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Free keywords:
Condensed Matter, Mesoscale and Nanoscale Physics, cond-mat.mes-hall, Physics, Optics, physics.optics,Quantum Physics, quant-ph
Abstract:
We investigate the spectral properties of a non-Hermitian quasi-one-dimensional lattice in two possible dimerization configurations.
Specifically, we focus 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, we introduce non-reciprocal
intrasite 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 possible
configurations, we can characterize the presence of non-trivial edge states at zero energy by a real-space topological invariant known as the biorthogonal polarization. We show that this invariant, evaluated using the destructive interference method, characterizes the non-trivial phase of the non-Hermitian
diamond chain. For the other possible non-Hermitian configuration, we find that there is a finite quantum metric associated with the flat band. Additionally, we observe the skin effect despite having the system a purely real or imaginary spectrum. For both configurations, we show that two non- Hermitian diamond
chains can be mapped into two models of the Su-Schrieffer-Heeger chains, either non-Hermitian and Hermitian, in the presence of a flat band. This mapping allows us to draw valuable insights into the behavior and properties of these systems.
