Unlocking the Non-Hermitian Skin Effect in Higher Dimensions

A groundbreaking study published in Science Bulletin has shed light on the non-Hermitian skin effect (NHSE), a unique phenomenon observed in non-Hermitian systems. NHSE is characterized by the concentration of eigenstates at the system’s boundaries, making it highly sensitive to boundary conditions. This study, led by Dr. Haiping Hu from the Institute of Physics, Chinese Academy of Sciences, delves into the intricacies of NHSE in higher dimensions, revealing its profound connection to point-gap topology. The research introduces a novel approach, utilizing virtual gauge transformations, to systematically account for spectral windings in all dimensions. By eliminating these windings, the study derives non-Bloch spectra that remain independent of the specific lattice geometry. This breakthrough provides a framework for understanding and manipulating NHSE across diverse lattice configurations. Furthermore, the study demonstrates the equivalence between the derived non-Bloch spectra and those obtained using the renowned Amoeba theory, solidifying its accuracy and applicability. Notably, the study also elucidates the relationship between NHSE and different lattice geometries, demonstrating how skin modes can be manipulated through tailored lattice design. These findings hold significant implications for advancing the understanding and control of wave phenomena in a wide range of non-conservative systems, including optical and photonic systems, cold atoms, and metamaterials.