Topology (electrical circuits)

Topological insulator

Quantization (signal processing)

Mathematics

Topological quantum number

Quadrupole

Computer science

Multipole expansion

Quantum mechanics

Physical chemistry

Polarization (electrochemistry)

Condensed matter physics

Metamaterial

Computer vision

State of matter

Combinatorics

Dipole

Chemistry

Physics

Geometric phase

Nature

A two-dimensional phononic quadrupole topological insulator is demonstrated experimentally using mechanical metamaterials, which has both the one-dimensional edge states and the zero-dimensional corner states predicted by theory. The properties of many materials with topological band structures can be understood in terms of a quantization of the electric polarization. By considering a quantization of higher-order polarizations, a new class of higher-order topological insulators has recently been predicted. Marc Serra-Garcia et al. use a mechanical metamaterial to demonstrate such a system experimentally: a two-dimensional phononic quadrupole topological insulator, which has both one-dimensional states at the edges as well as zero-dimensional states at the corners. As these topological corner states are two dimensions lower than the bulk, they could provide a route to engineering one-dimensional channels along the edges of three-dimensional systems. The modern theory of charge polarization in solids1,2 is base...

Observation of a phononic quadrupole topological insulator