Band topology of pseudo-Hermitian phases through tensor Berry connections and quantum metric

TL;DR

This paper explores pseudo-Hermitian topological phases in 2D and 3D systems using algebraic methods, revealing unique band geometries and nearly-flat topological bands, with potential for experimental realization.

Contribution

It introduces a tensor Berry connection and quantum metric framework for pseudo-Hermitian phases, extending known topological models with new geometric insights.

Findings

Pseudo-Hermitian phases can be constructed using q-deformed matrices.

Pseudo-Hermitian models share topological invariants with Hermitian counterparts.

Some phases support nearly-flat topological bands.

Abstract

Among non-Hermitian systems, pseudo-Hermitian phases represent a special class of physical models characterized by real energy spectra and by the absence of non-Hermitian skin effects. Here, we show that several pseudo-Hermitian phases in two and three dimensions can be built by employing $q$-deformed matrices, which are related to the representation of deformed algebras. Through this algebraic approach we present and study the pseudo-Hermitian version of well known Hermitian topological phases, raging from two-dimensional Chern insulators and time-reversal-invariant topological insulators to three-dimensional Weyl semimetals and chiral topological insulators. We analyze their topological bulk states through non-Hermitian generalizations of Abelian and non-Abelian tensor Berry connections and quantum metric. Although our pseudo-Hermitian models and their Hermitian counterparts share the same topological invariants, their band geometries are different. We indeed show that some of our pseudo-Hermitian phases naturally support nearly-flat topological bands, opening the route to the study of pseudo-Hermitian strongly-interacting systems. Finally, we provide an experimental protocol to realize our models and measure the full non-Hermitian quantum geometric tensor in synthetic matter.