Acoustic real second-order nodal-loop semimetal and non-Hermitian modulation

The unique features of spinless time-reversal symmetry and tunable ℤ2 gauge fields in artificial systems facilitate the emergence of topological properties in the landscape, such as the recently explored Möbius-twisted phase and real second-order nodal-loop semimetals. However, these properties have predominantly been proposed only in theoretical frameworks. In this study, we present a cunningly designed blueprint for realizing an acoustic real second-order nodal-loop semimetal through the incorporation of projective translation symmetry into a three-dimensional stacked acoustic graphitic lattice. Additionally, we introduce non-Hermitian modulation to the topologically protected propagation of degenerate drumhead surface and hinge states, which depend on the specific on-site gain and loss textures. It should be emphasized that this demonstration can be extended to other classical wave systems, thereby potentially opening up opportunities for the design of functional topological devices.