Orbital dependent band degeneracy and edge states in single layer and AA bilayer honeycomb lattice systems with p orbital degeneracy

We have investigated band structure and edge states of single and AA bilayer honeycomb lattice systems with p orbital degeneracy which would be relevant for relatively heavy metals such as Pb and Bi. The p electrons, which are triply degenerate in the atomic limit, form quadruple degeneracy at K point in a single layer honeycomb lattice. The spin-orbit interaction splits the quartet at K point into two singlets and one doublet which are mixtures of p(x) , p(y) and p (z) orbitals. In the AA bilayer honeycomb lattice, the Dirac node at K point is deformed into circular line node around it. With the intermediate interlayer coupling, there is a degenerate point along Gamma-K with p(z) character. A p(x) /p(y) type degenerate point exists under the strong interlayer coupling. This degenerate point is robust against the spin-orbit interaction and the antiferromagnetic spin arrangement only along the intralayer bonds. Without SOI, localized edge states with p(x) /p(y) or p(z) character are created at the zigzag edges both in the single and AA bilayer systems. In the AA bilayer system with SOI, only the p(x) /p(y) edge states exhibit the Dirac-like dispersion.