Algebraic States in Continuum in d>1 Dimensional Non-Hermitian Systems

Area of Science:

• Condensed Matter Physics
• Quantum Mechanics
• Topological Materials

Background:

• Non-Hermitian systems exhibit unique phenomena not found in Hermitian counterparts.
• Understanding the behavior of eigenstates in continuum spectra is crucial for quantum device applications.
• Localized states in continuum pose a challenge in characterizing quantum systems.

Purpose of the Study:

• To report the existence of algebraically localized eigenstates in the continuum of 2D non-Hermitian systems.
• To introduce and define algebraic states in continuum (AICs) and their properties.
• To establish the conditions for AICs formation and their experimental detectability.

Main Methods:

• Analytical derivation of the threshold condition for impurity strength.
• Characterization of AICs decay as 1/|r| from the impurity site.
• Investigation of AICs within the bulk continuum spectrum under periodic boundary conditions.

Main Results:

• Demonstrated the existence of algebraically localized eigenstates (AICs) in 2D non-Hermitian systems.
• AICs decay algebraically (1/|r|) and are embedded within the continuum spectrum.
• Derived the critical impurity strength for AICs generation and proved their absence in Hermitian/1D systems.

Conclusions:

• AICs are a novel phenomenon unique to 2D and higher-dimensional non-Hermitian systems.
• The local density of states is proposed as a viable experimental observable for detecting AICs.
• Findings open new possibilities for manipulating quantum states in non-Hermitian platforms.