Pumping with Symmetry

Résumé : Re-configurable materials and meta-materials can jump between space symmetry classes during their deformations. Here, we introduce the concept of singular symmetry enhancement, which refers to an abrupt jump to a higher symmetry class accompanied by an un-avoidable reduction in the number of dispersion bands of the excitations of the material. Such phenomenon prompts closings of some of the spectral resonant gaps along singular manifolds in a parameter space. In this work, we demonstrate that these singular manifolds carry topological charges. As a concrete example, we show that a deformation of an acoustic crystal that encircles a $p11g$-symmetric configuration of the cavity resonators results in an adiabatic cycle that carries a Chern number in the bulk and displays Thouless pumping at the edges. The outcome is a very general principle for recognizing or engineering topological adiabatic processes in complex materials and meta-materials.