Dear Sir,
I am trying to plot the energy as a function of magnetic field for a 3D
case, but I am getting tedious results. The system is infinite in two
directions and has some width in the third direction. Please have a look at
the code attached below. I tried a lot but failed. Is the code correct or I
am wrong somewhere.
Thank you.
*import kwantimport scipy.sparse.linalg as slaimport matplotlib.pyplot as
pltimport tinyarrayimport numpy as npfrom numpy import cos, sin, piimport
cmathfrom cmath import expsigma_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]])def make_system(a=1, L=30, W=10, H=10, t=1.0, t_x=1.0, t_y=1.0,
t_z=1.0, lamda=0.1, beta=1.05): def onsite(site): return (t_z *
cos(beta) + 2 * t) * sigma_z def hoppingx(site0, site1):
return (-0.5 * t * sigma_z - 0.5 * 1j * t_x * sigma_x) def
hoppingy(site0, site1): return -0.5 * t * sigma_z - 0.5 * 1j * t_y *
sigma_y def hoppingz(site0, site1, B): y = site1.pos[1]
return (-0.5 * t_z * sigma_z - 0.5 * 1j * lamda * sigma_0) * exp(2 * pi *
1j * B * a * (y-40)) syst = kwant.Builder() lat =
kwant.lattice.cubic(a) syst[(lat(z, y, x) for z in range(H) for y in
range(W) for x in range(L))] = onsite syst[kwant.builder.HoppingKind((1,
0, 0), lat, lat)] = hoppingz syst[kwant.builder.HoppingKind((0, 1, 0),
lat, lat)] = hoppingy syst[kwant.builder.HoppingKind((0, 0, 1), lat,
lat)] = hoppingx
lead1=kwant.Builder(kwant.TranslationalSymmetry((0,-a,0)))
lead1[(lat(z,y,x) for z in range(H)for y in range(W)for x in
range(L))]=onsite lead1[kwant.builder.HoppingKind((1, 0, 0), lat, lat)]
= hoppingz lead1[kwant.builder.HoppingKind((0, 1, 0), lat, lat)] =
hoppingy lead1[kwant.builder.HoppingKind((0, 0, 1), lat, lat)] =
hoppingx syst.attach_lead(lead1) syst.attach_lead(lead1.reversed())
lead2=kwant.Builder(kwant.TranslationalSymmetry((-a,0,0)))
lead2[(lat(z,y,x) for z in range(H)for y in range(W)for x in
range(L))]=onsite lead2[kwant.builder.HoppingKind((1, 0, 0), lat, lat)]
= hoppingz lead2[kwant.builder.HoppingKind((0, 1, 0), lat, lat)] =
hoppingy lead2[kwant.builder.HoppingKind((0, 0, 1), lat, lat)] =
hoppingx syst.attach_lead(lead2) syst.attach_lead(lead2.reversed())
syst = syst.finalized() return systdef analyze_system(): syst =
make_system() kwant.plot(syst) Bfields = np.linspace(0, 0.002, 100)
energies = [] for B in Bfields: ham_mat =
syst.hamiltonian_submatrix(params=dict(B=B), sparse=True) ev, evec =
sla.eigsh(ham_mat.tocsc(), k=20, sigma=0) energies.append(ev)
#print(energies) plt.figure() plt.plot(Bfields, energies)
plt.xlabel("magnetic field [${10^-3 h/e}$]") plt.ylabel("energy [t]")
plt.ylim(0, 0.11) plt.showdef main(): syst = make_system()
analyze_system()main()*
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With Best Regards
NAVEEN YADAV
Ph.D Research Scholar
Deptt. Of Physics & Astrophysics
University Of Delhi.
