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 <sinhapriyanka2016@iitg.ac.in> wrote:

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