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.This work was supported by National Key R&D Program of China (2017YFA0303702), NSFC (11834008, 11874215, 11674172, and 11574148), Jiangsu Provincial NSF (BK20160018), the Fundamental Research Funds for the Central Universities (020414380001) and Nanjing University Innovation and Creative Program for PhD candidate (CXCY17-11). Z. Z. acknowledges the support from the China Scholarship Council. J. C. acknowledges the support from the European Research Council (ERC) through the Starting Grant No. 714577 PHONOMETA and from the MINECO through a Ramón y Cajal grant (Grant No. RYC- 2015-17156)