Quasiperiodic and periodic extended Hatano-Nelson model: Anomalous complex-real transition and non-Hermitian skin effect
arxiv(2024)
摘要
We study the effect of quasiperiodic and periodic onsite potentials in a
Hatano-Nelson model with next-nearest-neighbour hopping. By considering a
non-reciprocal next-nearest-neighbour hopping and a quasiperiodic onsite
potential under periodic boundary conditions, we show a breakdown of the
typical correspondence between the delocalization-localization and complex-real
transitions as a function of the potential strength. Moreover, we reveal that
in the delocalized regime, when the potential strength increases, the
eigenstates under open boundary conditions exhibit a bidirectional
non-Hermitian skin effect, i.e., they tend to localize on both the edges
instead of localizing on either of the edges. However, when a periodic onsite
potential is considered, the system not only exhibits a bidirectional skin
effect but also shows a complete direction reversal of the skin effect as a
function of the onsite periodic potential.
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