Coupled electron-hole states are realized in a system consisting of a combination of an electrostatic potential barrier and ring-shaped potential well, which resembles a circular dipole. A perpendicular magnetic field induces confined states inside the Landau gaps which are mainly located at the barrier or ring. Hybridizations between the barrier and ring states are seen as anticrossings in the energy spectrum. As a consequence, the energy levels show an oscillating dependence on the electrostatic potential strength in combination with an oscillating migration of the wave functions between the barrier and ring. At the anticrossing points the quantum state consists of a mixture of electron and hole. The present system mimics closely the behavior of a relativistic dipole on gapped graphene.

• Received 21 December 2018
• Revised 8 March 2019

DOI:https://doi.org/10.1103/PhysRevB.99.125426