Fractional charged edge states in ladder topological insulators.

We propose a model of two-leg ladder topological insulator in which the spin-orbit couplings are
 presented in both intra-chain and inter-chain interactions. The topological phase supports four
 fractional charged edge states localized at opposite ends of the ladder, which belongs to the chiral
 symplectic (CII) class protected by time-reversal symmetry and chiral symmetry. In our model, the
 presence of time-reversal and chiral symmetry generates fourfold degeneracy for the edge states, and
 the two edge states with same chirality at one end of the ladder each carries half charge. In contrast
 to the two edge states spatially localized at one end of the ladder being not distinguished, these
 two edge states can be detected by the momentum density. The experimental scheme for realizing
 our model with cold atoms in optical lattice is discussed. By introducing a magnetic field in the x
 direction, the system is driven from CII class to AIII class. In AIII class, there exist two distinct
 topological phases that exhibit four degenerate edge states and two degenerate edge states in the
 gap respectively. As same as the system in CII class, each edge state carries a half charge in AIII
 class.