Intrinsic Curvature and the Robustness of Band Topology in Non-Hermitian Systems

This paper investigates the interplay between intrinsic quantum geometry and the stability of topological phases in non-Hermitian systems. We explore the generalization of the quantum geometric tensor (QGT) to non-Hermitian frameworks, analyzing the distinct roles of its real part, the quantum metric, and its imaginary part, the Berry curvature. The study focuses on how non-Hermiticity, introduced through gain and loss, modifies the underlying geometric structure of the Bloch state space, leading to phenomena not observed in Hermitian systems, such as the non-Hermitian skin effect and the emergence of exceptional points. We establish a connection between the intrinsic curvature of the energy bands and the robustness of topological invariants, such as the Chern number and winding numbers, against non-Hermitian perturbations. Our analysis reveals that the quantum metric provides crucial information about the stability of topological phases, complementing the topological classification provided by the Berry curvature. Furthermore, we discuss how the geometric properties encoded in the QGT influence wavepacket dynamics, demonstrating that both the quantum metric and a generalized Berry curvature are essential for a complete description of anomalous transport phenomena. This work provides a unified geometric framework for understanding the stability and dynamical signatures of band topology in the presence of non-Hermiticity, highlighting the profound impact of intrinsic curvature on the robustness of these quantum phases.