Massless Dirac fermions in two dimensions: Confinement in nonuniform magnetic fields
Physical Review B - Condensed Matter and Materials
American Physical Society
This is the final version. Available from the American Physical Society via the DOI in this record.
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.
We acknowledge financial support from the CNRS through the PICS program (Contract No. 6384 APAG) and from the ANR under Grant No. ANR-14-CE26-0005 Q-MetaMat, as well as support from the EU H2020 RISE project CoExAN (Grant No. H2020-644076), EU FP7 ITN NOTEDEV (Grant No. FP7-607521), and the FP7 IRSES projects CANTOR (Grant No. FP7-612285), QOCaN (Grant No. FP7-316432), and InterNoM (Grant No. FP7-612624).
Vol. 94, No. 16, Article number: 165407