  Higher-order topology realizes topologically robust corner modes as a
manifestation of nontriviality. We theoretically propose non-Hermitian skin
effects which stem from 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 the non-Hermitian skin modes emerge
by using a relationship between second-order and conventional first-order
topology.
