Graphene, a 2D honeycomb lattice of carbon first isolated in 2004, boasts a wealth of fascinating electronic properties, many of which come from the fact that it is a semiconductor with a zero-energy gap between its valence and conduction bands. Near where the two bands meet, the relationship between the energy and momentum of charge carriers (electrons and holes) in the material is described by the Dirac equation and resembles that of a photon. These bands, called Dirac cones, enable these charge carriers to travel through graphene at extremely high speeds, which means that graphene-based electronic devices, like transistors, could be faster than any that exist today.

Klein tunnelling

The behaviour of charge carriers in graphene is governed by Klein tunnelling – a counterintuitive effect in which relativistic particles can pass through a potential barrier with 100% probability. Since graphene’s charge carriers behave like relativistic particles, Klein tunnelling is thus predicted to exist in potential barriers (or p-n junctions) fabricated in the material.

“This exotic behaviour, albeit very interesting, makes trapping and controlling graphene’s charge carriers very difficult,” explains team member Jairo Velasco Jr. of the University of California, Berkeley, and the University of California, Santa Cruz. “It is, however, important for us to be able to map the behaviour of these Dirac fermions at p-n junction boundaries to explore Klein tunnelling physics in the carbon material and to better control and confine the electrons in it.”

Creating circular p-n junctions

The researchers, led by Michael Crommie, created circular p-n junctions in graphene by positioning the tip of a scanning tunnelling microscope (STM) about 2 nm above the surface of a graphene sample while applying a voltage pulse to the tip. “While doing this, we also apply a constant voltage on a silicon slab that is below the graphene, but separated from it by a silicon oxide capping layer and a boron nitride (BN) flake (see figure above),” says Velasco. “The intense electric field emanating from the STM tip ionizes defects in the BN region directly beneath the tip and the released charge migrates through the BN to the graphene. This leaves behind a space-charge build-up in the BN that screens the electric field from the silicon slab.”

The researchers are now ready to image the Dirac fermions in their graphene sample. “To do this, we position our STM tip about an angstrom above the graphene surface,” continues Velasco. “This allows us to measure a tunnelling current between the suspended STM tip and the graphene surface. Such a measurement directly probes the wavefunctions of electrons in the carbon material, and moving the STM tip to different lateral positions on the sample means we can image how the wavefunction varies inside and outside our engineered circular p-n junctions (see figure above).”

Directly imaging electron wavefunctions in graphene has been notoriously difficult until now. This was because the systems in which researchers were trying to observe them (lithographically patterned structures, graphene edges and chemically synthesized graphene islands, for example) contained too many defects.

Overcoming a major challenge in graphene physics

Mark Fromhold of Nottingham University in the UK, who was not involved in this work, says that defects are “often problematic in solid-state devices because they produce unwanted electrical or optical behaviour. But in this beautiful new experiment, the Crommie group has shown how defects can be used, together with a scanning probe, to overcome a major challenge in graphene physics, namely how to stop electrons leaking through p-n junctions by Klein tunnelling. Not only did the researchers manage to confine the electrons in a quantum dot created in the graphene layer, but they were also able to directly map both the resulting energy level spectrum and the corresponding quantum wavefunctions.”

According to Velasco and colleagues, the techniques developed in this work could now be used to study more complicated systems as well, such as multiple quantum dots with arbitrary geometries. “This is because the graphene circular p-n junctions we made (which can be considered as quantum dots too) are fully exposed and so we can directly access them with real-space imaging probes,” Velasco tells “This is completely different to conventional semiconductor quantum dots, which are generally inaccessible.”

The team, reporting its work in Nature Physics doi:10.1038/nphys3805, says that it now also plans to investigate bilayer graphene, which hosts massive Dirac charge carriers. “These charge carriers are expected to completely reflect upon impinging on a p-n junction barrier, independent of the barrier width.”