Size effects on atomic collapse in the dice lattice

Area of Science:

• Condensed Matter Physics
• Materials Science
• Quantum Mechanics

Background:

• Flat band systems exhibit unique electronic properties.
• Atomic collapse of charged impurities is a critical phenomenon in condensed matter.
• Quantum dots confine electrons, leading to size-dependent effects.

Purpose of the Study:

• To investigate the impact of system size on atomic collapse of charged impurities in flat band systems.
• To explore the role of in-gap edge states and spatial quantization.
• To analyze the creation of supercritical localized potential wells.

Main Methods:

• Tight-binding simulations on a dice lattice with circular quantum dot geometries.
• Analysis of the mixing between in-gap edge states and impurity-bound states.
• Investigation of resonant tunneling phenomena.

Main Results:

• Mixing of in-gap edge states increases the critical charge for atomic collapse.
• Spatial quantization enhances the band gap, hindering dive-into-continuum observation in small quantum dots.
• Filling in-gap states enables resonant tunneling at smaller charges, showing non-monotonous size dependence.
• Supercritical potentials can only be formed on rim sites, not hub sites.

Conclusions:

• Size effects significantly influence atomic collapse in flat band systems.
• Observation of dive-into-continuum is challenging in small quantum dots due to specific electronic interactions.
• Tailoring in-gap states offers pathways for controlling impurity effects.
• The findings are relevant for artificial flat band lattice designs.