In metals, the outermost electrons of atoms are not bound tightly to the nuclei of the atoms that make up a rigid crystal lattice, allowing them to move freely within it. It is this property that gives metals their electrical conductivity, thermal conductivity, magnetism, and superconductivity.

Usually, these electrons are uniformly distributed, but in some metals, due to the quantum mechanics, electrons behave more like waves with periodic patterns, forming what physicists call a charge density wave.

When not subjected to any external influence, the charge density wave does not change with time and appears “frozen”. However, if the wave is disturbed — for example, by irradiating the material with light — then it begins to “move”, such that both its amplitude and phase start to oscillate.

Classically, this behavior looks like a continuous change in charge density, but quantum mechanics claims that any collective excitation is not smooth and should be described as the dynamics of discrete portions of energy called quasiparticles. The name indicates that they are not the same as fundamental elementary particles, such as electrons and protons.

The best-known example of this is phonons, the quanta or discrete energy unit of compression waves associated with the propagation of sound in solids. The physics of charge density waves is similar to that of sound waves in that their dynamics is also best described in terms of dynamic quasiparticles, which in case of fluctuations in the phase of a charge density wave are called phasons.

Measuring “massive” phasons

These quantum quasiparticles are usually massless, like particles of light, but more than 45 years ago, two physicists named Patrick Lee and Hidetoshi Fukuyama at Bell Laboratories in the US predicted that in some materials with very low free electron density, phasons could acquire mass.

This happens because these materials contain a small number of free electrons, which means that compared to other materials with high electron densities, fewer electrons are around to shield each other’s electromagnetic fields, leading to the emergence of a long-range Coulomb interaction, which allows phasons to interact quite intensively with the crystal lattice. This interaction is in many ways similar to the interaction between elementary particles and the Higgs field whose quanta are well-known Higgs bosons.

Until recently, scientists were unable to observe massive phasons due to difficulties in obtaining a suitable material. But in a new study published in Nature Materials, a team of physicists have finally managed to observe this quasiparticle.

The group led by Fahad Mahmood and Soyeun Kim at the University of Illinois at Urbana-Champaign studied an insulator with a low concentration of free electrons called tantalum selenium iodide, in which a phason with a mass was expected to form if the temperature of the material was sufficiently low.

The physicists exposed thin needles of the material cooled to around 7 degrees Kelvin (roughly -260℃) to an ultrafast pulse of infrared radiation lasting less than 150 femtoseconds and studied its response to this influence. What they observed was the emission of electromagnetic waves of a very special kind whose properties corresponded to the excitation of a charge density wave in the form of a phason with mass.

“It is gratifying to see that a collective mode predicted many years ago is finally seen experimentally,” said Patrick Lee, who is currently the William & Emma Rogers Professor of Physics at MIT. “It speaks to the power of modern nonlinear optical techniques and the ingenuity of the experimentalists. The method is general, and we may see applications to other collective modes as well.”

Confirming theory

Theory states that as the temperature of the sample rises, the phason should lose mass. The scientists tested this prediction too and found that it was correct — the phason did become massless as the temperature rose.

“This is the first known demonstration of a massive phason in a charge density wave material and settles the long-standing question of whether a charge density wave phason acquires mass by coupling to long-range Coulomb interactions,” said Mahmood, who summarized the results of the study in a press release.

“This is a major result that will have a profound impact on the field of strongly correlated materials, and in the understanding of the interplay between interactions, density-wave ordering and superconductivity in materials,” he continued.

In addition to the importance of this result from the point of view of fundamental science, the authors note that it could also find practical application. The spectrum of radiation emitted by a material in response to an infrared pulse is very narrow, occurring at an average frequency of about a terahertz, making tantalum selenium iodide an excellent source of coherent terahertz radiation used, for example, in spectroscopy.

Reference:  Soyeun Kim, et al, Observation of a massive phason in a charge-density-wave insulator, Nature Materials (2023). DOI: 10.1038/s41563-023-01504-5

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