Ballistic electrons, crossing a p-n junction in high-purity graphene, can experience negative refraction. The long-predicted phenomenon, which has now been observed and quantified by a team headed by Columbia University and University of Virginia researchers, could lead to new kinds of electronic switches, according to the researchers. [Image: Cory Dean/Columbia University]
A team of scientists has coaxed electrons into displaying a behavior—negative refraction at a boundary—that’s previously been reserved for light passing through exotic metamaterials (Science, doi: 10.1126/science.aaf5481). The researchers believe that the finding could open up new prospects in so-called electron optics, in which components such as electronic switches are designed based on the principles of geometrical optics.
Bending at junctions
The idea of electron optics is itself not new; it has been known for decades that, for materials of sufficient purity, electrons paths can bend at semiconductor junctions, analogous to the behavior of light rays at material boundaries. The magnitude of the effect for electrons depends on the relative carrier density at either side of the junction, which plays a role similar to that of the relative refractive index in optical materials. The principle has enabled observations such as electron refraction and lensing in semiconductors such as GaAs, albeit only at very low temperatures.
The observation of negative refraction, though, has proved a tougher proposition in the electron world. In optics, achieving negative refraction has required the design of custom metamaterials, finely engineered at the nanoscale to achieve a negative refractive index. This “reverse bending” of light has underpinned a wide variety of emerging applications, including optical cloaking and so-called superlenses that can focus beyond the diffraction limit.
In principle, negative refraction for electrons should be much simpler to design, as it’s expected to arise naturally as electrons cross any p-n junction in a solid-state semiconductor. But although achieving negative refraction for electrons is “conceptually straightforward,” actually observing it has proved elusive. The reason: the gap between the conduction and valence bands in ordinary semiconductor junctions leads to electron scattering at the interface, swamping any readable sign of negative refraction.
Graphene testbed
To get around these problems, the research team—led by Cory R. Dean of Columbia University, N.Y. (USA), and Avik W. Ghosh of the University of Virginia (USA)—turned to a material that has gained increasing prominence as a platform for exotic physics: graphene. The celebrated 2-D material can support ballistic transport of electrons over relatively long, micrometer length scales at room temperature. And its zero band gap raises the prospect of actually observing negative refraction across a junction without the signal-obscuring scattering observed at conventional semiconductor p-n junctions.
While the use of graphene to observe negative refraction was suggested in 2007, it has taken almost a decade to develop material of sufficient purity to make such observation a practical possibility. By 2013, a team at Columbia had made progress enough on that head to develop graphene that could support ballistic, non-scattering electron transport across lengths of 20 microns. Using that highly pure graphene and a transverse magnetic field for focusing, Dean’s team, in the current work, fired ballistic electrons at varying incidence angles into a thin, split-gate graphene p-n junction separating regions of different carrier density. The researchers then measured the transmission on either side of the junction as a function of carrier density.
Snell’s law and Fresnel equations for electrons
The Columbia team found that the behavior of the electrons, including the observed negative refraction, agreed well with numerical simulations by Ghosh’s group at Virginia, which predicted the electron flows in the material under various parameter combinations, taking into account details such as edge effects and quantum tunneling. The team was even able to confirm that the electrons behaved in accordance with an electron analog of Snell’s law—the relationship between the incident and refracted angles—and to develop an equation relating refraction angle to transmission intensity “which can be viewed the electron equivalent of the Fresnel equations in optics.”
Another key finding for the team, which could have implications for future electron optics devices, involved Veselago lensing, a consequence of negative refraction in which, under the right conditions, a planar p-n junction can act as an electron-focusing lens. While predicted almost a decade ago, a Veselago lens proved difficult to develop even in the high-purity graphene that has emerged in the past few years. The team’s modeling revealed why: it turns out that creating such a lens requires extremely tight control (on the order of 5 nm or less) over the effective width of the junction boundary layer.
Manipulating electrons like photons
The team believes that the ability to use ballistic electrons in 2-D materials could make it possible “to manipulate electrons like photons, by using components inspired by geometrical optics, such as mirrors, lenses, prisms and splitters.” The result, says team leader Dean, could be “entirely new ways of thinking about electronics.”
He cites the possibility of faster and more efficient electronic switches, for example, that use lensing to steer electron beams in the same way that optical lenses are used to bend light rays. He even suggests the prospect of an ultraminiaturized, on-chip version of an electron microscope that takes advantage of electron lensing. These and other applications, however, will hinge on the ability to scale junction widths “to the few-nm limit,” which the study concludes will be “an important criteria for realizing electron optics based on negative refraction in graphene.”