Coulomb impurity on a Dice lattice: atomic collapse and bound states

TL;DR

This paper studies how Coulomb impurities affect the electronic states in a Dice lattice, revealing bound states, atomic collapse phenomena, and interactions with flat band states using tight binding calculations.

Contribution

It demonstrates the transformation of flat band states into localized bound states and the emergence of atomic collapse states in a Dice lattice with Coulomb impurities.

Findings

Flat band states become localized on a ring around the impurity.

Atomic collapse states appear beyond a critical Coulomb strength.

Flat band bound states anti-cross with atomic collapse states at high impurity strength.

Abstract

The modification of the quantum states in a Dice lattice due to a Coulomb impurity are investigated. The energy band structure of a pristine Dice lattice consists of a Dirac cone and a flat band at the Dirac point. We use the tight binding formalism and find that the flat band states transform into a set of discrete bound states whose electron density is localized on a ring around the impurity mainly on two of the three sublattices. The energy is proportional to the strength of the Coulomb impurity. Beyond a critical strength of the Coulomb potential atomic collapse states appear that have some similarity with those found in graphene with the difference that the flat band states contribute with an additional ring-like electron density that is spatially decoupled from the atomic collapse part. At large value of the strength of the Coulomb impurity the flat band bound states anti-cross with the atomic collapse states.