Self-ordering induces multiple topological transitions for in-plane bulk waves in solid phononic crystals

Topological defects with symmetry-breaking phase transitions have captured much attention. A vortex generated by topological defects exhibits exotic properties, and its flow direction can be switched by altering the spin configurations. Contrary to electromagnetic and acoustic domains, the topological transport of in-plane bulk waves in periodic structures with topological defects is not well explored due to the mode conversion between longitudinal and transverse modes. Here, we propose an elastic topological insulator with spontaneously broken symmetry based on the topological theory of defects and homotopy theory. Multiple topological transitions for in-plane bulk waves are achieved by topologically modifying the ellipse orientation in a triangular lattice of elliptical cylinders. The solid system, independent of the number of molecules in order-parameter space, breaks through the limit of point-group symmetry to emulate elastic pseudospin-orbit coupling. The transport robustness of the edge states is experimentally demonstrated. Our approach provides new possibilities for controlling and transporting in-plane bulk waves.