This article is from the Monthly Science et Avenir – La Recherche n°901, dated March 2022.

Almost 100 kilometers per second! It is at this astronomical speed that electrons diffuse into metals such as copper, thus carrying electricity. But these microscopic particles, of negative electric charge, can become stable under certain conditions and interact to form perfectly arranged crystals, as in diamonds or snowflakes. Visualized by the Hungarian physicist Eugene Wigner nearly a century ago, this “electron ice” had never been directly observed before. This is now done thanks to the ease of use and a new family of extremely thin materials. ,The crystallization of electrons is now very clear, surprises Marc-Olivier Goerbig, a theoretical physicist at CNRS and the University of Paris-Saclay. We even visualize the geometry of these little structures!,

purely theoretical motivations

This work originated in the 1930s, shortly after the birth of quantum mechanics, which shed light on the properties of atomic and subatomic particles. Eugene Wigner then tried to answer the following question: Like atoms that, upon cooling, pass from a gaseous or liquid state to a solid form, can electrons crystallize? ,Eugene Wigner’s motivations were purely theoretical, Recalls Emmanuel Trizac from the Laboratory of Theoretical Physics and Statistical Models in Orsay (Esson). He wanted to better understand the interactions between electrons in metals. And made a surprising discovery in this regard.“He thus understood that electrons were subject to two types of phenomena: the so-called Coulomb interaction, which repels two particles of the same charge; and the intrinsic motion of electrons, both by thermal movement and purely quantum fluctuations. operates.

Electrons move even at absolute zero

,However, the intensity of these fluctuations is inversely proportional to the mass of the particles.“, specifies Emmanuel Trizac. Therefore they are relatively vulnerable to “large” objects such as atoms or molecules: the motion of these objects is low enough to reduce the temperature which can then interact and solidify Quite different to electrons which are thousands of times lighter and weigh… only one thousandth of a billionth of a billionth of a gram!Even at absolute zero, i.e. -273.15 °C, they are affected by quantum fluctuations and move very fast, Mark-Oliver insists Goerbig. Thus the electrons permanently behave like a fluid, which allows them to conduct electricity.,

Wigner found a way to overcome this frenzy. By calculation, he understood that if electrons are confined to a small space and their density drops below a certain threshold, the Coulomb interaction will take precedence over quantum fluctuations. Trying to repel each other, the electrons will then “feel” the presence of their progenitors. And in order to minimize the energy of the system, they will keep themselves at a certain distance from each other and automatically form a regular structure… a crystal, in other words! At least in theory. Because it would be very difficult to put into practice the terms envisaged by Eugene Wigner.both at the purity of the medium where the electrons had to be confined and at the very low densities to obtain“, description of Mark-Olivier Goerbig. Thus many decades will be necessary before experimental proof can be obtained.

They were provided from the 1980s by researchers at Bell Laboratories (United States), and specifically from the CEA’s Center for Nuclear Studies in Sackley (Esson). He confined a cloud of electrons between two semiconductors (gallium arsenide) before applying a very strong magnetic field. Under the influence of this field, all electrons found themselves in the same energy state, the lowest possible. The result: the quantum fluctuations were kind of “frozen”, allowing the electrons to organize themselves into networks. But the configurations created with strong magnetic fields did not actually correspond to the situation described by Eugene Wigner. Not to mention that no technology made it possible to probe these alleged crystals between two semiconductors. Thus the leads were very indirect, such as the transition from a conductive to an insulator state. Stationary in a crystal, electrons certainly cannot propagate current.

Maize “If this condition was necessary, it was not sufficient, Mark-Olivier Goerbig notes. Other phenomena may explain the insulating state, such as the presence of impurities that trap electrons.“In the mid-2000s, the discovery of two-dimensional materials would completely change the situation. Like graphene, which is made of carbon, their thickness corresponds to an atom or a few atoms.”These extremely fine sheets make it possible to very precisely control and measure the density of electrons. They are now synthesized with exceptional purity“, explains Marc-Olivier Goerbig. And it is with this type of sheet that great progress has been made in the identification of Wigner crystals.

Crystals for a sheet of graphene unveiled

The first demonstration was carried out in June 2021 by two independent teams – one from the Institute of Quantum Electronics in Zurich, Switzerland, the other from Harvard University, USA. They used a sheet of molybdenum diselenide (a semiconductor) sandwiched between two insulating compounds. The temperature had dropped a few degrees below absolute zero. And the graphene electrodes very precisely tuned the electron density. Bingo! Because by illuminating the semiconductor with a laser and analyzing the reflected radiation, the researchers were able to establish that the crystals of electrons actually formed on a two-dimensional layer, right above. The spectroscopic data clearly show, in fact, that the electrons are arranged in a hexagonal lattice, each about twenty billionths of a meter across. By increasing the density or temperature of electrons, scientists were also able to observe their “liquefaction,” as if a piece of ice were melting in the sun.

Three months later, physicists from the University of California at Berkeley (USA) also exploited the two-dimensional material to create Wigner crystals, which they were able to examine, this time, electron by electron! The device was essentially the same, but it was covered with a sheet of graphene. This made it possible to reach the tip of a scanning tunneling microscope and measure small currents without destroying the crystal. Thanks to this device, the position of each electron on the hexagonal lattice can be determined,”First images of these fascinating structures unveiled“, delights Michael Cromey, one of the study’s authors. And thus provides a definitive answer to Eugene Wigner’s question.

Electronics, superconductors, storage: applications becoming clearer

Research on electron crystals could lead to applications, particularly in electronics. To achieve this, physicists must study their precise characteristics, and “Learn specifically whether they behave like normal crystals: presence of defects, effects of vibration, magnetic properties, etc.“, notes physicist Marc-Olivier Goerbig of CNRS and Paris-Saclay University. Another purpose: to catalog the various possible crystal lattice. In addition to the recently observed hexagonal lattice, theorists believe that there may be dozens of them. are (square, orthorhombic…) depending on the surfaces used.”However, the most stable configurations can prove to be very useful for coding and storing information.“That, conjectures Emmanuel Trizac of the Laboratory of Theoretical Physics and Statistical Models in Orsay. More generally, Wigner’s crystals make it possible to better understand systems where electrons interact. Stronger.”But the problem becomes frighteningly complicated when the electrons are both free and interacting, Mark-Olivier Goerbig notes. For example as superconducting materials made of metal oxides, which are used in MRI instruments but whose mechanisms remain mysterious,