Graphene Quantum Dots and Wavefunction Imaging
The Crommie group has developed a new technique for locally gating nanoscale regions of atomically-clean graphene by injecting charge directly into the boron nitride (BN) insulator just below the graphene.1,2 Both polarities of charge can be independently implanted at different locations in the insulator by using a scanning tunneling microscope (STM) tip. This allows nanoscale confinement potentials to be “drawn” directly into graphene, thus allowing the graphene electronic wavefunction to be directly manipulated. The resulting graphene wavefunctions can then be imaged using STM spectroscopic techniques.2
Fig. 1a shows a sketch of the process of injecting negative charge into a BN insulator under graphene, which then causes the graphene overlayer to have a local p-doped region as shown in Fig. 1b. The results of the experimental process are shown in Fig. 2. Here the graphene is seen before charge injection in Fig. 2a and after charge injection in Fig. 2b (charge was injected at the right upper hand corner). This process creates a circular p-n junction as sketched in the inset of Fig. 2b.
Fig. 3 shows an image of the quantum mechanical eigenstate that is experimentally measured both inside and outside of the graphene quantum dot. A circular nodal pattern is observed inside the dot, as well as Friedel-like oscillations in the exterior region.
A larger-scale view of the dot can be seen in Fig. 4. This can be thought of as a relativistic quantum corral,3 since the confined electrons are now Dirac fermions. The energy-dependent nodal structure of the dot is shown in Fig. 5a.
We are able to model the quantum mechanical behavior of these quantum dots by solving the Dirac equation in the presence of a 2D parabolic confinement potential (theory performed by L. Levitov’s group). This is essentially a 2D relativistic simple harmonic oscillator. The fit is good (Fig. 2b), and shows that the nodal structure can be explained by a hierarchy of principal and total angular momentum quantum numbers.2 Here the total angular momentum is the sum of orbital angular momentum and pseudospin.
This new quantum dot fabrication technique is quite general and the Crommie group is exploring its application to other 2D materials.
1. J. Velasco, L. Ju, D. Wong, S. Kahn, J. Lee, H.-Z. Tsai, C. Germany, S. Wickenburg, J. Lu, T. Taniguchi, K. Watanabe, A. Zettl, F. Wang & M. F. Crommie, "Nanoscale Control of Rewriteable Doping Patterns in Pristine Graphene/Boron Nitride Heterostructures", Nano Letters 16, 1620 (2016).
2. J. Lee, D. Wong, J. Velasco Jr, J. F. Rodriguez-Nieva, S. Kahn, H.-Z. Tsai, T. Taniguchi, K. Watanabe, A. Zettl, F. Wang, L. S. Levitov & M. F. Crommie, "Imaging electrostatically confined Dirac fermions in graphene quantum dots", Nature Physics 12, 1032 (2016).
3. M. F. Crommie, C. P. Lutz & D. M. Eigler, "Confinement of Electrons to Quantum Corrals on a Metal Surface", Science 262, 218 (1993).