I am dealing with cubic lattice with first nearest neighbour hopping in all directions but second nearest neighbour hopping only in z-direction. Like c_{j}^{/dagger} c_{j+2a/hat{z}} /sigma_0 + h.c. So I get cos(2k_z) term in the Hamiltonian. If I expand this cosine term in polynomial form upto second order. The discretizer does not give any second neighbour hopping term like Hoppingkind(0,1, 1). The discretizer mix it with the first nearest neighbour hopping in z-direction. but If I write the cosine term like [exp(i2k_z)+exp(-i2k_z)]/2. So I have to assign 0.5 /sigma_0 to the Hoppingkind(0 1 1) and other similar type of second neighbour hoppings only in z direction. I am confused that which is the correct way to deal with this problem. I hope you understand what I mean.

Thank you.