非厄米赝能隙

Non-Hermitian pseudo-gaps

能隙是表征物态的重要概念之一.其中,能态密度极低但非零的区域被称为赝能隙,其出现与高温超导等现象有着重要的联系.本研究发现对于一些非厄米格点系统,引入开边界条件能够导致赝能隙的产生.这一现象通常在两个或更多不对称的非厄米泵浦通道相互影响时出现,并且没有厄米对应.非厄米赝能隙的出现同时也伴随着一些其他新奇的物理现象.与普通拓扑能隙类似,非厄米赝能隙中也能出现受对称性保护的隙间态,但这些隙间态具有扩展的空间分布,而不是局域在系统边缘,且对破坏对称性的扰动具有很高的敏感性.在传统的拓扑相变点处,非厄米赝能隙中同样可以存在与拓扑态类似的局域边界态,但并不直接对应相应赝能带的拓扑不变量:这些赝能带可能具有分数的拓扑数,甚至不具有良好定义的陈数.非厄米赝能隙的概念挑战了传统拓扑对应以及能带的概念,有望对分数陈绝缘体等多体现象产生重要的影响.

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 electrical conductor.A non-Hermitian pseudo-gap can host symmetry-protected mid-gap modes like ordinary 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 integer 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 concept of a band,pseudo-gaps post profound implications that extend to many-body settings,such as fractional Chern insulators.