Revealing Topology in Metals using Experimental Protocols Inspired by $K$-Theory

Abstract

Topological metals are special conducting materials with gapless band structures and nontrivial edge-localized resonances, whose discovery has proved elusive because the traditional topological classification methods do not apply in this context. Inspired by recent theoretical developments that leveraged techniques from the field of $C^{\ast }$-algebras to identify topological metals \cite{cerjan_local_2021}, here, we directly observe topological phenomena in gapless acoustic crystals and provide a general experimental technique to demonstrate their topology. Specifically, we not only observe robust boundary-localized states in a topological acoustic metal, but also re-interpret a composite operator, mathematically derived from the K-theory of the problem, as a new Hamiltonian, whose physical implementation allows us to directly observe a topological spectral flow and measure the topological invariants. Our observations and experimental protocols may offer insights for discovering topological behavior across a wide array of artificial and natural materials that lack bulk band gaps.

References in corpus (5)

• Classification of topological insulators and superconductors in three spatial dimensions
• Building Blocks of Topological Quantum Chemistry: Elementary Band Representations
• Realization of an acoustic third-order topological insulator
• Observation of degenerate zero-energy topological states at disclinations in an acoustic lattice
• Quadratic pseudospectrum for identifying localized states

Cited by in corpus (11)

• Local markers for crystalline topology
• Classifying topology in photonic heterostructures with gapless environments
• Mixed higher-order topology: boundary non-Hermitian skin effect induced by a Floquet bulk
• Spectral localizer for line-gapped non-hermitian systems
• Tutorial: Classifying Photonic Topology Using the Spectral Localizer and Numerical $K$-Theory
• Probing topology in nonlinear topological materials using numerical $K$-theory
• Dirac surface states, multiorbital dimerization and superconductivity in Nb- and Ta-based A15 compounds
• Real-space topological localizer index to fully characterize the dislocation skin effect
• Versatile Control of Nonlinear Topological States in Non-Hermitian Systems
• Even spheres as joint spectra of matrix models
• Dimensional crossover of class D real-space topological invariants