  The tuneability and control of quantum nanostructures in two-dimensional
materials offer promising perspectives for their use in future electronics. It
is hence necessary to analyze quantum transport in such nanostructures.
Material properties such as a complex dispersion, topology, and charge carriers
with multiple degrees of freedom, are appealing for novel device
functionalities but complicate their theoretical description. Here, we study
quantum tunnelling transport across a few-electron bilayer graphene quantum
dot. We demonstrate how to uniquely identify single- and two-electron dot
states' orbital, spin, and valley composition from differential conductance in
a finite magnetic field. Furthermore, we show that the transport features
manifest splittings in the dot's spin and valley multiplets induced by
interactions and magnetic field (the latter splittings being a consequence of
bilayer graphene's Berry curvature). Our results elucidate spin- and
valley-dependent tunnelling mechanisms and will help to utilize bilayer
graphene quantum dots, e.g., as spin and valley qubits.
