Embedding Independent Length Scale of Flat Bands

Area of Science:

• Condensed Matter Physics
• Quantum Materials

Background:

• Conventional length scales in flat-band systems are often ineffective due to quenched kinetic energy.
• Existing geometric length scales, like quantum metric length, suffer from embedding dependence, limiting their universality.

Purpose of the Study:

• To introduce a novel, embedding-independent length scale for flat-band systems.
• To establish a universal measure governing localization phenomena in these systems.
• To connect this new length scale to observable physical properties.

Main Methods:

• Definition of an intrinsic length scale (ξ_flat) based on the localization length of in-gap states.
• Analytical derivation of the superconducting coherence length in terms of ξ_flat for weak-coupling flat-band superconductors.
• Numerical simulations on various lattice models to validate theoretical predictions.

Main Results:

• ξ_flat is introduced as an intrinsic, embedding-independent length scale for flat bands.
• The superconducting coherence length in the weak-coupling limit is shown to be equal to ξ_flat.
• Numerical simulations confirm the theoretical predictions and the correspondence between ξ_flat and superconducting coherence length.

Conclusions:

• ξ_flat provides a robust, universal length scale for flat-band systems.
• This length scale is crucial for understanding many-body phenomena, particularly superconductivity.
• The findings offer a new perspective on the fundamental properties of flat bands and their associated localization effects.