energies, pdos_ne[0], label='bonding') pylab.plot(tcalc.energies, pdos_ne[1], label='anti-bonding') pylab.title('Projected density of states') pylab.legend() pylab.show() # Cut the coupling to the anti-bonding orbital. print('Cutting the coupling to the renormalized molecular state at %.2f eV' % ( eps_n[1])) h_rot_cut, s_rot_cut = tcalc.cutcoupling_bfs([bfs[1]]) tcalc.set(h=h_rot_cut, s=s_rot_cut) pylab.plot(tcalc.energies, tcalc.get_transmission()) pylab.title('Transmission without anti-bonding orbital') pylab.show()