Using the four-band continuum model we derive a general expression for the infinite-mass boundary condition in bilayer graphene. Applying this new boundary condition we analytically calculate the confined states and the corresponding wave functions in a bilayer graphene quantum dot in the absence and presence of a perpendicular magnetic field. Our results for the energy spectrum show an energy gap between the electron and hole states at small magnetic fields. Furthermore the electron (e) and hole (h) energy levels corresponding to the K and K' valleys exhibit the EKe(h)(m)=-EK' h(e)(m) symmetry, where m is the angular momentum quantum number.
Bibliographical noteFunding Information:
This work was financially supported by CNPq , under contract NanoBioEstruturas 555183/2005-0, PRONEX/FUNCAP , CAPES Foundation under the process number BEX 7178/13-1, the Flemish Science Foundation (FWO-Vl), the European Science Foundation (ESF) under the EUROCORES program EuroGRAPHENE (project CONGRAN), the Bilateral programme between CNPq and FWO-Vl, and the Brazilian Program Science Without Borders (CsF). We thank M. Ramezani Masir and M. Grujić for helpful comments and discussions.