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We construct a two-leg ladder dimer model by using two orbitals instead ofone in Su-Schrieffer-Heeger (SSH) dimer chain and find out a chiral symmetry init. In this model, the otherwise-hidden additional chiral symmetry allows us todefine two chiral massless fermions and show that there exist interestingtopological states characterized by $\mathbb{Z}\oplus\mathbb{Z}$ andcorresponding zero mode edge states. Our complete phase diagram reveals thatthere is an anomalous topologically nontrivial region in addition to the normalone similar to that of SSH model. The anomalous region features that theinter-cell hopping constants can be much smaller than the intra-cell ones,being opposite to the normal region, and the zero mode edge states do not havewell-defined parity each. Finally, we suggest that this ladder dimer model canbe realized in double-well optical lattices, ladder polymer systems, and adatomdouble chains on semiconductor surfaces.

Hidden chiral symmetry protected $\mathbb{Z}\oplus\mathbb{Z}$ topological insulators in a ladder dimer model