The Topological Origin of Non-Hermitian Skin Effect

Explore the topological origins of the non-Hermitian skin effect in this 50-minute lecture by Chen Fang from the PCS Institute for Basic Science. Delve into the unique bulk-edge correspondence in non-Hermitian systems, starting with a one-dimensional analysis of spectral winding and its relation to skin modes. Examine the concept in two and higher dimensions, where the skin effect's existence is determined by the vanishing of the bulk's spectral area. Discover how spatial symmetries interact with the skin effect in higher dimensions, potentially leading to new phenomena such as geometry-dependent skin effects. Investigate topics including Hamiltonians, non-reciprocity, spectrum analysis, wave functions, topological attributes, corner skin effects, and the universal skin effect theorem. Gain insights into the compatibility of symmetries with skin effects and the characteristics of skin effect states in various dimensions.

Introduction
Hamiltonians
Nonresprosity
Spectrum
Wave Function
Nonzero Winding
Summary 1D
Summary 2D
Topological Attributes
Skin Effect in Two Dimensions
Symmetries
Corner Skin Effect
Geometric Skin Effect
Universal Skin Effect Theorem
Summary
Symmetry Compatibility
Skin Effect States
Skin Effect in 1D
Local Symmetry