[Kwant] Regarding spin-orbit term in Bilayer graphene

[MS. PRIYANKA SINHA]

Dear Sir,

I have two questions.

(1) I want to study the intralayer intrinsic spin-orbit coupling in bilayer graphene. For the monolayer case, it is easy to put the nnn hopping by,


sys[graphene.neighbors(2)] = spin_orbit


But for the bilayer case, as there are two planes and the intralayer coupling which I want to calculate should be in those two planes, Can I use the above code to get the effect. If not, then how can I put the effect in bilayer system.


(2) When I am calculating the Hamiltonian submatrix between two sites to see the full matrix without spin-orbit ( only for tight-binding in bilayer where t=1 and interlayer coupling ,t_prep= 0.2) it is showing


[[7.+0.j 0.+0.j 0.+0.j 0.+0.j]
[0.+0.j 7.+0.j 0.+0.j 0.+0.j]
[0.+0.j 0.+0.j 7.+0.j 0.+0.j]
[0.+0.j 0.+0.j 0.+0.j 7.+0.j]]


where 7 is for onsite element (sys[graphene.shape(rect, (0, 0, 0))] = 7 * sigma_0).


Thanks in advance.


sincerely,

Priyanka Sinha

[Abbout Adel]

Dear Priyanka,

1) To use the second nearest neighbours for the intra-layer spin orbit
coupling, you just need to be sure that the distance between the two planes
is larger than the distance between two next neighbouring sites in the
planes.

2) You are getting that matrix Hamiltonian because the two sites you are
choosing are not neighbours, so you mainly get the onsite potential.

I hope this helps
Adel



On Tue, Aug 14, 2018 at 8:30 AM, MS. PRIYANKA SINHA <

Post by MS. PRIYANKA SINHA
Dear Sir,
I have two questions.
(1) I want to study the intralayer intrinsic spin-orbit
coupling in bilayer graphene. For the monolayer case, it is easy to put the
nnn hopping by,
sys[graphene.neighbors(2)] = spin_orbit
But for the bilayer case, as there are two planes and the intralayer
coupling which I want to calculate should be in those two planes, Can I use
the above code to get the effect. If not, then how can I put the effect in
bilayer system.
(2) When I am calculating the Hamiltonian submatrix between two sites to
see the full matrix without spin-orbit ( only for tight-binding in bilayer
where t=1 and interlayer coupling ,t_prep= 0.2) it is showing
[[7.+0.j 0.+0.j 0.+0.j 0.+0.j]
[0.+0.j 7.+0.j 0.+0.j 0.+0.j]
[0.+0.j 0.+0.j 7.+0.j 0.+0.j]
[0.+0.j 0.+0.j 0.+0.j 7.+0.j]]
where 7 is for onsite element (sys[graphene.shape(rect, (0, 0, 0))] = 7 * sigma_0).
Thanks in advance.
sincerely,
Priyanka Sinha