  Experimental realization of graphene-based stadium-shaped quantum dots (QDs)
have been few and incompatible with scanned probe microscopy. Yet, direct
visualization of electronic states within these QDs is crucial for determining
the existence of quantum chaos in these systems. We report the fabrication and
characterization of electrostatically defined stadium-shaped QDs in
heterostructure devices composed of monolayer graphene (MLG) and bilayer
graphene (BLG). To realize a stadium-shaped QD, we utilized the tip of a
scanning tunneling microscope to charge defects in a supporting hexagonal boron
nitride flake. The stadium states visualized are consistent with
tight-binding-based simulations, but lack clear quantum chaos signatures. The
absence of quantum chaos features in MLG-based stadium QDs is attributed to the
leaky nature of the confinement potential due to Klein tunneling. In contrast,
for BLG-based stadium QDs (which have stronger confinement) quantum chaos is
precluded by the smooth confinement potential which reduces interference and
mixing between states.
