Topological boundary modes in jammed matter

TL;DR

This paper investigates topological boundary modes in jammed granular matter, revealing protected surface phonons, Weyl points, and challenging existing theories of the jamming transition.

Contribution

It introduces the concept of topological classes in jammed matter and identifies protected surface modes and Weyl points in model systems.

Findings

Identification of topological classes in jammed systems

Presence of protected surface phonons and Weyl points

Some aspects of the jamming transition theory are invalid

Abstract

Granular matter at the jamming transition is poised on the brink of mechanical stability, and hence it is possible that these random systems have topologically protected surface phonons. Studying two model systems for jammed matter, we find states that exhibit distinct mechanical topological classes, protected surface modes, and ubiquitous Weyl points. The detailed statistics of the boundary modes enable tests of a standard understanding of the detailed features of the jamming transition, and show that parts of this argument are invalid.