Dynamical Degeneracy Splitting and Directional Invisibility in Non-Hermitian Systems

The non-Hermitian skin effect (NHSE) refers to extensive bulk modes localized at the open boundaries, which makes the energy spectra and wave functions sensitive to the change in boundary conditions. In higher dimensions, the geometry-dependent skin effect has recently been proposed, i.e., the NHSE disappears in some specified open-boundary geometries but reappears in generic open-boundary geometries. Although theoretically, the geometry-dependent skin effect can universally exist in higher-dimensional non-Hermitian systems, a detectable signature experimentally is still lacking.

Here, we establish the scattering theory in the two-dimensional non-Hermitian lattice and propose directional invisibility in non-Hermitian systems. Directional invisibility means that the reflected wave of an incident wave packet can be seen in several directions but is invisible in most spatial directions. It originates from the anisotropic decay of the non-Hermitian system and can be utilized to probe the geometry-dependent skin effect. In addition, we define the frequency-resolved NHSE based on the non-Hermitian scattering theory.