Can graphene transform an apple into a doughnut?

"We were able to prove the existence of a Lifshitz transition," says Anastasia Varlet. (Credit: Alan Levine/Flickr)

More than 50 years ago, a Russian physicist predicted that it’s possible to transform from one topography to another. The phenomenon is known as the Lifshitz transition, and now researchers have used a double layer of graphene to demonstrate that it is indeed possible.

“We were able to prove the existence of a Lifshitz transition,” says Anastasia Varlet, a doctoral candidate at ETH Zurich who was part of the research team that made the discovery.


The physicist uses the example of a coffee cup and a water glass to explain what this means. A cup has a handle with a hole. Using mathematical functions, it is possible to transform a geometrically designed object from the form of a cup to that of a doughnut, given that a doughnut also features a hole.

A glass, on the other hand, can not be reshaped into a doughnut because it does not have a hole. Mathematically speaking, a cup has the same topology as a doughnut.

“A glass is topologically the same as an apple,” explains Professor Klaus Ensslin, who led the research detailed in two papers published in Physical Review Letters. (View the first paper and the second paper.)

Changing the topology of an object can improve its usefulness, for example, by transforming a beaker into a cup with handle. In reality, this should not be possible at all; nevertheless, the researchers have achieved exactly that by using a double layer of graphene.

The Lifshitz transition does not apply to objects in our normal environment; rather, the physicists are researching an abstract topology of surfaces with which the energy state of electrons is described with electronic materials. In particular, the researchers examined surfaces of constant energy, as these determine the conductivity of the material and its application potential.

Three islands in a lake

Ensslin makes another comparison to demonstrate the mathematical concept behind these energy surfaces: “Imagine a hilly landscape in which the valleys fill up with electrical charges, just as the water level rises between the hills when it rains.”

This is how a conductive material is formed from an initial isolator–when it stops raining, the water has formed a lake from which the individual hilltops emerge like islands. This is exactly what Varlet observed when experimenting with the double layer of graphene: at a low water level, there are three independent, but equivalent lakes. When the water level increases, the three lakes join to form a large ocean.

“The topology has changed altogether,” Varlet concludes. In other words, this is how a doughnut is transformed into an apple.

Until now, scientists have lacked the right material to be able to demonstrate a Lifshitz transition in an experiment. Metals are not suitable and initially the ETH team was unaware it had found the material that others had been looking for.

“We observed something strange in our measurements with the graphene sandwich construction that we were not able to explain,” says Varlet.

A Russian theoretician, Vladimir Falko, was able to interpret these measurements in discussions with the team.

Low-cost raw materials

To produce the sandwich construction, Varlet enclosed the double layer of graphene in two layers of boron nitride, a material otherwise used for lubrication and one that has an extremely smooth surface.

Although both materials are cheap, a lot of work is required in the cleanroom–the carbon flakes must be exceptionally clean to produce a functioning component.

“A significant part of my work consists of cleaning the graphene,” says Varlet. The samples can withstand enormously strong electrical fields.

At present, a practical use for the phenomenon is speculation only. The topology of quantum states, for example, offers a way of decoupling them from their environment and perhaps achieving extremely stable quantum states that can be used for information processing.

The team is part of the research group Quantum Science and Technology, which comprises groups from the universities of Basel, Lausanne, Geneva and ETH Zurich, and representatives from IBM.

Source: ETH Zurich