Berry phase induced valley level crossing in bilayer graphene quantum dots

We study the confined bound states in circular bilayer graphene quantum dots. Using the semiclassical Einstein-Brillouin-Keller quantization rule, we predict that valley levels inside the quantum dot undergo three stages: splitting, crossing, and recombining when varying the applied magnetic field. This exotic phenomenon originates from the Berry phase, which increases from zero to $2\ensuremath{\pi}$ with the magnetic field and has opposite signs for the two inequivalent valleys. To further confirm this phenomenon, we perform a fully quantum mechanical calculation based on a low-energy continuum model and a real space tight-binding model, and show that the valley effect can be explicitly observed by scanning-tunneling spectroscopy measurements. Moreover, we propose an efficient valley filter device as an application of this valley effect, which can be used to manipulate the valley degree of freedom in valleytronics.