Critical Non-Hermitian Skin Effect in Two or More Dimensions and Curved Spaces

Critical systems, known for their unique properties at phase transition boundaries, have traditionally been studied in Hermitian models. However, the advent of non-Hermitian physics has introduced the critical non-Hermitian skin effect, characterized by discontinuous changes in eigenenergies and eigenstates. This phenomenon typically occurs when a pair of anti-parallel chains with different non-reciprocal accumulations are weakly coupled. In particular, we find that the critical non-Hermitian skin effect can be induced not only in two or more dimensions and in curved spaces, but it can also introduce the higher-order critical non-Hermitian skin effect. Unlike the usual critical non-Hermitian skin effect, this higher-order criticality can be toggled on and off by adjusting the number of coupled chains. Our work provides insights into the intricate interplay between criticality at phase boundaries and higher-order systems.