Nearest neighbor tight binding models with an exact mobility edge in one dimension

Area of Science:

• Condensed Matter Physics
• Quantum Mechanics
• Materials Science

Background:

• Investigating electron localization in disordered systems is crucial for understanding material properties.
• Quasiperiodic potentials offer a unique platform to study localization phenomena beyond traditional disorder models.

Purpose of the Study:

• To explore localization properties in deterministic tight-binding models with quasiperiodic on-site modulation.
• To identify a self-duality symmetry and its role in defining a mobility edge.

Main Methods:

• Developed a generalized duality transformation for nearest-neighbor tight-binding models.
• Introduced and calculated the typical density of states as an order parameter.
• Computed the inverse participation ratio to verify theoretical predictions.

Main Results:

• Proved that the studied model family is self-dual under the generalized duality transformation.
• Derived a simple closed-form condition for self-duality based on model parameters and energy.
• Numerically verified that the self-dual line acts as a mobility edge, separating localized and extended states.

Conclusions:

• The self-dual line in this quasiperiodic model acts as a duality-protected mobility edge.
• This work presents the first nearest-neighbor tight-binding model with a duality-protected mobility edge.
• Proposed experimental realization in atomic optical lattices and photonic waveguides.