Impurity-induced counter skin-effect and linear modes in non-Hermitian systems
arXiv:2408.01265 · doi:10.1063/5.0270893
Abstract
Non-reciprocal lattice systems are among the simplest non-Hermitian systems, exhibiting several key features absent in their Hermitian counterparts. In this study, we investigate the Hatano-Nelson model with impurity and unveil how the impurity influences the intrinsic non-Hermitian skin effect of the system. We present an exact analytical solution to the problem under open and periodic boundary conditions, irrespective of the impurity's position and strength. Numerical simulations thoroughly validate this exact solution. Our analysis reveals a distinctive phenomenon where a specific impurity strength, determined by the non-reciprocal hopping parameters, induces a unique skin state at the impurity site. This impurity state exhibits a skin effect that counterbalances the boundary-induced skin effect, a phenomenon we term the \emph{impurity-induced counter skin-effect}. These findings offer insights into the dynamics of non-Hermitian systems with impurities, elucidating the complex interplay between impurities and the system's non-reciprocal nature. We propose a possible implementation of this system for a non-Hermitian discrete-time quantum walk, and we demonstrate that an impurity-induced counter skin-effect also exists in multi-band models.
References in corpus (42)
- Edge states and topological invariants of non-Hermitian systems
- Anderson Transitions
- Exceptional Topology of Non-Hermitian Systems
- Quantum random walks - an introductory overview
- Topological Origin of Non-Hermitian Skin Effects
- Universal computation by quantum walk
- Correspondence between winding numbers and skin modes in non-hermitian systems
- Observation of bulk boundary correspondence breakdown in topolectrical circuits
- Efficient Light Funneling based on the non-Hermitian Skin Effect
- Topological phases in the non-Hermitian Su-Schrieffer-Heeger model
- Biorthogonal Quantum Mechanics
- Universal non-Hermitian skin effect in two and higher dimensions
- Non-Hermitian Topological Sensors
- Observation of Non-Hermitian Skin Effect and Topology in Ultracold Atoms
- Interplay of non-Hermitian skin effects and Anderson localization in non-reciprocal quasiperiodic lattices
- Observation of arbitrary topological windings of a non-Hermitian band
- Topological Non-Hermitian skin effect
- Controlling discrete quantum walks: coins and intitial states
- Exact solution of non-Hermitian systems with generalized boundary conditions: size-dependent boundary effect and fragility of skin effect
- Exponentially-enhanced quantum sensing with non-Hermitian lattice dynamics
- Impurity induced scale-free localization
- Inner Skin Effects on Non-Hermitian Topological Fractals
- Trapping a particle of a quantum walk on the line
- Explicit definition of symmetry for non-unitary quantum walks with gain and loss
- Anomalous Skin Effects in Disordered Systems with a Single non-Hermitian Impurity
- Bulk-boundary correspondence in non-Hermitian systems: stability analysis for generalized boundary conditions
- Exact solution of single impurity problem in non-reciprocal lattices: impurity induced size-dependent non-Hermitian skin effect
- Non-Hermitian skin effect as an impurity problem
- Exact eigenvectors and eigenvalues of the finite Kitaev chain and its topological properties
- Review on Quantum Walk Computing: Theory, Implementation, and Application
- Observation of non-Hermitian topology in a multi-terminal quantum Hall device
- Sensitivity of non-Hermitian systems
- Linear and non-linear transport across a finite Kitaev chain: an exact analytical study
- Diagnosis of bulk phase diagram of non-reciprocal topological lattices by impurity modes
- Exact analogue of the Hatano-Nelson model in 1D continuous nonreciprocal systems
- Topological properties of a non-Hermitian quasi-1D chain with a flat band
- Exploring the impact of fluctuation-induced criticality on non-hermitian skin effect and quantum sensors
- Observables in non-Hermitian systems: A methodological comparison
- Fate of non-Hermitian free fermions with Wannier-Stark ladder
- Localization in Quantum Walks with a Single Lattice Defect: A Comparative Study
- Lack of near-sightedness principle in non-Hermitian systems
- On symmetric Tetranacci polynomials in mathematics and physics