Higher-order non-Hermitian skin effect

The non-Hermitian skin effect is a unique feature of non-Hermitian systems, in which an extensive number of boundary modes appear under the open boundary conditions. Here, we discover higher-order counterparts of the non-Hermitian skin effect that exhibit new boundary physics. In two-dimensional systems with the system size L×L, while the conventional (first-order) skin effect accompanies O(L2) skin modes, the second-order skin effect accompanies O(L) corner skin modes. This also contrasts with Hermitian second-order topological insulators, in which only O(1) corner zero modes appear. Moreover, for the third-order skin effect in three dimensions, O(L) corner skin modes appear from all O(L3) modes. We demonstrate that the higher-order skin effect originates from intrinsic non-Hermitian topology protected by spatial symmetry. We also show that it accompanies the modification of the non-Bloch band theory in higher dimensions.