LAUSR

The electronic energy spectrum of bilayer graphene with a magnetic quantum dot (MQD) and a magnetic quantum ring (MQR) are investigated. The energy eigenvalues and wavefunctions of quasiparticle states are calculated analytically by solving decoupled fourth-order differential equations. For the MQD, in the case of a negative inner magnetic field, two peculiar characteristics of the eigenvalue evolution are found: (a) the energy eigenstates change in a stepwise manner owing to energy anticrossing and (b) the quantum states approach zero energy. For the MQR, there is an angular momentum transition of eigenvalue as the inner radius of the ring varies, and the Aharonov–Bohm effect is observed in the eigenvalue spectra for both positive and negative magnetic fields inside the inner radius.