Size effects on atomic collapse in the dice lattice

TL;DR

This study investigates how size effects influence atomic collapse phenomena in dice lattice systems, revealing that quantum dot size and in-gap state filling significantly affect critical charge and tunneling behaviors.

Contribution

It introduces a detailed analysis of size-dependent atomic collapse in dice lattices, highlighting the role of edge states, quantum dot size, and sublattice site differences in supercritical phenomena.

Findings

Critical charge increases with edge state mixing and quantum dot size.

In-gap state filling enables resonant tunneling at lower charges.

Supercritical potential wells are feasible only on rim sites, not hub sites.

Abstract

We study the role of size effects on atomic collapse of charged impurity in the flat band system. The tight-binding simulations are made for the dice lattice with circular quantum dot shapes. It is shown that the mixing of in-gap edge states with bound states in impurity potential leads to increasing the critical charge value. This effect, together with enhancement of gap due to spatial quantization, makes it more difficult to observe the dive-into-continuum phenomenon in small quantum dots. At the same time, we show that if in-gap states are filled, the resonant tunneling to bound state in the impurity potential might occur at much smaller charge, which demonstrates non-monotonous dependence with the size of sample lattice. In addition, we study the possibility of creating supercritical localized potential well on different sublattices, and show that it is possible only on rim sites, but not on hub site. The predicted effects are expected to naturally occur in artificial flat band lattices.