Topological properties of metamaterials

Topological insulators and topological semimetals have caused a paradigm shift in our understanding of phases of matter. They exhibit a remarkable symbiosis between elegant mathematical theories, accurate material prediction and technological applications. The experimental discovery of many predicted topological materials seals the triumph of the predicting potential of ab initio calculations combined with symmetry analysis in solid state physics.

A new field called Topological Quantum Chemistry [1] has stablished that symmetry-based considerations complement chemical theories of bonding, ionization and covalence, redefining the concept of topology by means of elementary band representations [2]. Our goal consists in extending this formalism to study the topology of non.-electronic lattices such as 3D phonons, to reveal their topoligical mnusteries [3,4].

[1] Barry Bradlyn, L Elcoro, Jennifer Cano, MG Vergniory, Zhijun Wang, C Felser, MI Aroyo, B Andrei Bernevig, Nature 547 (7663), 298 (2018)
[2] Jennifer Cano, Barry Bradlyn, Zhijun Wang, L Elcoro, MG Vergniory, C Felser, MI Aroyo, B
Andrei Bernevig; Physical Review B 97 (3), 035139 (2018)
[3] J. L. Mañes, arXiv:1904.06997
[4] María Blanco de Paz, Maia G Vergniory, Dario Bercioux, Aitzol García-Etxarri, Barry Bradlyn, Physical Review Research 1 (3), 033074 (2019)