Linear Localization of Zero Modes in Weakly Coupled Non‐Hermitian Reservoirs

Abstract Topological and symmetry‐protected non‐Hermitian zero modes have attracted considerable interest in the past few years. Here, it is revealed that they can exhibit an unusual behavior when transitioning between the extended and localized regimes: When weakly coupled to a non‐Hermitian reservoir, such a zero mode displays a linearly decreasing amplitude as a function of space, which is not caused by an EP of a Hamiltonian, either of the entire system or the reservoir itself. Instead, this phenomenon is due to the non‐Bloch solution of a linear homogeneous recurrence relation, together with the underlying non‐Hermitian particle‐hole symmetry and the zeroness of its energy.