Zero-energy states in graphene quantum dots and rings

TL;DR

This paper provides exact analytical solutions demonstrating that graphene quantum dots and rings can achieve full charge carrier confinement using electrostatic potentials alone, without magnetic fields, revealing key conditions for such confinement.

Contribution

It introduces exact solutions for zero-energy states in graphene quantum structures, clarifying conditions for electrostatic confinement without magnetic fields.

Findings

Full confinement achievable with specific potential parameters

Critical potential strength needed for confinement

Analytical solutions applicable to smooth decaying potentials

Abstract

We present exact analytical zero-energy solutions for a class of smooth decaying potentials, showing that the full confinement of charge carriers in electrostatic potentials in graphene quantum dots and rings is indeed possible without recourse to magnetic fields. These exact solutions allow us to draw conclusions on the general requirements for the potential to support fully confined states, including a critical value of the potential strength and spatial extent.