Imaging electrostatically confined Dirac fermions in graphene quantum dots

Electrostatic confinement of charge carriers in graphene is governed by Klein tunnelling, a relativistic quantum process in which particle–hole transmutation leads to unusual anisotropic transmission at p–n junction boundaries1–5. Reflection and transmission at these boundaries a ect the quantum interference of electronic waves, enabling the formation of novel quasi-bound states6–12. Here we report the use of scanning tunnellingmicroscopy tomap the electronic structure of Dirac fermions confined in quantum dots defined by circular graphene p–n junctions. The quantum dots were fabricated using a technique involving local manipulation of defect charge within the insulating substrate beneath a graphene monolayer13. Inside such graphene quantum dots we observe resonances due to quasi-bound states and directly visualize the quantum interference patterns arising from these states. Outside the quantum dots Dirac fermions exhibit Friedel oscillation-like behaviour. Bolstered by a theoretical model describing relativistic particles in a harmonic oscillator potential, our findings yield insights into the spatial behaviour of electrostatically confined Dirac fermions. Quantum confinement in graphene has previously been accomplished through lithographically patterned structures14–17, graphene edges18, and chemically synthesized graphene islands19–22. These systems, however, are either too contaminated for direct wavefunction visualization or use metallic substrates that prevent electrostatic gating. Electron confinement in graphene has also been induced through high magnetic fields23 and supercritical impurities24, but thesemethods are unwieldy formany technological applications. An alternative approach for confining electrons in graphene relies on using electrostatic potentials. However, this is notoriously difficult because Klein tunnelling renders electric potentials transparent to massless Dirac fermions at non-oblique incidence1–5. Nevertheless, it has been theoretically predicted that a circular graphene p–n junction can localize Dirac electrons and form quasi-bound quantum dot states6–11. A recent tunnelling spectroscopy experiment12 revealed signatures of electron confinement induced by the electrostatic potential created by a charged scanning tunnelling microscope (STM) tip. However, since the confining potential moves with the STM tip, this method allows neither spatial imaging of the resulting confined modes nor patterning control of the confinement potential. Here we employ a new patterning technique that allows the creation of stationary circular p–n junctions in a graphene layer on top of hexagonal boron nitride (hBN). Figure 1a illustrates how stationary circular graphene p–n junctions are created.We startwith a graphene/hBN heterostructure resting on a SiO2/Si substrate. The doped Si substrate acts as a global backgate while the hBN layer provides a tunable local embedded gate after being treated by a voltage pulse from an STM tip13. To create this embedded gate the STM tip is first retracted approximately 2 nm above the graphene surface and a voltage pulse ofVs=5V is then applied to the STM tip while simultaneously holding the backgate voltage toVg=40V. The voltage pulse ionizes defects in the hBN region directly underneath the tip25 and the released charge migrates through the hBN to the graphene13. This leads to a local space-charge build-up in the hBN that effectively screens the backgate and functions as a negatively charged local embedded gate13 (using the opposite polarity gate voltage during this process leads to an opposite polarity space charge). AdjustingVg afterwards allows us to tune the overall doping level so that the graphene is n-doped globally, but p-doped inside a circle centred below the location where the tip pulse occurred (it is also possible to control the charge carrier density profile as well as create opposite polarity p–n junctions by changing the Vg applied during the tip pulse). As shown schematically in Fig. 1b, the STM tip can then be moved to different locations to probe the electronic structure of the resulting stationary circular p–n junction. To confirm that this procedure results in a circular p–n junction, we measured STM differential conductance (dI/dVs) as a function of sample bias (Vs) on a grid of points covering the graphene area near a tip pulse. The Dirac point energy, ED, was identified at every pixel, allowing us to map the charge carrier density, n, through the relation n(x , y)=−(sgn(ED)E D)/(π(h̄vF)), where vF=1.1×10ms is the graphene Fermi velocity and h̄ is the reduced Planck constant. Figure 1c shows the resulting n(x ,y) for a tip pulse centred in the top right corner (the carrier density n can be adjusted by changing Vg). The interior blue region exhibits positive charge density (p-type) whereas the red region outside has negative charge density (n-type). To spatially map the local electronic properties of such circular p–n junctions, we examined a rectangular sector near a p–n junction, as indicated in Fig. 2a. Figure 2b shows a topographic image of the clean graphene surface in this region. A 2.8 nm moiré