Massless Dirac fermions in two dimensions: Confinement in nonuniform   magnetic fields
  We show how it is possible to trap two-dimensional massless Dirac fermions in spatially inhomogeneous magnetic fields, as long as the formed magnetic quantum dot (or ring) is of a slowly decaying nature. It is found that a modulation of the depth of the magnetic quantum dot leads to successive confinement-deconfinement transitions of vortexlike states with a certain angular momentum, until a regime is reached where only states with one sign of angular momentum are supported. We illustrate these characteristics with both exact solutions and a hitherto unknown quasi-exactly solvable model utilizing confluent Heun functions. 
C. A. Downing and M. E. Portnoi
cond-mat.mes-hall math-ph math.MP quant-ph