Edge theory of the non-Hermitian skin modes in higher dimensions

Abstract

In this Letter, we propose a universal edge theory for the higher-dimensional non-Hermitian edge-skin modes. In contrast to the well-understood corner-skin effect, we demonstrate that the edge-skin effect requires the protection of reciprocity or inversion. Through an exact mapping, we show that these skin modes share the same bulk-edge correspondence as the Fermi-arc states in a Hermitian Dirac semimetal. Based on this mapping, we introduce a bulk projection criterion to identify the skin edge, and utilize the non-Bloch Hamiltonian under specific cylinder geometry to characterize the localization features of edge-skin modes. We find that the edge-skin modes are made of components with real-valued momenta along the edge, and interestingly the decay direction typically deviates from the normal direction of the edge, a phenomenon we term skewness. Furthermore, we reveal the remarkable sensitivity of the cylinder-geometry spectrum to disturbances that violate fragile reciprocity. When this symmetry is disrupted, the cylinder-geometry spectrum undergoes an abrupt transition towards the near open-boundary spectrum, underscoring a key difference between corner-skin and edge-skin effects.Comment: 15 pages, 8 figure