Zero-energy states in graphene quantum dots and rings
  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. 
C. A. Downing, D. A. Stone, M. E. Portnoi
cond-mat.mes-hall math-ph math.MP quant-ph