Topological Order and Non-Hermitian Skin Effect in Generalized Ideal Chern Bands

TL;DR

This paper extends the concept of ideal Chern bands to non-Hermitian systems, revealing novel topological phenomena like the non-Hermitian skin effect and skin-Laughlin states, and uncovers an unconventional phase transition.

Contribution

It introduces a generalized ideal condition for non-Hermitian Chern bands, linking complex Berry curvature and quantum metric, and explores the resulting topological and boundary effects.

Findings

The lowest band satisfies a generalized ideal condition with complex Berry curvature.

The system exhibits a non-Hermitian skin effect without spectral winding.

Unconventional phase transition occurs at critical non-Hermiticity strength.

Abstract

Fractionalization in ideal Chern bands and non-Hermitian topological physics are two active but so far separate research directions. Merging these, we generalize the notion of ideal Chern bands to the non-Hermitian realm and uncover several striking consequences both on the level of band theory and in the strongly interacting regime. Specifically, we show that the lowest band of a Kapit--Mueller lattice model with an imaginary gauge potential satisfies a generalized ideal condition with complex Berry curvature in sync with a complex quantum metric. The ideal band remains purely real and exactly flat yet all right and left eigenstates accumulate at the boundaries on a cylinder, implying a non-Hermitian skin effect without an accompanying spectral winding. The skin effect is inherited by the many-body zero modes, yielding skin-Laughlin states with an exponential profile on the lattice. Moreover, at a critical strength of non-Hermiticity there is an unconventional phase transition on the torus, which is absent on the cylinder. Our findings lead to an extension of topological order in non-Hermitian systems.