BME-HAS and Israeli researchers prove the existence of the Wigner crystals

The unique quantum crystal, foreseen by the Nobel laureate physicist, was detected by experts using a nanotube. Their results were published in Science magazine.

The discovery by the researchers at the BME-HAS (Hungarian Academy of Sciences) Exotic Quantum Phases 'Momentum' Research Group and the Strongly Correlated Systems 'Momentum' Research Group at the HAS Wigner Research Centre for Physics, published in Science magazine jointly with the team from Israel's Weizmann Institute of Science, represents a significant development in the field of quantum and nanotechnology, providing evidence for the theoretical prediction made by Eugene Wigner around 80 years ago. According to this, electrons are able to form ordered quantum crystals if the Coulomb interactions between them are strong enough. Researchers were able to identify the so-called Wigner crystal in a carbon nanotube by combining experiments and detailed numerical simulations. (The abstract of the original article is available on the website of Science magazine here – Editor's note.)

The role of Coulomb interactions intensifies in thin electron gases, because a lot of energy is required when two electrons come close to each other. On observing this, Eugene Wigner predicted that electrons form crystals at absolute zero temperature in order to avoid this. Although for almost a century there has been a fierce competition to demonstrate this fragile quantum mechanical state in ultra pure materials, so far only the existence of the so-called classic Wigner crystals, formed at high temperatures, could be proven conclusively by experiments. This is the first time that the charge distribution of a quantum crystal formed has been detected directly at low temperatures.

The discovery is based on a novel method: the newly formed crystal is very 'fragile', therefore researchers in Israel used the charge of a single electron as a 'soft' detector, with which they scanned the spatial structure of the crystal that had been formed in the nanotube. ”In our experiment we used one nanotube to hosts the electrons to be imaged and another as a probe”, explained Gergely Zaránd, head of the BME-HAS Exotic Quantum Phases 'Momentum' Research Group and the director of the Institute of Physics at BME. The number of electrons and the potential used to trap them are controlled by electrodes in the scanned nanotube. By scanning the system with the probe nanotube, the charge distribution and the wave function of the confined electrons can be determined directly. By adding one, two, three, etc., electrons to the system, the charge distribution reveals one, two, three, etc. peaks, located just a few nanometres from each other.

The five peaks seen in the experimental measurement (left panel) and the DMRG calculations (right panel) show the position of the first five electrons in the quantum crystal. The numerical simulation also allows for the theoretical study of the strength of the interaction, represented by the rs parameter along the vertical axis. Source: Shapir et al., Science 364, 870 (2019)

Theoretical calculations and numerical simulations were required to identify the interactions that lead to this quantum mechanical state. These quantum mechanical calculations, vital for interpreting the results of the experiment, were conducted by the researchers of BME and the HAS Wigner Research Centre for Physics by using the latest methods in quantum chemistry to describe the carbon nanotube. ”The so-called DMRG calculations alone represent a breakthrough in this field. We developed several algorithmic solutions, without which the calculations would not have been possible”, said Örs Legeza, head of the Strongly Correlated Systems 'Momentum' Research Group at the HAS Wigner Research Centre for Physics. Mr Legeza has been awarded the Humboldt Research Award and is currently in charge of several research projects in Germany.

The accuracy of the match between the structure of the electron crystal, defined as a result of the theoretical calculations, and the measurement results was surprising, thus proving that this quantum phase is in fact the quantum crystal predicted by Eugene Wigner.

Source: HAS
Main photo from: Librarius
Thumbnail from: Wikipedia