ℤ-Classified Topological Phases and Bound States in the Continuum Induced by Multiple Orbitals.

ℤ-classified higher-order topological insulators (HOTIs) with chiral-symmetric higher-order topological phases protected by multipole chiral numbers (MCNs) have attracted extensive interest recently. However, how to design artificial ℤ-classified HOTIs with multiple topological phases remains an unresolved issue. Here, multiorbital degrees of freedom are introduced to acoustic crystals and the various methods of topological phase transitions are achieved for the orbital ℤ-classified HOTIs. Experimental results demonstrate the realization the coexistence of corner modes with distinct mechanisms within one single model. This provides a pathway for finding ℤ-classified with large MCNs independent of long-range coupling. Additionally, a universal approach is introduced here to fabricate topological bound states in the continuum derived from the discrepant onsite energy of degenerate p-orbitals. These findings provide new insights into the study of topological wave physics using orbital degrees of freedom and may pave the way for designing innovative orbital topological devices for sensing and computing.