Higher-Order Non-Hermitian Skin Effect: Corner Modes Defy Conventional Physics

In non-Hermitian systems, where energy isn't conserved, the skin effect causes waves to pile up at boundaries—a phenomenon impossible in standard quantum mechanics. Now, researchers have discovered higher-order versions that localize not just at edges, but specifically at corners.

In two dimensions, the conventional skin effect produces O(L²) boundary modes, but the second-order variant yields O(L) modes exclusively at corners. This contrasts sharply with Hermitian second-order topological insulators, which host only O(1) corner states. The difference stems from intrinsic non-Hermitian topology protected by spatial symmetries like four-fold rotation.

Moving to three dimensions reveals third-order skin effects with O(L) corner modes emerging from O(L³) total states. These findings necessitate modifications to non-Bloch band theory, the framework describing non-Hermitian systems under open boundaries.

The discovery opens new avenues for controlling wave localization in photonic systems, mechanical metamaterials, and other non-conservative platforms where non-Hermitian physics dominates.

Reference: Kawabata, K., Sato, M., & Shiozaki, K. (2020). Higher-order non-Hermitian skin effect. arXiv:2008.07237v2.