Imaging electrostatically confined Dirac fermions in graphene quantum dots

Abstract

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 boundaries 1-5 . Reflection and transmission at these boundaries a ect the quantum interference of electronic waves, enabling the formation of novel quasi-bound states 6-12 . Here we report the use of scanning tunnelling microscopy to map 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 monolayer 13 . 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 structures 14-17 , graphene edges 18 , and chemically synthesized graphene islands [19][20][21][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 fields 23 and supercritical impurities 24 , but these methods are unwieldy for many 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 incidence 1-5 . Nevertheless, it has been theoretically predicted that a circular graphene p-n junction can localize Dirac electrons and form quasi-bound quantum dot states 6-11 . A recent tunnelling spectroscopy experiment 12 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 start with a graphene/hBN heterostructure resting on a SiO 2 /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 tip 13 . To create this embedded gate the STM ...

Generating atomically sharp p−n junctions in graphene and testing quantum electron optics on the nanoscale

“…The emergence of the resonant peaks below the Dirac point in the tunneling spectra, as shown in Fig. 1e, is a clearly evidence of the formation of quasi-bound states in the GQDs 14,[17][18][19] .…”

“…However, such a goal has been demonstrated to be quite difficult to achieve [14][15][16][17] and seems to be not within the grasp of today's technology. Until very recently, substrate engineering exhibits the ability to create sharp potential wells in graphene 18,19 , which makes it possible to manipulate the massless Dirac fermions in the same way as lights.…”

Chiral interface states in graphene p−n junctions

“…1, namely for a straight and for a circularly symmetric junction. The latter case is closely related to recent experiments, where circular junctions have been created by direct gating [24,27], by scanning tunneling microscopy (STM) tips [21], or by local manipulation of defect charges in the substrate [26]. Using the established STM resolution capabilities in both space and energy, experiments could monitor the eigenstates of this system in full detail, cf.…”

“…We here consider the electronic properties of graphene p-n junctions in a perpendicular magnetic field B. This system has attracted considerable attention and many interesting experimental transport studies have already appeared [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. In such setups, the gapless Dirac fermion spectrum of low-energy quasiparticles in graphene [3,5] allows for the controlled electron or hole doping of parts of the sample by backgate voltage changes.…”

“…For sufficiently disordered samples, their existence allows for a simple physical picture of the observed conductance quantization [29,30]. Over the past few years, experiments have approached the ballistic regime [15][16][17][18][19][20][21][22][23][24][25][26][27], thereby realizing gate-controlled electron waveguides.…”