Imaging electrostatically confined Dirac fermions in graphene quantum dots (1606.03654v1)

Abstract: Electrostatic confinement of charge carriers in graphene is governed by Klein tunneling, a relativistic quantum process in which particle-hole transmutation leads to unusual anisotropic transmission at pn junction boundaries. Reflection and transmission at these novel potential barriers should affect the quantum interference of electronic wavefunctions near these boundaries. Here we report the use of scanning tunneling microscopy (STM) to map the electronic structure of Dirac fermions confined by circular graphene pn junctions. These effective quantum dots were fabricated using a new technique involving local manipulation of defect charge within the insulating substrate beneath a graphene monolayer. Inside such graphene quantum dots we observe energy levels corresponding to quasi-bound states and we spatially visualize the quantum interference patterns of confined electrons. Dirac fermions outside these quantum dots exhibit Friedel oscillation-like behavior. Bolstered with a theoretical model describing relativistic particles in a harmonic oscillator potential, our findings yield new insight into the spatial behavior of electrostatically confined Dirac fermions.

Imaging Electrostatically Confined Dirac Fermions in Graphene Quantum Dots

In the paper titled "Imaging electrostatically confined Dirac fermions in graphene quantum dots," the authors present a comprehensive examination of the phenomena associated with Dirac fermions confined within circular graphene pn junctions. The paper utilizes scanning tunneling microscopy (STM) to map the electronic structures of these confined systems. The innovative approach taken in this research facilitates the spatial visualization of quasi-bound states induced by electrostatic potentials, thereby offering new insights into quantum interference patterns of Dirac fermions in graphene.

The confinement of electrons in graphene is a challenging endeavor mainly due to Klein tunneling, which renders conventional electrostatic potentials transparent to Dirac fermions when they strike the potential barrier perpendicularly. Previous methods of electron confinement, such as lithographic patterning and utilization of magnetic fields, have proved inadequate for STM-based spatial imaging due to contamination or gating issues. In contrast, this paper introduces an innovative technique to create stationary circular pn junctions within a graphene layer, employing a voltage pulse through an STM tip to ionize defects beneath a graphene/boron nitride (BN) heterostructure. This method allows for precise spatial imaging and manipulation of quantum dots, overcoming limitations of prior methodologies.

The empirical results reveal marked energy levels corresponding to quasi-bound states inside the graphene quantum dots. Notably, the quantization of energy levels and the spatial interference patterns suggest the formation of a quantum dot, highlighting the complex wavefunctions resulting from the relativistic properties of Dirac fermions. For example, at the center of these quantum dots, the energy spacing (Δε) between levels is observed to be significantly larger than at points further out, which is indicative of the relativistic harmonics of graphene's band structure. The paper precisely measures this spacing, noting variations from 29 ± 2 mV at the pn junction center to 13 ± 2 mV at distances of 100 nm—data that align well with their theoretical model.

Theoretical insights provided by the authors are based on a model considering the two-dimensional massless Dirac Hamiltonian subjected to a harmonic oscillator potential. The numerical simulations rigorously replicate the spatial distribution of observed eigenstates, supporting the data collected through STM imaging. This model elucidates the angular momentum-driven confinement mechanisms that produce quasi-bound quantum dot states.

Importantly, the research holds significant implications for future developments within the field of quantum electronics. By establishing a framework for electrostatically gated and STM-imaged graphene quantum dots, the paper opens avenues for potential applications in quantum computing and nanoscale electronic devices where manipulation and visualization of quantum states are crucial.

Overall, the research advances the understanding of electrostatic confinement in graphene and provides a tangible methodology for further exploration of quantum dot systems within two-dimensional Dirac materials. The integration of theoretical modeling with empirical STM observations offers a promising foundation for continued investigations into the quantum electronic properties of graphene and other novel materials with similar properties. Future inquiries may be directed towards diverse quantum dot configurations, including those with adjustable coupling and varied geometries, thereby extending this work to complex quantum architectures.