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

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.

References in corpus (8)

• The electronic properties of graphene
• The Coulomb impurity problem in graphene
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• Atomic Collapse and Quasi-Rydberg States in Graphene
• Tuning a Circular p-n Junction in Graphene from Quantum Confinement to Optical Guiding
• Electron states for gapped pseudospin-1 fermions in the field of charged impurity
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Cited by in corpus (2)

• Finite-temperature plasmons, damping and collective behavior for $\alpha -{\mathcal{T}}_3$ model
• Optical conductivity of bilayer dice lattices