Critical non-Hermitian skin effect

• Published in: Nature communications Vol. 11; no. 1; pp. 5491 - 8
• Main Authors: Li, Linhu, Lee, Ching Hua, Mu, Sen, Gong, Jiangbin
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 30.10.2020; Nature Publishing Group; Nature Portfolio
• Subjects: 639/766/119; 639/766/530/2795; Boundary conditions; Brillouin zones; Critical point; Eigenvectors; Energy gap; Humanities and Social Sciences; Lattice vibration; Localization; multidisciplinary; Optics; Phase transitions; RLC circuits; Science; Science (multidisciplinary); Skin; Skin effect; Subsystems
• ISSN: 2041-1723; 2041-1723
• DOI: 10.1038/s41467-020-18917-4

Critical systems represent physical boundaries between different phases of matter and have been intensely studied for their universality and rich physics. Yet, with the rise of non-Hermitian studies, fundamental concepts underpinning critical systems - like band gaps and locality - are increasingly called into question. This work uncovers a new class of criticality where eigenenergies and eigenstates of non-Hermitian lattice systems jump discontinuously across a critical point in the thermodynamic limit, unlike established critical scenarios with spectrum remaining continuous across a transition. Such critical behavior, dubbed the “critical non-Hermitian skin effect”, arises whenever subsystems with dissimilar non-reciprocal accumulations are coupled, however weakly. This indicates, as elaborated with the generalized Brillouin zone approach, that the thermodynamic and zero-coupling limits are not exchangeable, and that even a large system can be qualitatively different from its thermodynamic limit. Examples with anomalous scaling behavior are presented as manifestations of the critical non-Hermitian skin effect in finite-size systems. More spectacularly, topological in-gap modes can even be induced by changing the system size. We provide an explicit proposal for detecting the critical non-Hermitian skin effect in an RLC circuit setup, which also directly carries over to established setups in non-Hermitian optics and mechanics. In non-Hermitian systems, fundamental concepts like bandgaps and locality cannot be applied as in Hermitian systems. Here, the authors introduce a class of non-Hermitian critical scenarios where the eigenstates and energies jump discontinuously across a critical point, with anomalous scaling properties