Non-Hermitian Pseudo-Gaps

TL;DR

This paper introduces a novel non-Hermitian mechanism that creates pseudo-gaps in lattice systems, revealing unique spectral and topological properties with implications for advanced quantum phenomena.

Contribution

It uncovers a new non-Hermitian process for pseudo-gap formation due to boundary interference, distinct from Hermitian systems, and explores their topological and spectral characteristics.

Findings

Pseudo-gaps arise from asymmetric pumping channel interference.

Mid-gap modes in pseudo-gaps are extended and symmetry-sensitive.

Pseudo-gaps can host edge modes without well-defined Chern numbers.

Abstract

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 new non-Hermitian mechanism that induces pseudo-gaps when boundaries are introduced in a 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.