On Resonant Scattering States in Graphene Circular Quantum Dots

TL;DR

This paper investigates the nature of resonant scattering states in graphene quantum dots, highlighting the limitations of existing models in accurately describing these quasi-bound states due to Klein tunneling effects.

Contribution

It critically examines the resonance condition within the Dirac pseudo-fermion model, revealing inconsistencies in its application to complex energies and total reflection scenarios.

Findings

Resonance condition leads to inconsistent equations for complex energies.

The Dirac pseudo-fermion model does not reliably describe resonant states.

Challenges in modeling bound states in graphene quantum dots due to Klein tunneling.

Abstract

Due to effect of Klein tunneling two-dimensional graphene quantum dots do not possess genuine bound states but quasi-bound (resonant tunneling) states only. We discuss in detail the attempt to describe these states within the framework of the Dirac pseudo-fermion model for circular dot. We demonstrate explicitly that introduced earlier the so called "resonance condition" corresponds to inconsistent system of linear equations obtained from matching conditions on the boundary of the quantum dot when one try to use it for complex energy values and to the case of total reflection for the energies coincided with the potential well top.