Electron confinement in single layer graphene quantum dots: Semiclassical approach

A semiclassical approach is used to investigate the physics of electrons confined in a graphene quantum dot in a magnetic field. The states near the gap in the spectrum are localised between the turning points for classical massless particles. This fact is used to obtain approximate energies and states in the case of non-zero, positive angular momentum. The agreement with exact numerical energies is about 1.5% or better and the nodal structure of the exact states is predicted correctly. The exact and approximate quantum states also agree well. The approach is most accurate in the regime of large angular momentum, large magnetic field and small radial quantum number.