Edge states of mechanical diamond and its topological origin

TL;DR

This paper explores the topological properties of a mechanical diamond lattice, revealing how its nodal line structures and edge states are protected by symmetries and characterized by Zak phases, establishing a bulk-edge correspondence.

Contribution

It demonstrates the topological origin of edge states in a mechanical diamond model through analysis of nodal structures and Zak phases, linking bulk topology to boundary phenomena.

Findings

Nodal line structures are protected by chiral symmetry.

Topological changes occur with tension modifications.

Edge states correspond to Zak phases and winding numbers.

Abstract

A mechanical diamond, a classical mechanics of a spring-mass model arrayed on a diamond lattice, is discussed topologically. Its frequency dispersion possesses an intrinsic nodal structure in the three-dimensional Brillouin zone (BZ) protected by the chiral symmetry. Topological changes of the line nodes are demonstrated associated with modification of the tension. The line nodes projected into two-dimensional BZ form loops which are characterized by the quantized Zak phases by 0 and $\pi$. With boundaries, edge states are discussed in relation to the Zak phases and winding numbers. It establishes a bulk-edge correspondence of the mechanical diamond.