Edge states of mechanical diamond and its topological origin

Amechanical diamond, with the 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 the modification of the tension. The line nodes projected into two-dimensional BZ, form loops, which are characterized by the quantized Berry phases with 0 or p. With boundaries, the edge states are discussed in relation to the Berry phases and winding numbers, and the bulk-edge correspondence of the mechanical diamond is established.