Shell Filling and Trigonal Warping in Graphene Quantum Dots

Transport measurements through a few-electron circular quantum dot in bilayer graphene display bunching of the conductance resonances in groups of four, eight, and twelve. This is in accordance with the spin and valley degeneracies in bilayer graphene and an additional threefold "minivalley degeneracy" caused by trigonal warping. For small electron numbers, implying a small dot size and a small displacement field, a two-dimensional s shell and then a p shell are successively filled with four and eight electrons, respectively. For electron numbers larger than 12, as the dot size and the displacement field increase, the single-particle ground state evolves into a threefold degenerate minivalley ground state. A transition between these regimes is observed in our measurements and can be described by band-structure calculations. Measurements in the magnetic field confirm Hund's second rule for spin filling of the quantum dot levels, emphasizing the importance of exchange interaction effects.