A sheet of graphene one atom thick is like a perfectly smooth tablecloth on which electron marbles roll. Place an electric barrier in their path, and usually they'll bounce back. But in graphene, it's different: under certain conditions, electrons pass through the barrier without even noticing it, as if the wall were made of mist.
The authors of the new study considered a two-dimensional model of electrons in graphene under the influence of a tunable electric field. This field can be smoothly transformed from a continuous barrier into a chain of individual obstacles. They found that in such a system, super-Klein tunneling emerges — complete transmission of particles without reflection. The secret is that the model is mathematically connected to free particle motion: the barrier seems to vanish for electrons with a specific energy.
This connection was revealed using the methods of supersymmetric quantum mechanics — an elegant mathematical tool that allows reformulating a complex problem into a simpler one. Furthermore, the model exhibits scale invariance: if you change the system's size, the physics remains the same. And for particles with a specific energy, the potential becomes completely invisible. The authors discuss how to realize such a system in experiment — for example, using gates that create the desired electric field over graphene.
Such "invisible" electron transport could be useful in future electronics: if particles don't scatter off obstacles, devices will work faster and with lower losses. A sheet of graphene once again proves to be a magic tablecloth, but now for quantum wonders.
Graphene is the thinnest material in the world: a sheet the size of a football field would weigh less than one gram.
The idea of invisible barriers recalls the phase shields from Star Trek, which let some particles through while stopping others.