Pumping with Symmetry

TL;DR

This paper introduces the concept of singular symmetry enhancement in re-configurable materials, demonstrating how abrupt symmetry jumps can lead to topological phenomena like Chern numbers and Thouless pumping, with broad implications for complex material design.

Contribution

It presents the novel idea of singular symmetry enhancement and its topological implications, supported by an acoustic crystal example showing topological pumping driven by symmetry changes.

Findings

Singular symmetry enhancement causes spectral gap closings.

Deformations can carry topological charges like Chern numbers.

Adiabatic cycles can induce topological pumping in materials.

Abstract

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 can carry topological charges. As a concrete example, we show that a deformation of an acoustic crystal that encircles a p11g-symmetric configuration of an array of cavity resonators results in an adiabatic cycle that carries a Chern number in the bulk and displays Thouless pumping at the edges. This points to a very general guiding principle for recognizing cyclic adiabatic processes with high potential for topological pumping in complex materials and meta-materials, which rests entirely on symmetry arguments.