Acoustic M\"obius insulators from projective symmetry

TL;DR

This paper introduces a new class of topological phases called M"obius insulators, realized in acoustic crystals, which are enabled by projective crystalline symmetries and exhibit unique edge and hinge states.

Contribution

The work demonstrates the first experimental realization of M"obius topological insulators in acoustic systems using projective translation symmetry.

Findings

Realized two M"obius insulators in acoustic crystals

Observed M"obius edge and hinge states via visualization and spectroscopy

Established a new framework for topological physics with projective symmetry

Abstract

Symmetry plays a critical role in classifying phases of matter. This is exemplified by how crystalline symmetries enrich the topological classification of materials and enable unconventional phenomena in topologically nontrivial ones. After an extensive study over the past decade, the list of topological crystalline insulators and semimetals seems to be exhaustive and concluded. However, in the presence of gauge symmetry, common but not limited to artificial crystals, the algebraic structure of crystalline symmetries needs to be projectively represented, giving rise to unprecedented topological physics. Here we demonstrate this novel idea by exploiting a projective translation symmetry and constructing a variety of M\"obius-twisted topological phases. Experimentally, we realize two M\"obius insulators in acoustic crystals for the first time: a two-dimensional one of first-order band topology and a three-dimensional one of higher-order band topology. We observe unambiguously the peculiar M\"obius edge and hinge states via real-space visualization of their localiztions, momentum-space spectroscopy of their 4{\pi} periodicity, and phase-space winding of their projective translation eigenvalues. Not only does our work open a new avenue for artificial systems under the interplay between gauge and crystalline symmetries, but it also initializes a new framework for topological physics from projective symmetry.