Observation of ring states in a delicate topological insulator

TL;DR

This study demonstrates that impurity-induced ring states in a phononic metamaterial serve as effective probes for detecting delicate topological phases, which are challenging to diagnose with conventional methods.

Contribution

The paper introduces a novel spectroscopic approach using local impurities to identify delicate topological insulators in phononic systems, revealing persistent ring states.

Findings

Ring states remain pinned in frequency even with strong impurities.

Ring states form a pronounced ring around impurity sites.

Ring states persist despite removal of multicellularity by hybridization.

Abstract

Topological insulators are typically characterized by particularly stable properties, such as global invariants, and can be identified by probing their robust surface states. A recently discovered novel form of band topology, delicate topology, challenges this paradigm: its defining property, multicellularity, can be removed by introducing a coupling to local orbitals anywhere in the spectrum, even far above the relevant band gap. This makes it hard to diagnose delicate topology with conventional probes that access only low-energy degrees of freedom. Here, we introduce strong local impurities as a spectroscopic probe of a delicate topological insulator which we realize in a phononic metamaterial. By tuning the impurity strength and performing orbital-resolved readout, we observe recently proposed indicators of topology: ring states, in-gap bound states whose frequencies remain pinned in the strong-impurity limit while their real-space profiles form a pronounced ring around the impurity site. We find that these ring states persist even when the multicellularity in our system is removed by a weakly hybridizing additional orbital. Our results establish impurity-induced ring states as probes of complex multiband physics, including delicate topological phases.