Hey Anton,
I should have thought of the physics behind my hopping values when calling
the conservation law
I have used realistic hopping values instead of np.eye(2, 6) and it is
working now.
Regards,
Adel
Le dim. 15 août 2021 à 14:43, Anton Akhmerov <anton.akhmerov...@gmail.com>
a écrit :
> Hi Adel,
>
> Running the code you provided also produces the following warning.
>
> > UserWarning: Hamiltonian breaks Conservation law, ignoring the symmetry
> in the computation.
>
> This should explain what is happening.
>
> Best,
> Anton
>
> On Sun, 15 Aug 2021 at 14:19, Adel Belayadi <adelp...@gmail.com> wrote:
> >
> > Dear Anton;
> >
> > Thank you for your reply
> >
> > I have used the conservation_law as you have suggested. In fact, a
> dictionary or function definition of the conservation law is working fine
> now. I am not getting an error while defining the conservation law.
> However, when calling smatrix.transmission((1, 1), (0, 1)) which stands
> for spin up-up transmittance it raises: index 2 is out of bounds for axis 0
> with size 2.
> >
> > Please see for example the following script which have two site
> families, one with 2 orbitals and the second with 6 orbitals
> >
> > Cheers, Adel
> >
> >
> > import kwant
> > from matplotlib import pyplot
> > import numpy as np
> > from math import sqrt
> > lat = kwant.lattice.honeycomb(a=1, norbs=[2, 6] , name=["a", "b"])
> > a, b =lat.sublattices
> > def make_sys(l, w, cons_law):
> > def rect(pos):
> > x, y = pos
> > return abs(x) < l and abs(y) < w
> > sys=kwant.Builder()
> > sys[a.shape(rect, (0, 0))] = np.eye(2)
> > sys[b.shape(rect, (0, 0))] = np.eye(6)
> > ab_hopps= (((0, 0), a, b), ((0, 1), a, b), ((-1, 1), a, b))
> > sys[[kwant.builder.HoppingKind(*hopping) for hopping in ab_hopps]] =
> np.eye(2,6)
> > sys.eradicate_dangling()
> > sys[a.neighbors(1)] = np.eye(2)
> > sys[b.neighbors(1)] = np.eye(6)
> > ### creating leads
> > def lead_shape(pos):
> > x, y = pos
> > return abs(y)< w
> > sym = kwant.TranslationalSymmetry(lat.vec((-1, 0)))
> > sym.add_site_family(lat.sublattices[0], other_vectors=[(-1, 2)])
> > sym.add_site_family(lat.sublattices[1], other_vectors=[(-1, 2)])
> > lead = kwant.Builder(sym, conservation_law=cons_law)
> > lead[a.shape(rect, (0, 0))] = np.eye(2)
> > lead[b.shape(rect, (0, 0))] = np.eye(6)
> > lead[[kwant.builder.HoppingKind(*hopping) for hopping in ab_hopps]]
> = np.eye(2,6)
> > lead.eradicate_dangling()
> > lead[a.neighbors(1)] = np.eye(2)
> > lead[b.neighbors(1)] = np.eye(6)
> > sys.attach_lead(lead)
> > sys.attach_lead(lead.reversed())
> > return sys
> >
> >
> > syst = make_sys(l=3, w=2, cons_law= None)
> > kwant.plot(syst ,fig_size=(8, 8))
> > pyplot.show()
> >
> > print('************ calling the conservation law **************')
> > sigma_z = np.array([[1, 0], [0, -1]])
> > cons_law = {a: -sigma_z , b: -np.kron(sigma_z, np.eye(3))}
> > syst = make_sys(l=3, w=2, cons_law=cons_law)
> > smatrix = kwant.smatrix(syst.finalized(), 0.01)
> > total_trans = smatrix.transmission(1, 0)
> > up_up_trans = smatrix.transmission((1, 0), (0, 0))
> > dn_dn_trans = smatrix.transmission((1, 1), (0, 1))
> > up_dn_trans = smatrix.transmission((1, 1), (0, 0))
> > dn_up_trans = smatrix.transmission((1, 0), (0, 1))
> > print(total_trans)
> > print(up_up_trans)
> > print(dn_dn_trans)
> > print(up_dn_trans)
> > print(dn_up_trans)
> > print(round(total_trans,
> 3)==round(up_up_trans+dn_dn_trans+up_dn_trans+dn_up_trans, 3))
> >
> >
> >
> > Le sam. 14 août 2021 à 17:06, Anton Akhmerov <
> anton.akhmerov...@gmail.com> a écrit :
> >>
> >> Hi Adel,
> >>
> >> Please check the documentation [1]. Since you have multiple site
> >> families, you need to specify the conservation law as a dictionary, so
> >> {metal_like_sub: -np.kron(sigma_z, np.eye(3)), C_like_sub1: -sigma_z,
> >> C_like_sub2: -sigma_z}.
> >>
> >> Best,
> >> Anton
> >>
> >>
> https://kwant-project.org/doc/1/reference/generated/kwant.builder.Builder#kwant.builder.Builder
> >>
> >> On Sat, 14 Aug 2021 at 16:08, Adel Belayadi <adelp...@gmail.com> wrote:
> >> >
> >> > Dear Kwant user,
> >> > Good day and I hope this email finds you well.
> >> > Using conservation law was fully explained, in the Kwant mailing
> list, while we are having sublattices with the same degree of freedom (same
> number of orbitals). For instance, if we have two sites with 3 orbitals in
> the case of a spin full Hamiltonian, the onsite matrix is
> (onsite_matrix(6*6) for each site ). So in this case, the conservation law
> will be straightforward: conservation_law=-np.kron(sigma_z, np.eye(3)).But
> what would be the case if we are dealing with sublattices which have
> different numbers of orbitals?
> >> >
> >> > In my case, I am interested in spin conductance. I am using 3
> sublattices with different orbitals. Let us say for instance
> >> > sublattice0 has (6-orbitals), sublattice1 with (2-orbitals) and
> sublattice2 with (2-orbitals). In fact I am working on hetero-structure
> with two sites of C-like(pz with spin up and down) and one site of
> metal-like(3d-orbitals with spin up and down). I can resume my lattice as
> follow
> >> >
> >> > lat = kwant.lattice.general(prim_vecs, basis=[ [...], [...], [...]] ,
> norbs=[6, 2, 2])
> >> > metal-like_sub, C-like_sub1, C-like_sub2 = lat.sublattices
> >> >
> >> > According to my understanding the conservation law would be something
> like
> >> > conservation_law=-np.kron(sigma_z, np.eye(5)). However Kwant raises
> an error with my choice of the conservation law.
> >> >
> >> > Is there something missing with my understanding of the conservation
> law!. Or in the case of different orbitals per site, we need to define two
> lattices (lattice1 for spin up and lattice2 for spindown).
> >> > Thanks in advance,
> >> > Best
> >> >
> >> >
> >> >
>
