Topological Properties of a Non‐Hermitian Quasi‐1D Chain with a Flat Band

The spectral properties of a non‐Hermitian quasi‐1D lattice in two of the possible dimerization configurations are investigated. Specifically, it focuses on a non‐Hermitian diamond chain that presents a zero‐energy flat band. The flat band originates from wave interference and results in eigenstates with a finite contribution only on two sites of the unit cell. To achieve the non‐Hermitian characteristics, the system under study presents non‐reciprocal hopping terms in the chain. This leads to the accumulation of eigenstates on the boundary of the system, known as the non‐Hermitian skin effect. Despite this accumulation of eigenstates, for one of the two considered configurations, it is possible to characterize the presence of non‐trivial edge states at zero energy by a real‐space topological invariant known as the biorthogonal polarization. This work shows that this invariant, evaluated using the destructive interference method, characterizes the non‐trivial phase of the non‐Hermitian diamond chain. For the second non‐Hermitian configuration, there is a finite quantum metric associated with the flat band. Additionally, the system presents the skin effect despite the system having a purely real or imaginary spectrum. The two non‐Hermitian diamond chains can be mapped into two models of the Su‐Schrieffer‐Heeger chains, either non‐Hermitian, and Hermitian, both in the presence of a flat band. This mapping allows to draw valuable insights into the behavior and properties of these systems. This study presents the spectral properties of two non‐Hermitian quasi‐1D chains characterized by a flat band in the band structure, the dimerized diamond chains. It has characterized the two systems in terms of biorthogonal polarization and quantum metric. After a unitary rotation, it shows the equivalence to the non‐Hermitian SSH chains and the appearance of a novel skin effect.