Experimentally Detecting Quantized Zak Phases without Chiral Symmetry in Photonic Lattices

Symmetries play a major role in identifying topological phases of matter and in establishing a direct connection between protected edge states and topological bulk invariants via the bulk-boundary correspondence. One-dimensional lattices are deemed to be protected by chiral symmetry, exhibiting quantized Zak phases and protected edge states, but not for all cases. Here, we experimentally realize an extended Su-Schrieffer-Heeger model with broken chiral symmetry by engineering one-dimensional zigzag photonic lattices, where the long-range hopping breaks chiral symmetry but ensures the existence of inversion symmetry. By the averaged mean displacement method, we detect topological invariants directly in the bulk through the continuous-time quantum walk of photons. Our results demonstrate that inversion symmetry protects the quantized Zak phase but edge states can disappear in the topological nontrivial phase, thus breaking the conventional bulk-boundary correspondence. Our photonic lattice provides a useful platform to study the interplay among topological phases, symmetries, and the bulk-boundary correspondence.

Automated summary

Symmetries play a crucial role in identifying topological phases and connecting protected edge states with topological bulk invariants through the bulk-boundary correspondence. One-dimensional lattices are believed to be protected by chiral symmetry, but this is not always the case. By experimentally detecting topological invariants in the bulk through continuous-time quantum walks of photons, it has been shown that inversion symmetry protects the quantized Zak phase but edge states may disappear in the topological nontrivial phase.