Edge state in AB-stacked bilayer graphene and its correspondence with the Su-Schrieffer-Heeger ladder

We study edge states in AB-stacked bilayer graphene (BLG) ribbon where the Chern number of corresponding two-dimensional (2D) bulk Hamiltonian is zero. The existence and topological features when two layers ended with same or different terminations (zigzag, bearded, armchair) are discussed. (non-dispersive bands near Fermi level) localized at nanoribbon that only exists certain range momentum $k_y$. Their level protected by chiral symmetry topology well described coupled Su-Schrieffer-Heeger (SSH) chains model, i.e., SSH ladder, based on bulk-edge correspondence one-dimensional (1D) systems. These zero-energy can exist whole $k_y$ region have zigzag bearded edges, respectively. Winding calculation shows a phase transition between distinct non-trivial phases crossing Dirac points. Interestingly, we find stacking configuration BLG important since they lead to unexpected without protection from both armchair-armchair case gap within away general case. influence interlayer next nearest neighbor (NNN) interaction bias also discussed fit realistic materials, which suggest robust