Impact of competing energy scales on the shell-filling sequence in elliptic bilayer graphene quantum dots

We report on a detailed investigation of the shell-filling sequence in electrostatically defined elliptic bilayer graphene quantum dots (QDs) in the regime of low charge carrier occupation, $N\ensuremath{\le}12$, by means of magnetotransport spectroscopy and numerical calculations. We show the necessity of including both short-range electron-electron interaction and wave-function-dependent valley $g$-factors for understanding the overall fourfold shell-filling sequence. These factors lead to an additional energy splitting at half filling of each orbital state and different energy shifts in out-of-plane magnetic fields. Analysis of 31 different bilayer graphene (BLG) QDs reveals that both valley $g$-factor and electron-electron interaction-induced energy splitting increase with decreasing QD size, validating theory. However, we find that the electrostatic charging energy of such gate-defined QDs does not correlate consistently with their size, indicating complex electrostatics. These findings offer significant insights for future BLG QD devices and circuit designs.