I was trying to generate the band structures of ZB structures like Si, Ge, GaAs etc. using sp3d5s* orbital basis tight binding method with parameter set from Boykin. If I use 2 atom basis then the band structure is perfect. When I use 8 atom unit cell with the concept of unit cell basis, I am not getting the right dispersion. Can anyone see the glitch in the procedure that I followed? It is described below:
First I generate the atomic coordinates of 8 atom and this is my central unit cell (0). Then, using a translational vector, I generate additional 12 unit cells to capture all the neighbors of central unit cell atoms. The 12 translational vectors are T1 = Ra, T2 = -Ra, T3 = Rb, T4 = -Rb, T5 = Rc, T6 = -Rc, T7 = Ra+Rb, T8 = -(Ra+Rb), T9 = Rb+Rc, T10 = -(Rb+Rc), T11 = Ra+Rc, and T12 = -(Ra+Rc). These T's are added to the atom coordinates of central cell to get 12 neighboring cells' atoms. Here Ra = a0(1,0,0), Rb = a0(0,1,0), Rc = a0(0,0,1) and a0 is the lattice constant. Now I generate central cell Hamiltonian, H00 and its coupling Hamiltonian, H0i (i = 1 to 12) and band structure is calculated from the eigen values of HK = H00 + sum(i = 1 to 12) H0i*exp(1i*dot(k,Ti)). Although the dispersion is wrong, it is giving the right band gap and there is no bands in the gap state. What is wrong in the procedure?