A picture with a Wigner crystal

Exotic electronic states, so-called Wigner crystals, in which electrons spontaneously form ordered arrangements through mutual repulsion, were observed by two groups independently of one another almost 80 years after their first prediction. The researchers argue that their results, using a new type of spectroscopy, are more conclusive than previous observations.

Electrons in a material carry both potential energy from their mutual repulsion and kinetic energy from heat, much like atoms in a lattice. While atoms can freeze relatively easily, the kinetic energy of electrons almost always dominates because electrons have so little mass that they need little energy to move. In addition, the electron density is usually too high for individual electrons to be differentiated in terms of their quantum uncertainty in their position. The result is a homogeneous smear of the electronic charge. In 1934, however, the great theoretical physicist Eugene Wigner predicted that electrons could form a crystalline solid – if their kinetic energy and density were sufficiently reduced.

Such structures were later observed in magnetic fields, where the kinetic energy is artificially suppressed. However, demonstrations in the zero field were based on indirect measurements such as resistivity. “When you think about how you can prove that a piece of a crystal is really a crystal, you shine a wave on the crystal and observe the Bragg diffraction,” says Tomasz Smoleński from ETH Zurich in Switzerland.

In the first of the new publications, Smoleński and colleagues observed monolayers of molybdenum diselenide trapped between hexagonal boron nitride using a technique they developed called exciton flip spectroscopy.1 They shot at the grid with optically excited, neutrally charged dipole particles. “This dipole interacts with electrons,” explains Ataç Imamoğlu, who headed ETH research. “If the electrons are translation invariant, they don’t see a lattice; but when the electrons form a lattice, they scatter from that lattice. ‘ Using this technique, the researchers concluded that Wigner crystals formed at around 11 K.

In the second publication, Hongkun Park and colleagues from Harvard University, USA, report on studies on molybdenum diselenide bilayers separated by hexagonal boron nitride.2 As part of an independent experiment, they made devices that allow different electrostatic doping of the upper and lower layers. “We found that surprising isolating states formed when we started doping the top and bottom gates with electrons, especially at specific density ratios like 1: 1, 4: 1, or 7: 1,” says Park.

Dramatic improvement

Scheme of a quantum phase transition from an electronic liquid to a two-layer Wigner crystal

Theorists suggested that these two-layered Wigner crystals could signal, and electron flip spectroscopy supported this. The crystals withstood temperatures of up to 40 K and much higher electron densities than the single-layer Wigner crystals observed by the Swiss group. “There was some older theoretical work that suggested bilayers might be useful in stabilizing Wigner crystals, but what is surprising about the Hongkun experiments is that they saw a much more dramatic improvement,” says the theoretical physicist Eugene Demler from Harvard University and ETH Zurich, author of both papers.

Both research groups now want to deal more closely with the phase transitions between normal matter and this exotic state. “There is a theorem that shows that you cannot simply go from this phase to the liquid phase in a single first-order phase transition,” says Imamoğlu. “In between there must be other phases that are still completely unexplored.”

Theoretical physicist Steven Kivelson of Stanford University in the USA states that from a theoretical point of view there is no absolutely sharp definition of what is a Wigner crystal and what is just an insulator … The question is how long a correlation length is needed before you call it a Wigner crystal. One of the problems with these and previous experiments is that they don’t have a good measure of the correlation length. ”He also sees important differences between electron flip spectroscopy and Bragg diffraction. “While ideally one would extract the correlation length from a diffraction experiment because no one has an exact idea how to do it, the present authors rely on indirect measurements, which require a certain amount of theoretical modeling for interpretation,” he says . “The results alone are obviously no more or less convincing than previous measurements using more traditional techniques.” Nevertheless, he concludes, “there is something really new here and it could very well open up a whole new way of addressing electrons in highly correlated systems”.

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