Shell Filling and Trigonal Warping in Graphene Quantum Dots

TL;DR

This paper investigates electron filling, degeneracies, and band-structure effects in bilayer graphene quantum dots, revealing the influence of trigonal warping and confirming Hund's rule through transport measurements.

Contribution

It demonstrates the impact of trigonal warping on degeneracies and electron filling in graphene quantum dots, supported by experimental data and band-structure calculations.

Findings

Observation of conductance resonance bunching due to degeneracies

Transition from shell filling to minivalley ground state with increasing dot size

Confirmation of Hund's second rule in quantum dot spin filling

Abstract

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- and then a p-shell are successively filled with four and eight electrons, respectively. For electron numbers larger than twelve, as the dot size and the displacement field increase, the single-particle ground state evolves into a three-fold degenerate minivalley ground state. A transition between these regimes is observed in our measurements and can be described by band-structure calculations. Measurements in magnetic field confirm Hund's second rule for spin filling of the quantum dot levels, emphasizing the importance of exchange interaction effects.