Boundary-Driven Complex Brillouin Zone in Non-Hermitian Electric Circuits

TL;DR

This paper demonstrates how the generalized Brillouin zone in non-Hermitian electric circuits can be actively manipulated through boundary conditions, revealing boundary-sensitive topological phase transitions and complex wave behaviors.

Contribution

It introduces a method to control the GBZ in non-Hermitian circuits by boundary adjustments, uncovering boundary-driven topological phase transitions and complex wave phenomena.

Findings

GBZ forms multiple separated manifolds with decaying and growing waves

Topological phase transitions are governed by boundary conditions

Boundary manipulation enables control over non-Hermitian topological properties

Abstract

Complex-valued physical quantities, often non-conserved, represent key phenomena in non-Hermitian systems such as dissipation and localization. Recent advancements in non-Hermitian physics have revealed boundary-condition-sensitive band structures, characterized by a continuous manifold of complex-valued momentum known as the generalized Brillouin zone (GBZ). However, the ability to actively manipulate the GBZ and its associated topological properties has remained largely unexplored. Here, we demonstrate a controllable manipulation of the GBZ by adjusting the boundary Hamiltonian and leveraging the boundary sensitivity in a circuit lattice. Our observations reveal that the GBZ forms multiple separated manifolds containing both decaying and growing wave functions, in contrast to the previously observed non-Hermitian skin effect under open boundary condition (OBC). By continuously deforming the GBZ, we observe the topological phase transitions of innate topological structure of GBZ that are enriched by complex properties of non-Hermitian physical variables. Notably, such topological phase transition is governed by boundary conditions rather than bulk properties, underscoring the extreme boundary sensitivity unique to non-Hermitian systems.