Abstract
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 Möbius-twisted topological phases. Experimentally, we realize two Möbius 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 Möbius edge and hinge states via real-space visualization of their localiztions, momentum-space spectroscopy of their 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.
- Received 6 September 2021
- Accepted 25 January 2022
DOI:https://doi.org/10.1103/PhysRevLett.128.116803
© 2022 American Physical Society
Physics Subject Headings (PhySH)
Viewpoint
Acoustic Crystals with a Möbius Twist
Published 14 March 2022
By manipulating symmetries in acoustic lattices, two independent groups have created a topological insulator with a new, exotic topology.
See more in Physics