Revealing topology in metals using experimental protocols inspired by K-theory

Area of Science:

• Condensed matter physics
• Acoustic metamaterials
• Topological materials science

Background:

• Topological metals possess unique conducting properties with gapless band structures and edge-localized states.
• Traditional topological classification relies on band gaps, hindering the discovery of topological metals.
• Recent theoretical advances utilize C*-algebras for topological metal identification.

Purpose of the Study:

• To experimentally observe topological phenomena in gapless acoustic crystals.
• To develop a general experimental technique for demonstrating the topology of such materials.
• To provide insights for discovering topological behavior in materials lacking bulk band gaps.

Main Methods:

• Direct observation of robust boundary-localized states in a topological acoustic metal.
• Re-interpretation of a composite operator (derived from K-theory) as a new Hamiltonian.
• Physical implementation of the new Hamiltonian to observe topological spectral flow.

Main Results:

• Demonstration of robust boundary-localized states in gapless acoustic crystals.
• Successful observation of topological spectral flow using a K-theory derived Hamiltonian.
• Measurement of topological invariants in a gapless system.

Conclusions:

• Topological phenomena can be directly observed and characterized in gapless acoustic crystals.
• The developed experimental technique offers a general approach for identifying topological properties in materials lacking band gaps.
• This work expands the scope of topological materials discovery beyond traditional gapped systems.