def gb_vs_iters_disp(sigma_0,iters,strength):
"""
Calculate Gilbert Damping versus number of iterations for displacement regime.
"""
with open('result_disp_'+str(strength)+'_'+str(iters)+'.txt', 'w') as f:
system = topological_insulator.make_topo_displacement(50.+0.j, 3.645+0.j, -68.6+0.j, -0.1+0.j, -51.2+0.j, -0.05+0.j, -0.067+0.j, 1.+0.j,sigma_0,0.5,500,20,1,strength)
sys = system[0]
sys.update_hamil_2(calc.build_fm_island(calc.make_hamil_layers(sys.hamil, 20, system[1],20),np.radians(0),0,0.02+0.j,20,20),20,20)
x_list = []
y_list = []
gb = calc.find_gb(0,0,sys)
for num in range(2,iters+2):
system = topological_insulator.make_topo_displacement(50.+0.j, 3.645+0.j, -68.6+0.j, -0.1+0.j, -51.2+0.j, -0.05+0.j, -0.067+0.j, 1.+0.j,sigma_0,0.5,500,20,1,strength)
sys = system[0]
sys.update_hamil_2(calc.build_fm_island(calc.make_hamil_layers(sys.hamil, 20, system[1],20),np.radians(0),0,0.02+0.j,20,20),20,20)
x_list.append(num)
gb = (gb*(num-1) + calc.find_gb(0,0,sys)) / num
y_list.append(gb)
f.write(str(gb) + '\n')
fig = plt.figure()
ax = fig.add_axes([0.1, 0.1, 0.8, 0.8])
ax.plot(x_list,y_list,color='g')
fig.savefig('output_disp_'+str(strength)+'_'+str(iters)+'.png')
plt.close(fig)
return gb
def test_topo_soc_cond_2():
"""
Test conductance with spin-orbit coupling included - version 2.
"""
sigma_0 = 1.e-4+1.e-4j
N = 10
f, ((ax1, ax2, ax3), (ax4, ax5, ax6), (ax7,ax8,ax9)) = plt.subplots(3, 3, sharex='col', sharey='row')
ax_dict = {1: ax1, 2: ax2, 3: ax3, 4: ax4, 5: ax5, 6: ax6, 7: ax7, 8: ax8, 9: ax9}
i = 1
topo = make_topo(50.+0.j, 3.645+0.j, -68.6+0.j, -0.09+0.j, -51.2+0.j, -0.01+0.j, -0.09+0.j, 1.+0.j,sigma_0,0.5,500,N,1.)
topo_sys = topo[0]
t_x = topo[1]
hamil = topo_sys.hamil
for energy in range(-15,-6, 1):
x_list = []
y_list = []
phi_rad = 0
#energy = energy / 100
topo_sys = topo[0]
topo_sys.update_energy( energy / 100)
for theta in range(0,180,18):
theta_rad = np.radians(theta)
hamil = calc.make_hamil_layers(topo_sys.hamil, 50, topo[1],N)
theta_rad = theta * (np.pi / 180)
topo_sys.update_hamil_2(calc.build_fm_island(hamil,theta_rad,phi_rad,0.02+0.j,N,50),N,50)
if np.array_equal(topo_sys.hamil, hamil):
print("unchanged")
x_list.append(theta_rad)
y_list.append(-topo_sys.cond)
ax_dict[i].plot(x_list,y_list)
i += 1
plt.show()
def inf_rashba_integrand(k,energy,layers=20,so_strength=0.0, theta=0.0, randomize=False,rando_strength=0.0, collector=[]):
"""
Integrand function for infinite Rashba plane k-integration.
"""
sigma_0 = 1.e-4+1.e-4j
sites = 1
mag = 100
ener = energy
delt = 0.1
on_site = -0.067+0.j
rashba_sys = build_rashba(on_site,1,1,so_strength,sigma_0, 500, 0.5, sites, 1,ener+0.j)
ras = rashba_sys[0]
if randomize:
ras = gd.randomize_hamil(ras,rando_strength,orbitals=1)
t_x = rashba_sys[1]
hamil_new = ras.hamil + ras.t_y * np.exp((k)*1.j) + calc.hermitian(ras.t_y) * np.exp((-k)*1.j)
hamil_se = sparse.kron(on_site,np.identity(2)) + ras.t_y * np.exp((k)*1.j) + calc.hermitian(ras.t_y) * np.exp((-k)*1.j)
hamil_new = calc.build_fm_island(calc.make_hamil_layers(hamil_new, layers, t_x,sites),theta,0,delt+0.j,sites,layers,padding=False,topo=False)
off_diag = np.diag(hamil_new,1)
print(off_diag)
ras.update_hamil_2(hamil_new, sites, layers,no_mag_leads = True, hamil_sub = hamil_se)
gb = gd.find_gb_local(theta,0,ras,fm_width=layers,n_orbitals=1,topo=False,delta=delt)
gil = gb[0]
s = 0
for i in range(gil.shape[0]):
s+=gil[i]
print("k = " + str(k))
print("s = " + str(s))
if randomize:
collector.append(s)
return s
def test_gb_greens(): sigma_0 = 1.e-4+1.e-4j topo = topological_insulator.make_topo(50.+0.j, 3.645+0.j, -68.6+0.j, -0.1+0.j, -51.2+0.j, -0.05+0.j, -0.067+0.j, 1.+0.j,sigma_0,0.5,500,20,1) system = topo[0] system.update_hamil_2(calc.build_fm_island(calc.make_hamil_layers(system.hamil, 20, topo[1],20),0,0,0.02+0.j,20,20,padding=False),20,20) gb_1 = find_gb_theta_phi(0,0,system) system.greens_ret = mod_greens(system,1e-6) gb_2 = find_gb_theta_phi(0,0,system) return gb
def test_rashba_local():
"""
Compute and plot the local Gilbert Damping and LDOS of finite Rashba plane.
"""
process = psutil.Process(os.getpid())
sigma_0 = 1.e-4+1.e-4j
layers = 100
sites = 20
so_strength = 0.01
mag = 100
ener = -0.2
delt = 0.1
rashba_sys = build_rashba(-0.067+0.j,1,1,so_strength,sigma_0, 500, 0.5, sites, 1,ener+0.j)
ras = rashba_sys[0]
t_x = rashba_sys[1]
ras.update_hamil_2(calc.build_fm_island(calc.make_hamil_layers(ras.hamil, layers, t_x,sites),0,0,delt+0.j,sites,layers,padding=False,topo=False),sites,layers)
ras.greens_ret = gd.mod_greens(ras,1e-2,magmom=mag,delta=delt)
gb = gd.find_gb_local(0,0,ras,fm_width=layers,n_orbitals=1,topo=False,delta=delt)
maj = gb[1]
print(maj.size)
grid = maj.reshape((layers,sites))
fig, ax = plt.subplots()
cax = ax.imshow(grid, extent=(0, sites, 0, layers), interpolation='spline16', cmap=cm.OrRd)
cbar = fig.colorbar(cax)
fig.savefig('rashba_majority'+str(sites)+'x'+str(layers)+'SO'+str(so_strength)+'magmom'+str(mag)+'E'+str(ener)+'.png')
plt.close(fig)
mino = gb[2]
grid = mino.reshape((layers,sites))
fig, ax = plt.subplots()
cax = ax.imshow(grid, extent=(0, sites, 0, layers), interpolation='spline16', cmap=cm.OrRd)
cbar = fig.colorbar(cax)
fig.savefig('rashba_minority'+str(sites)+'x'+str(layers)+'SO'+str(so_strength)+'magmom'+str(mag)+'E'+str(ener)+'.png')
plt.close(fig)
gil = gb[0]
s = 0
for i in range(gil.shape[0]):
s+=gil[i]
grid = gil.reshape((layers,sites))
fig, ax = plt.subplots()
cax = ax.imshow(grid, extent=(0, sites, 0, layers), interpolation='spline16', cmap=cm.OrRd)
cbar = fig.colorbar(cax)
fig.savefig('rashba_gilbert'+str(sites)+'x'+str(layers)+'SO'+str(so_strength)+'magmom'+str(mag)+'E'+str(ener)+'.png')
plt.close(fig)
print("gilbert = " + str(s))
print(process.memory_info().rss)
def test_gb(): energy_low = -0.11 energy_high = -0.07 efermi = -0.09 sigma_0 = 1.e-4+1.e-4j temp = 0.01 topo = topological_insulator.make_topo(50.+0.j, 3.645+0.j, -68.6+0.j, -0.1+0.j, -51.2+0.j, -0.01+0.j, 2.+0.j, 1.+0.j,sigma_0,0.5,500,20,1) system = topo[0] system.update_hamil_2(calc.build_fm_island(calc.make_hamil_layers(system.hamil, 20, topo[1],20),0,0,0.02+0.j,20,20),20,20) x_list = [] y_list = [] for omega in [1e-2]: x_list.append(omega) y_list.append(find_gb_omega(omega,energy_low,energy_high,system,efermi,temp, 0.02)) fig = plt.figure() ax = fig.add_axes([0.1, 0.1, 0.8, 0.8]) ax.plot(x_list,y_list,color='g') plt.show()
def inf_rashba_integrand_cond(k, energy, second=False,layers=20): """ Integrand for calculating conductance of infinite Rashba Plane """ sigma_0 = 1.e-4+1.e-4j sites = 1 so_strength = 0.00 mag = 100 delt = 0.1 on_site = -0.067+0.j rashba_sys = build_rashba(on_site,1,1,so_strength,sigma_0, 500, 0.5, sites, 1,energy+0.j) ras = rashba_sys[0] t_x = rashba_sys[1] hamil_new = ras.hamil + ras.t_y * np.exp((k)*1.j) + calc.hermitian(ras.t_y) * np.exp((-k)*1.j) hamil_se = sparse.kron(np.identity(2),on_site) + ras.t_y * np.exp((k)*1.j) + calc.hermitian(ras.t_y) * np.exp((-k)*1.j) hamil_new = calc.build_fm_island(calc.make_hamil_layers(hamil_new, layers, t_x,sites),np.radians(45),0,delt+0.j,sites,layers,padding=False,topo=False) ras.update_hamil_2(hamil_new, sites, layers,no_mag_leads = True, hamil_sub = hamil_se) cond = -ras.cond return cond
def test_gb_greens_local_2(): sigma_0 = 1.e-4+1.e-4j topo = topological_insulator.make_topo(50.+0.j, 3.645+0.j, -68.6+0.j, -0.1+0.j, -51.2+0.j, -0.05+0.j, -0.067+0.j, 1.+0.j,sigma_0,0.5,500,20,1) system = topo[0] system.update_hamil_2(calc.build_fm_island(calc.make_hamil_layers(system.hamil, 20, topo[1],20),0,0,0.02+0.j,20,20,padding=False),20,20) system.greens_ret = mod_greens(system,1e-3) gb = find_gb_local(0,0,system) xs = [] ys_1 = [] ys_2 = [] s = 0 for i in range(gb[0].shape[0]): xs.append(i) ys_1.append(gb[0][i]) ys_2.append(gb[2][i]) s+=gb[0][i] plt.plot(xs,ys_1) plt.show()
def build_fm_topo(): """ Build a topological insulator with a ferromagnetic island. """ sigma_0 = 1.e-4+1.e-4j topo = make_topo(50.+0.j, 3.645+0.j, -68.6+0.j, -0.1+0.j, -51.2+0.j, -0.05+0.j, -0.067+0.j, 1.+0.j,sigma_0,0.5,500,20,1) topo_sys = topo[0] topo_sys.update_hamil_2(calc.build_fm_island(calc.make_hamil_layers(topo_sys.hamil, 20, topo[1],20),np.radians(0),0,0.02+0.j,20,20),20,20) x_list = [] y_list = [] for theta in range(0,180,18): theta_rad = np.radians(theta) gb = calc.find_gb(theta_rad,0,topo_sys) x_list.append(theta) y_list.append(gb) fig = plt.figure() ax = fig.add_axes([0.1, 0.1, 0.8, 0.8]) ax.plot(x_list,y_list,color='g') plt.show()
def self_energy_vs_location(): """ Plot the self-energy of the system versus site location. """ sigma_0 = 1.e-4+1.e-4j sites = 5 so_strength = 0.01 mag = 100 delt = 0.1 on_site = -0.067+0.j layers = 20 rashba_sys = build_rashba(on_site,1,1,so_strength,sigma_0, 500, 0.5, sites, 1,energy+0.j) ras = rashba_sys[0] t_x = rashba_sys[1] hamil_new = ras.hamil + ras.t_y * np.exp((k)*1.j) + calc.hermitian(ras.t_y) * np.exp((-k)*1.j) hamil_se = sparse.kron(np.identity(2),on_site) + ras.t_y * np.exp((k)*1.j) + calc.hermitian(ras.t_y) * np.exp((-k)*1.j) hamil_new = calc.build_fm_island(calc.make_hamil_layers(hamil_new, layers, t_x,sites),np.radians(45),0,delt+0.j,sites,layers,padding=False,topo=False) ras.update_hamil_2(hamil_new, sites, layers,no_mag_leads = True, hamil_sub = hamil_se) greens = ras.greens_ret self_e = self_energy_integrand(greens, 0, 0, delta) print(self_e)
def gb_versus_temp():
sigma_0 = 1.e-4+1.e-4j
for energy in range(-80,-50):
with open('gbvstemp_result_'+str(energy/1000)+'.txt', 'w') as f:
xs = []
ys = []
energy = energy / 1000
for temp in range(10,410,20):
xs.append(temp)
topo = topological_insulator.make_topo(50.+0.j, 3.645+0.j, -68.6+0.j, -0.1+0.j, -51.2+0.j, -0.05+0.j, energy, 1.+0.j,sigma_0,0.5,500,20,1)
system = topo[0]
system.update_hamil_2(calc.build_fm_island(calc.make_hamil_layers(system.hamil, 20, topo[1],20),0,0,0.01+0.j,20,20,padding=False),20,20)
system.greens_ret = mod_greens(system,5e-3,magmom=100,boson_dist=boson_dist(0.01,temp))
gb = find_gb_local(0,0,system)
s = 0
for i in range(gb[0].shape[0]):
s+=gb[0][i]
ys.append(s)
f.write(str(energy)+' '+str(temp)+' '+str(s))
plt.plot(xs,ys)
plt.savefig('gb_vs_temp_' + str(energy)+'.png')
plt.close()
def test_rashba_cond():
"""
Test conductance of Rashba plane over range of energies.
"""
sigma_0 = 1.e-4+1.e-4j
layers = 30
sites = 20
so_strength = 0.01
mag = 100
xs = []
ys = []
for energy in range(-600,600, 5):
rashba_sys = build_rashba(-0.067+0.j,1,1,so_strength,sigma_0, 500, 0.5, sites, 1,energy/1000)
ras = rashba_sys[0]
t_x = rashba_sys[1]
ras.update_hamil_2(calc.build_fm_island(calc.make_hamil_layers(ras.hamil, layers, t_x,sites),0,0,0.01+0.j,sites,layers,padding=False,topo=False),sites,layers)
xs.append(energy/1000)
ys.append(-ras.cond)
fig = plt.figure()
ax = fig.add_axes([0.1, 0.1, 0.8, 0.8])
ax.plot(xs,ys,color='g')
fig.savefig('rashba_cond'+str(sites)+'x'+str(layers)+'SO'+str(so_strength)+'magmom'+str(mag)+'.png')
plt.close(fig)
def test_gb_greens_local():
sigma_0 = 1.e-4+1.e-4j
layers = 50
sites = 20
topo = topological_insulator.make_topo(50.+0.j, 3.645+0.j, -68.6+0.j, -0.1+0.j, -51.2+0.j, -0.05+0.j, -0.067+0.j, 1.+0.j,sigma_0,0.5,500,sites,1)
system = topo[0]
system.update_hamil_2(calc.build_fm_island(calc.make_hamil_layers(system.hamil, layers, topo[1],sites),0,0,0.01+0.j,sites,layers,padding=False),sites,layers)
system.greens_ret = mod_greens(system,1e-2,magmom=100)
gb = find_gb_local(0,0,system,fm_width=layers)
maj = gb[1]
grid = maj.reshape((layers,sites))
fig, ax = plt.subplots()
cax = ax.imshow(grid, extent=(0, sites, 0, layers), interpolation='spline16', cmap=cm.OrRd)
cbar = fig.colorbar(cax)
#cbar.ax.set_yticklabels(['< -1', '0', '> 1'])
fig.savefig('majority'+str(sites)+'x'+str(layers)+'.png')
plt.close(fig)
mino = gb[2]
grid = mino.reshape((layers,sites))
fig, ax = plt.subplots()
cax = ax.imshow(grid, extent=(0, sites, 0, layers), interpolation='spline16', cmap=cm.OrRd)
cbar = fig.colorbar(cax)
#cbar.ax.set_yticklabels(['< -1', '0', '> 1'])
fig.savefig('minority'+str(sites)+'x'+str(layers)+'.png')
plt.close(fig)
#return gb
gil = gb[0]
s = 0
for i in range(gil.shape[0]):
s+=gil[i]
grid = gil.reshape((layers,sites))
fig, ax = plt.subplots()
cax = ax.imshow(grid, extent=(0, sites, 0, layers), interpolation='spline16', cmap=cm.OrRd)
cbar = fig.colorbar(cax)
#cbar.ax.set_yticklabels(['< -1', '0', '> 1'])
fig.savefig('gilbert'+str(sites)+'x'+str(layers)+'.png')
plt.close(fig)
