Non-Hermitian impurity problem

Area of Science:

• Condensed matter physics
• Quantum mechanics
• Materials science

Background:

• The single Hermitian impurity problem is key to understanding Anderson localization.
• Non-Hermitian lattices with defects are gaining interest, but the impurity problem is underexplored.
• Understanding localization in non-Hermitian systems is crucial for novel quantum devices.

Purpose of the Study:

• Investigate the role of a single complex impurity in various dimensional tight-binding lattices.
• Explore spectral and localization properties in non-Hermitian systems.
• Analyze finite-sized lattices for experimental relevance in photonic platforms.

Main Methods:

• Theoretical investigation of complex impurities in 1D, 2D, and 3D tight-binding lattices.
• Analysis of both infinite and finite lattice structures.
• Characterization of localized states and eigenstates.

Main Results:

• Observed counterintuitive phenomena: vanishing and re-emerging localization with impurity strength.
• Discovered scale-free localized states and peculiar cross-shaped eigenstates in finite lattices.
• Deviations from conventional exponential localization profiles were identified.

Conclusions:

• The non-Hermitian single impurity problem exhibits unique behaviors distinct from Hermitian systems.
• Exotic localized states in finite lattices offer new avenues for experimental exploration.
• This research provides a foundation for studying transport in non-Hermitian disordered systems.