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 (40)

• Topological Insulators
• Topological insulators and superconductors
• Topological Photonics
• Classification of topological insulators and superconductors in three spatial dimensions
• Classification of topological quantum matter with symmetries
• Discovery of a Three-dimensional Topological Dirac Semimetal, Na3Bi
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Dirac semimetal and topological phase transitions in A3Bi (A=Na, K, Rb)
• Periodic table for topological insulators and superconductors
• Topological nodal semimetals
• Three Dimensional Dirac Semimetal and Quantum Transports in Cd3As2
• Topological quantum chemistry
• Colloquium: Topological Band Theory
• Experimental observation of Weyl points
• Observation of Weyl nodes in TaAs
• Observation of a phononic quadrupole topological insulator
• Acoustic higher-order topological insulator on a Kagome lattice
• Symmetry-based Indicators of Band Topology in the 230 Space Groups
• Synthetic gauge fields and Weyl point in Time-Reversal Invariant Acoustic Systems
• Stability of Fermi Surfaces and K-Theory
• Building Blocks of Topological Quantum Chemistry: Elementary Band Representations
• Realization of an acoustic third-order topological insulator
• Two-Dimensional Oxide Topological Insulator With Iron-Pnictide Superconductor LiFeAs Structure
• Demonstration of a quantized acoustic octupole topological insulator
• Observation of non-Abelian topological semimetals and their phase transitions
• Observation of acoustic Landau quantization and quantum-Hall-like edge states
• Experimental characterization of fragile topology in an acoustic metamaterial
• K-Theory and Pseudospectra for Topological Insulators
• Topological triply-degenerate point with double Fermi arcs
• Topological Insulators and C^*-Algebras: Theory and Numerical Practice
• Observation of topological edge modes in a quasi-periodic acoustic waveguide
• Experimental Demonstration of Dynamic Topological Pumping Across Incommensurate Bilayered Acoustic Metamaterials
• Observation of degenerate zero-energy topological states at disclinations in an acoustic lattice
• Local invariants identify topology in metals and gapless systems
• Topological metals and finite-momentum superconductors
• Index pairings in presence of symmetries with applications to topological insulators
• Quantized Nonlinear Conductance in Ballistic Metals
• Quadratic pseudospectrum for identifying localized states
• Topological metals induced by Zeeman effect
• Invariants of disordered semimetals via the spectral localizer

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