Fig. 3: Higher-order non-Hermitian skin effect.

a Calculated eigen-spectrum for a box-shaped SC (in the Hermitian regime) with OBC in both the x and y directions. There are eight corner states (dark red), sixteen edge states (dark blue), and eight bulk states (gray). The corresponding acoustic wavefunctions for the bulk, edge, and corner states (marked by arrows) are presented. b The same as a, but with acoustic loss. The higher-order non-Hermitian skin effect is manifested by the emergence of spin-polarized, corner-like skin-modes. Depending on the spin-polarizations, the corner-like skin modes reside near the lower-left (for spin-up modes) and upper-right (for spin-down modes) corners. c–e Experimental demonstration of the higher-order non-Hermitian skin effect. Both the transmission spectra (for the bulk, edge, and corner pump-probes) and the scanned acoustic pressure profiles are presented, which show consistency with the simulations.