Universal non-Hermitian skin effect in two and higher dimensions.

Area of Science:

• Condensed matter physics
• Topological physics
• Quantum mechanics

Background:

• The skin effect, observed in 1D, localizes eigenstates at the ends of open chains with non-Hermitian Hamiltonians.
• Its existence and universality in higher dimensions remained an open question.

Purpose of the Study:

• To establish a general theorem for the existence of the skin effect in two and higher dimensions.
• To introduce and characterize novel types of skin effects in higher-dimensional systems.
• To connect the skin effect to experimentally observable phenomena in various materials.

Main Methods:

• Establishing a mathematical theorem based on the properties of the Hamiltonian's periodic-boundary spectrum.
• Analyzing the localization of eigenstates in two and higher dimensions.
• Investigating the compatibility of the skin effect with point-group symmetries.

Main Results:

• A theorem proving the skin effect exists if and only if the Hamiltonian's periodic-boundary spectrum covers a finite area in the complex plane.
• Demonstration that this condition is generic for non-Hermitian Hamiltonians and compatible with all point-group symmetries.
• Identification of new phenomena: corner-skin effect and geometry-dependent-skin effect.
• Corollary: Non-Hermitian systems with exceptional points/lines in 2D/3D exhibit skin effect.

Conclusions:

• The skin effect is a universal phenomenon in non-Hermitian systems, extending beyond one dimension.
• New types of skin effects and their dependence on system geometry are identified.
• The theorem provides a pathway for experimental realization in systems like photonic crystals and topological insulators.