Abstract
A mechanical 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 π. 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.
Highlights
Topological semimetal is a system in which its band gap is finite almost everywhere in the Brillouin zone, except on some sets of isolated points
A singularity often serves as a source of a “twist” of Bloch wave functions captured by the Berry curvature, which gives rise to nontrivial topology
In the 3D Brillouin zone, the gapless points form line nodes, which are protected by the chiral symmetry
Summary
Topological semimetal is a system in which its band gap is finite almost everywhere in the Brillouin zone, except on some sets of isolated points. Topological properties of mechanical diamond are investigated by relating edge modes, the quantized Zak phase, and the winding number. We confirm that these features are well captured by the quantized Zak phase and the winding number, which establishes the bulk-edge correspondence in mechanical diamond.
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