Non-Hermitian Sonic Second-Order Topological Insulator

: Topological phases of matter that have been recently extended to topological phases of sound can confine acoustic energy at the corners of higher-order topological insulators. We broaden this concept by incorporating parity-time symmetry and show new topologically protected confinement rules that are dictated by the geometrical arrangement of gain and loss units. Particularly, our findings reveal how sound trapping occurs at all corners when parity-time symmetry is intact, beyond the exceptional point within the broken phase; however, opposite corners sustain either sink- or sourcelike states that could lead to novel non-Hermitian guides for sound.