Crystals have fascinated people through the ages. Who hasn’t admired the complex patterns of a snowflake at some point, or the perfectly symmetrical surfaces of a rock crystal? The magic doesn’t stop even if one knows that all this results from a simple interplay of attraction and repulsion between atoms and electrons. A team of researchers led by Ataç Imamoğlu, professor at the Institute for Quantum Electronics at ETH Zurich, have now produced a very special crystal. Unlike normal crystals, it consists exclusively of electrons. In doing so, they have confirmed a theoretical prediction that was made almost ninety years ago and which has since been regarded as a kind of holy grail of condensed matter physics. Their results were recently published in the scientific journal “Nature”.
A decades-old prediction
“What got us excited about this problem is its simplicity”, says Imamoğlu. Already in 1934 Eugene Wigner, one of the founders of the theory of symmetries in quantum mechanics, showed that electrons in a material could theoretically arrange themselves in regular, crystal-like patterns because of their mutual electrical repulsion. The reasoning behind this is quite simple: if the energy of the electrical repulsion between the electrons is larger than their motional energy, they will arrange themselves in such a way that their total energy is as small as possible.
For several decades, however, this prediction remained purely theoretical, as those “Wigner crystals” can only form under extreme conditions such as low temperatures and a very small number of free electrons in the material. This is in part because electrons are many thousands of times lighter than atoms, which means that their motional energy in a regular arrangement is typically much larger than the electrostatic energy due to the interaction between the electrons.
Electrons in a plane
To overcome those obstacles, Imamoğlu and his collaborators chose a wafer-thin layer of the semiconductor material molybdenum diselenide that is just one atom thick and in which, therefore, electrons can only move in a plane. The researchers could vary the number of free electrons by applying a voltage to two transparent graphene electrodes, between which the semiconductor is sandwiched. According to theoretical considerations the electrical properties of molybdenum diselenide should favour the formation of a Wigner crystal – provided that the whole apparatus is cooled down to a few degrees above the absolute zero of minus 273.15 degrees Celsius.
However, just producing a Wigner crystal is not quite enough. “The next problem was to demonstrate that we actually had Wigner crystals in our apparatus”, says Tomasz Smoleński, who is the lead author of the publication and works as a postdoc in Imamoğlu’s laboratory. The separation between the electrons was calculated to be around 20 nanometres, or roughly thirty times smaller than the wavelength of visible light and hence impossible to resolve even with the best microscopes.
