Title: The Topological Origin of Non-Hermitian Skin Effect
Abstract: In this talk, I will show that the skin effect is understood as a particular type of the bulk-edge correspondence that is unique to non-Hermitian systems: from the spectral winding in the bulk to the skin modes on the edge. Starting in 1D, I first show that the existence of skin effect is solely determined by the spectral winding of the U(1)-phase of the complex “energy”. Then I will show that in two and higher dimensions, the skin effect is absent if and only if the spectral area of the bulk vanishes. Different from 1D, in 2D and higher dimensions, the skin effect is completely compatible with all spatial symmetries, and certain spatial symmetries may protect a new type of skin effect, the geometry-dependent skin effect, that is unique to higher-than-one dimensions.