Experimentally Detecting Quantized Zak Phases without Chiral Symmetry in Photonic Lattices

TL;DR

This study experimentally demonstrates that in photonic lattices with broken chiral symmetry but preserved inversion symmetry, quantized Zak phases can be detected directly in the bulk, revealing a nuanced topological phase behavior.

Contribution

It introduces an extended Su-Schrieffer-Heeger model with broken chiral symmetry but preserved inversion symmetry, and demonstrates direct bulk detection of topological invariants in photonic lattices.

Findings

Inversion symmetry protects the quantized Zak phase.

Edge states can vanish despite nontrivial topology.

Bulk-boundary correspondence can be broken in these systems.

Abstract

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.