Topological boundary modes in jammed matter

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 shed surprising light on the properties of the jamming critical point and help inform a common theoretical description of the detailed features of the transition.

Topological Phonons and Weyl Lines in Three Dimensions

“…[3]. Together with the recent work on generalized square lattices [16] and 2d models of jammed matter [17], our work hints that Weyl singularities are a common feature in Maxwell lattices and that the GKL is special in that its unit cell does not provide enough degrees of freedom to have them. The present work indicates that the GPL is a candidate for detecting Weyl lines in mechanical experiments.…”

“…These are the analog of Weyl lines that exist in electronic [18][19][20][21] and photonic [22] systems. Analogous Weyl/Dirac points [19,25,26] can also be present in 2d, as in the electronic spectra of graphene [27][28][29] and phonon spectra in deformed square lattices [16] and 2d models of jammed matter [17], and they appear to be generic in large-unit-cell Maxwell lattices. We will show that the presence of Weyl lines in the bulk also has important consequences for the number and location of surface zero modes.…”

“…[3], which introduced the framework for a phononic version of topological band theory that is well known in electronic contexts, including polyacetylene [4], quantum Hall systems [5,6], and topological insulators [7][8][9][10][11][12]. So far, attention has focused on one- [13] and two-dimensional (2d) [14][15][16][17] model systems, such as the generalized kagome lattice (GKL) introduced in Ref. [3], which places masses and central-force springs on a lattice of corner-sharing triangles.…”

Edge waves in plates with resonators: an elastic analogue of the quantum valley Hall effect

“…The study of topologically protected phenomena in materials and metamaterials is an active area of research that draws inspiration from quantum systems [1,2]. Recent developments include classical areas such as acoustics [3], optomechanics [4,5], elastic [6,7] and photonic systems [8,9]. The topological properties of the band structure, that is, electronic bands in quantum mechanics or dispersion surfaces in photonic, acoustic and mechanical systems [10], can be exploited to achieve unique and exciting functionalities.…”

Topological Edge Floppy Modes in Disordered Fiber Networks

“…Most existing studies of topological mechanics are based on periodic lattices, with only few exceptions [28,29]. In general, topological order is robust against disorder, because topological attributes are integer valued and remain invariant upon the addition of disorder until they jump to a different integer value.…”