My watch list


When a doughnut becomes an apple

24-Sep-2014: In experiments using the wonder material graphene, ETH researchers have been able to demonstrate a phenomenon predicted by a Russian physicist more than 50 years ago. They analysed a layer structure that experts believe may hold unimagined promise.

Anastasia Varlet works as a doctoral candidate in the research group headed by ETH Professor Klaus Ensslin in the Laboratory for Solid State Physics and has had two research papers published consecutively in the American scientific journal Physical Review Letters. Both works are based on measurements made on the same electronic component, a sandwich construction using graphene – a material made of carbon with a honeycomb structure that is only a single atom thick. A single layer of graphene is extremely stable, elastic and conductive. This wonder material is of particular interest in electronic applications when two layers are on top of one another, as it becomes a semiconductor that can be used to engineer electronic switches.

The quality of Varlet’s double-layer graphene sample was so good that the researcher obtained completely unexpected results from her measurements. “We were able to prove the existence of a Lifshitz transition,” she says. The physicist uses the example of a coffee cup and 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 Ensslin.

Changing the topology of an object can improve its usefulness; e.g. by transforming a beaker into a cup with handle. In reality, this should not be possible at all; nevertheless, the ETH researchers have achieved exactly that by using a double layer of graphene. Named after a Russian physicist who predicted it in 1960, a Lifshitz transition is a transformation from one topology to another. However, it 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 which 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 special feature of the samples, says Varlet’s boss, is that they are able to withstand enormously strong electrical fields, enabling the work published in Physical Review Letters to be carried out.

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. In the meantime, however, the researchers will focus on gaining a better understanding of the structural elements of double-layered graphene.

National and European collaboration

The team is part of the research group Quantum Science and Technology (QSIT), which comprises groups from the universities of Basel, Lausanne, Geneva and ETH Zurich, and representatives from IBM. Klaus Ensslin is the director of this national research centre and his team is also participating in the ‘Graphene Flagship’ EU project. “The project’s primary aim is to develop completely new materials,” says the ETH professor. The focus lies on structures made of extremely thin layers, such as the component developed by Anastasia Varlet.

Original publication:
Varlet A, Bischoff D, Simonet P, Watanabe K, Taniguchi T, Ihn T, Ensslin K, Mucha-Kruczyński M, Falko VI: Anomalous Sequence of Quantum Hall Liquids Revealing a Tunable Lifshitz Transition in Bilayer Graphene. Physical Review Letters 2014, 113: 116602.
Varlet A, Liu MH, Krueckl V, Bischoff D, Simonet P, Watanabe K, Taniguchi T, Richter K, Ensslin K, Ihn T: Fabry-Pérot Interference in Gapped Bilayer Graphene with Broken Anti-Klein Tunneling. Physical Review Letters 2014, 113: 116601.

Facts, background information, dossiers

More about ETH Zürich

  • News

    Using electrical stimulus to regulate genes

    A team of researchers led by ETH professor Martin Fussenegger has succeeded in using an electric current to directly control gene expression for the first time. Their work provides the basis for medical implants that can be switched on and off using electronic devices outside the body. This ... more

    Lighting the path for cells

    ETH researchers have developed a new method in which they use light to draw patterns of molecules that guide living cells. The approach allows for a closer look at the development of multicellular organisms – and in the future may even play a part in novel therapies.  Highly complex organis ... more

    A new biosensor for the COVID-19 virus

    A team of researchers from Empa, ETH Zurich and Zurich University Hospital has succeeded in developing a novel sensor for detecting the new coronavirus. In future it could be used to measure the concentration of the virus in the environment - for example in places where there are many peopl ... more

  • q&more articles

    Analysis in picoliter volumes

    Reducing time, costs and human resources: many basic as well as applied analytical and diagnostic challenges can be performed on lab-on-a-chip systems. They enable sample quantities to be reduced, work steps to be automated and completed in parallel, and are ideal for combination with highl ... more

    Investment for the Future

    This is a very particular concern and at the same time the demand placed annually on Dr. Irmgard Werner, who, as a lecturer at the ETH Zurich, supports around 65 pharmacy students in the 5th semester practical training in “pharmaceutical analysis”. With joy and enthusiasm for her subject sh ... more

  • Authors

    Prof. Dr. Petra S. Dittrich

    Petra Dittrich is an Associate Professor in the Department of Biosystems Science and Engineering at ETH Zurich (Switzerland). She studied chemistry at Bielefeld University and the University of Salamanca (Spain). After completing her doctoral studies at the Max Planck Institute for Biophysi ... more

    Dr. Felix Kurth

    Felix Kurth studied bioengineering at the Technical University Dortmund (Germany) and at the Royal Institute of Technology in Stockholm (Sweden). During his PhD studies at ETH Zurich (Switzerland), which he completed in 2015, he developed lab-on-a-chip systems and methods for quantifying me ... more

    Lucas Armbrecht

    Lucas Armbrecht studied microsystems technology at the University of Freiburg (Breisgau, Germany). During his master’s, he focused on sensors & actuators and lab-on-a-chip systems. Since June 2015, he is PhD student in the Bioanalytics Group at ETH Zurich (Switzerland). In his doctoral stud ... more

q&more – the networking platform for quality excellence in lab and process

The q&more concept is to increase the visibility of recent research and innovative solutions, and support the exchange of knowledge. In the broad spectrum of subjects covered, the focus is on achieving maximum quality in highly innovative sectors. As a modern knowledge platform, q&more offers market participants one-of-a-kind networking opportunities. Cutting-edge research is presented by authors of international repute. Attractively presented in a high-quality context, and published in German and English, the original articles introduce new concepts and highlight unconventional solution strategies.

> more about q&more

q&more is supported by:


Your browser is not current. Microsoft Internet Explorer 6.0 does not support some functions on Chemie.DE