Second-order topological non-Hermitian skin effects

Higher-order topology realizes topologically robust corner modes as a manifestation of nontriviality. We theoretically propose non-Hermitian skin effects which stem from the second-order topology of chiral-symmetric Hermitian systems. It is found that the skin modes are localized at the corners. We demonstrate two types of second-order topological skin effects by two-dimensional intrinsic and extrinsic second-order topology. The intrinsic second-order topological skin effect is characterized topologically by bulk inversion symmetry as well as chiral symmetry. Meanwhile, the extrinsic second-order topological skin effect occurs from the topological correspondence between the edges and corners. We show that non-Hermitian skin modes emerge by using a relationship between second-order and conventional first-order topology.