The notion of a band gap is ubiquitous in the characterization of matter.Particularly interesting are pseudo-gaps,which are enigmatic regions of very low density of states that have been linked to novel phenomena like high temperature superconductivity.In this work,we discover a novel origin for pseudo-gaps when boundaries are introduced in a non-Hermitian lattice.It generically occurs due to the interference between two or more asymmetric pumping channels,and possess no analog in Hermitian systems.Mathematically,it can be visualized as being created by divergences of spectral flow in the complex energy plane,analogous to how sharp edges creates divergent electric fields near an elec-trical conductor.A non-Hermitian pseudo-gap can host symmetry-protected mid-gap modes like ordi-nary topological gaps,but the mid-gap modes are extended instead of edge-localized,and exhibit extreme sensitivity to symmetry-breaking perturbations.Surprisingly,pseudo-gaps can also host an inte-ger number of edge modes even though the pseudo-bands possess fractional topological windings,or even no well-defined Chern number at all,in the marginal case of a phase transition point.Challenging conventional notions of topological bulk-boundary correspondences and even the very con-cept of a band,pseudo-gaps post profound implications that extend to many-body settings,such as frac-tional Chern insulators.

Guangdong Provincial Key Laboratory of Quantum Metrology and Sensing&School of Physics and Astronomy,Sun Yat-sen University(Zhuhai Campus),Zhuhai 519082,China;Department of Physics,National University of Singapore,Singapore 117551,Singapore

[1]Linhu Li;Ching Hua Lee-.Non-Hermitian pseudo-gaps)[J].科学通报（英文版）,2022(07):685-690

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