Edge states of mechanical diamond and its topological origin

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.