Imaging Quantum Interference in Stadium-Shaped Monolayer and Bilayer Graphene Quantum Dots

Area of Science:

• Condensed Matter Physics
• Materials Science
• Quantum Physics

Background:

• Experimental realization of graphene stadium quantum dots (QDs) is limited and challenging.
• Direct visualization of electronic states in QDs is essential for studying quantum chaos.
• Existing methods are incompatible with scanned probe microscopy.

Purpose of the Study:

• To fabricate and characterize electrostatically defined stadium-shaped QDs in graphene heterostructures.
• To visualize electronic states within these QDs and investigate quantum chaos.
• To understand the influence of graphene type (monolayer vs. bilayer) on quantum chaos.

Main Methods:

• Fabrication of stadium-shaped QDs using scanning tunneling microscopy (STM) tip to charge defects in hexagonal boron nitride (hBN).
• Characterization of QDs in monolayer graphene (MLG) and bilayer graphene (BLG) heterostructures.
• Visualization of electronic states and comparison with tight-binding simulations.

Main Results:

• Successfully fabricated and characterized stadium-shaped QDs in MLG and BLG.
• Visualized electronic states consistent with simulations but lacking clear quantum chaos signatures.
• Absence of quantum chaos in MLG QDs attributed to Klein tunneling.
• Quantum chaos precluded in BLG QDs due to smooth confinement potential.

Conclusions:

• Graphene stadium QDs can be fabricated and visualized using STM.
• Klein tunneling in MLG and smooth confinement in BLG prevent clear observation of quantum chaos.
• Further research may be needed to engineer QDs that exhibit quantum chaos in graphene systems.