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

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.

Anomalous Transport Induced by Non-Hermitian Anomalous Berry Connection in Non-Hermitian Systems

“…where σx = 0 a b 0 , σy = 0 −ia ib 0 , σz = q −1 0 0 −q , (6) are q−deformed Pauli matrices with a = (1 + q 2 )/2, b = (1 + q −2 )/2 and q > 0 [66,67]. We first consider a system with time-reversal symmetry with…”