An international research team featuring scientists from the Terahertz Spectroscopy Lab at MIPT has made a direct observation of the Mott transition. In this phenomenon, the electrostatic repulsion of electrons in a metal causes it to lose the ability to conduct electricity, making it an insulator. By understanding the nature of this transition, it could be controlled and potentially used to develop new components for quantum computers. The research is reported in Nature Materials, the most frequently cited materials science journal with an impact factor close to 40.
“In this study, we set up an experiment that enabled us to observe for the first time the Mott transition from a metal to a dielectric in its pristine state. We examine the phenomenon in detail and compare the findings to theoretical predictions,” says Boris Gorshunov, who heads MIPT’s Terahertz Spectroscopy Lab. “Due to their molecular structure, the organic metals used in the study lack magnetic ordering of the electronic subsystem, when cooled to extremely low temperatures. As a result, the properties of the electrons are dominated by the electrostatic repulsion. The obtained results contribute to our understanding of strongly correlated materials, including high-temperature superconductors.”
Mott insulator: When electrons are ‘trapped’
What is the electric current? At school we learn that the wires powering your desktop or room lighting have electrons running along them. These electrons, we find, are elementary particles with a negative electric charge of about −1,6 × 10⁻¹⁹ coulombs. However, the actual processes involved in electrical conductivity are fairly complicated. The electrons running along a wire interact with the atoms making up the wire and with each other. Since each electron is negatively charged, Coulomb’s law says they must repel one another. This repulsion is negligible for most materials, because the potential energy due to Coulomb’s forces is much smaller than the kinetic energy the electrons have due to their motion. In some materials, however, the electrons have not enough kinetic energy to overpower their mutual repulsion and get trapped: The metal thus becomes an insulator. This phenomenon was first experimentally observed in 1937 by Jan Hendrik de Boer and Evert Verwey. A theoretical explanation was proposed the same year by Nevill Mott and Rudolf Peierls. Materials of this kind, with “trapped” electrons, are now called Mott insulators.
Theoretical predictions show that as the energy due to Coulomb repulsion gets lower, Mott insulators gradually undergo the so-called insulator-metal Mott transition. That is, they regain the ability to conduct electricity. It has been suggested that electronic correlations similar to those existing in Mott insulators are at play in cuprates exhibiting high-temperature superconductivity. However, observing the Mott transition is problematic, because the electronic properties of a material tend to be largely affected by magnetic interactions: The material enters a magnetically aligned phase, preventing the metal-insulator transition from being detected.
Many scientists are convinced that the Mott transition can be used to develop electronic components enabling faster computers. Such components could replace conventional transistors, which are bulkier and slower. However, researchers are only beginning to investigate this phenomenon experimentally.
Quantum spin liquids
A group of physicists led by MIPT visiting professor Martin Dressel studied the Mott transition using spin liquids instead of ordinary metals. A spin liquid is a magnetic state of matter in which interacting particles possessing a magnetic moment (called spin) are disordered. The term “liquid” is due to an analogy with how the particles making up a liquid are less organized, compared with those in a solid. As of today, only a handful of materials exhibiting the quantum spin liquid state are known.
The spin is a special quantum property characterizing an electron. It can be considered as an arrow assigned to the magnetic moment. It either points up when the spin equals +1/2 or points down when the spin equals −1/2. These two states can be superimposed, as if the spin were pointing in some other direction. When the temperature is high enough, the spins in a material are disordered. But at a lower temperature, the interactions between spins can to result in an ordered state. There are, however, some materials in which spins remain disordered even at ultralow temperatures. They merely form collective entangled states. This phenomenon is governed by the laws of quantum physics, and the associated state of matter is called a spin liquid. Loosely speaking, a spin liquid is a system where magnetized particles interact with each other but magnetic ordering does not emerge. The lack of magnetic ordering in spin liquids enables the effects caused by charge interactions to be isolated from those caused by spin interactions. This means that the phase transition from a Mott insulator to a conductor is easier to detect.
Mott transition revealed by experiment
The team performed experiments using three materials whose electrons are in a spin liquid state. These are rather complex organic compounds referred to by the simplified formulas EtMe, AgCN, and CuCN. The researchers employed terahertz and infrared spectroscopy methods. These two techniques involve exposing a thin material sample to a beam of electromagnetic radiation and measuring the ratio between the amount of radiation penetrating the sample and falling on it. During the experiments, the temperature of the sample, held in a cryostat, was varied. The physicists measured the spectra of the optical conductivity (or absorption) of the three materials — that is, how the amount of absorbed radiation depends on its frequency, which was also varied in the experiment, between 100 and 4,000 inverse centimeters. (An inverse centimeter is a unit reciprocal to the wavelength expressed in centimeters.) The team used the measured dependences to derive the two crucial values: the potential energy of the repulsion between the electrons and the kinetic energy of their motion. Once again, their ratio determines whether the material can conduct electricity.
Figure 1. Spectra of optical conductivity σ1 of three materials behaving as electron spin liquids: EtMe (a), AgCN (b), and CuCN (c). The red and blue curves correspond to temperatures of 200 and 5 kelvins, respectively. Each inlay illustrates the structure of the corresponding spin liquid. Credit: A. Pustogow et al./Nature Materials
The team plotted the points derived from the experiments on a phase diagram shown in figure 2. The horizontal axis corresponds to the ratio U/W, that is, the potential energy of electron-electron repulsion over the kinetic energy of a moving electron. A ratio T/W is on the vertical axis, where T is the temperature of the material. The diagram shows the so-called quantum Widom line, which separates the Mott insulator and the conductor phases. By tracking the values of the parameters as the temperature was lowered, the physicists pinpointed the moment when each of the three spin liquids made the transition to a Mott insulator. They found that the experimentally plotted Widom line agrees with the theoretical predictions within the margin of error of the experiments.
Figure 2. Points corresponding to the transitions of spin liquids from a conductor to a Mott insulator. The data on EtMe is given by the black diamonds, whereas AgCN and CuCN are shown as red circles and blue squares, respectively. The region enclosed by the dotted lines shows experimental uncertainty area. The experimentally plotted Widom line separates the white and the colored regions. Credit: A. Pustogow et al./Nature Materials
The physicists have thus for the first time experimentally observed the Mott transition in its pristine state. Furthermore, by experimenting with CuCN, they detected a state with metallic quantum fluctuations close to the border separating the two phases, which had not been observed before due to magnetic ordering.
This research will help develop electronic components with new properties.