English

Zero-energy states in graphene quantum dots and rings

Mesoscale and Nanoscale Physics 2011-11-01 v2 Mathematical Physics math.MP Quantum Physics

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.

Cite

@article{arxiv.1105.0891,
  title  = {Zero-energy states in graphene quantum dots and rings},
  author = {C. A. Downing and D. A. Stone and M. E. Portnoi},
  journal= {arXiv preprint arXiv:1105.0891},
  year   = {2011}
}

Comments

8 pages, 3 figures, references added, typos corrected, discussion section expanded

R2 v1 2026-06-21T18:02:53.339Z