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Low-temperature physics

Low-temperature physics

Wigner crystal appears in bilayer graphene

02 May 2024 Isabelle Dumé
Scanning tunnelling microscopy image of the Wigner crystal, which appears as a grid of triangular shapes containing blue-coloured circles in their interiors and red around the edges. Each blue circular region contains a single localized electron.
An image of a triangular Wigner crystal taken by scanning tunnelling microscopy. Each site (blue circular region) contains a single localized electron. (Courtesy: Yen-Chen Tsui and team, Princeton University)

Researchers at Princeton University in the US say they have made the first direct observation of a Wigner crystal – a structure consisting solely of electrons arranged in a lattice-like configuration. The finding, made by using scanning tunnelling microscopy to examine a material known as Bernal-stacked graphene, confirms a nearly century-old theory that electrons can assemble into a closely-packed lattice without having to orbit around an atom. The work could help scientists discover other phases of exotic matter in which electrons behave collectively.

Although electrons repel each other, at room temperatures their kinetic energy is high enough to overcome this, so they flow together as electric currents. At ultralow temperatures, however, repulsive forces dominate, and electrons spontaneously crystallize into an ordered quantum phase of matter. This, at least, is what the physicist Eugene Wigner predicted 90 years ago would happen. But while scientists have seen evidence of this type of crystalline lattice forming before (for example, in a one-dimensional carbon nanotube and in a quantum wire), it had never been observed directly.

A pristine sample of graphene

In the new work, which is detailed in Nature, researchers led by Princeton’s Ali Yazdani used a scanning tunnelling microscope (STM) to study electrons in a pristine sample of graphene (a sheet of carbon one atom thick). To keep the material as pure as possible, and so avoid the possibility of electron crystals forming in lattice defects or imperfections, they placed one sheet of graphene atop another in a configuration known as a bilayer Bernal stack.

Next, they cooled the sample down to just above absolute zero, which reduced the kinetic energy of the electrons. They also applied a magnetic field perpendicular to the sample’s layers, which suppresses kinetic energy still further by restricting the electrons’ possible orbits. The result was a two-dimensional gas of electrons located between the graphene layers, with a density the researchers could tune by applying a voltage across the sample.

Scanning tunnelling microscopy involves scanning a sharp metallic tip across a sample. When the tip passes over an electron, the particle tunnels through the gap between the sample surface and the tip, thereby creating an electric current. By measuring this current, researchers can determine the local density of electrons. Yazdani and colleagues found that when they increased this density, they observed a phase transition during which the electrons spontaneously assembled into an ordered triangular lattice structure – just as Wigner predicted.

Forcing a lattice to form

The team explains that this spontaneous assembly is the natural outcome of a “battle” between the electrons’ increased density (which pushes them closer together) and their mutual repulsion (which pushes them apart). An organized lattice configuration – a Wigner crystal – is, in effect, a compromise that lets electrons maintain a degree of distance from each other even when their density is relatively high. If the density increases still further, this crystalline phase melts, producing a phase known as a fractional quantum Hall electron liquid as well as an anisotropic quantum fluid in which the electrons organize themselves into stripes.

By analysing the size of each electron site in the Wigner crystal, the researchers also found evidence for the crystal’s “zero-point” motion. This motion, which comes about because of the Heisenberg uncertainty principle, occupies a “remarkable” 30% of the lattice constant of a crystal site, Yazdani explains, and highlights the crystal’s quantum nature.

The Princeton team now aims to use this same STM technique to image a Wigner crystal made of “holes”, which are regions of positive charge where electrons are absent. “We also plan to image other types of electron solid phases, so-called skyrme crystals and ‘bubble phases’,” Yazdani says. “In addition to even more exotic phases such as quasiparticle Wigner crystals made of fractional charges, there is also the possibility to study how these quantum crystals would change in the presence of a net electrical current.”

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