# A universal tool for the measurement of electron−phonon coupling in conducting low-dimensional systems

Superconductivity is a physical phenomenon in which some materials exhibit zero electrical resistance when cooled down below a certain critical temperature. As surprising as it can be, the critical temperature of these materials can be modified by reducing the sample size to about a million times the size of the objects we are used to handling every day.

Superconductivity is caused by the interactions between atomic vibrations (phonons) and electrons in a lattice. The interaction strength is determined by something called the electron-phonon coupling constant. Determining how this interaction changes as a function of size allows us to determine how the critical temperature changes with size too. In the limit, we face the case of reduced dimensions, from the everyday 3D to 2D or less when the size of our sample is very small. Thus, knowledge of the electron−phonon interaction at conducting surfaces and the specific role of dimensionality are of great relevance both from a fundamental point of view and for various applications, such as 2D and quasi-1D superconductivity in nanotechnology.

Similarly, the electron−phonon interaction plays a relevant role in other transport properties, e.g., thermoelectricity, in low-dimensional systems such as layered Bi and Sb chalcogenides and in quasi-crystalline materials which are often viewed as periodic solids in higher dimensions.

In a series of recent experimental and theoretical works, it was shown that the electron−phonon coupling constants both for individual phonons and their average (also known as the mass-enhancement parameter or factor) can be measured directly with helium atom scattering. In the case of multilayer metallic structures, this technique can detect subsurface phonons as deep as those that contribute to the electron−phonon interaction. For example, phonons spanning as many as 10 atomic layers in Pb films can be detected this way (by the way, this is called quantum sonar effect), thus providing the individual values for the phonons that contribute the most to the average. The values of this average obtained from helium atom scattering generally are close to the most reliable values found in the literature.

Now, a team of researchers has investigated ^{1} the specific role of dimensionality in the electron−phonon mass-enhancement factor as derived from helium atom scattering. They show that the theory linking this factor to the thermal attenuation of atom scattering spectra (the Debye−Waller factor) can be applied to topological semimetal surfaces.

The method is shown to be particularly suitable for different classes of conducting 2D materials, such as the layered chalcogenides, topological insulators, and systems characterized by a quasi-1D free electron gas, including Bi(114). The present analysis shows that the charge density wave transition in Bi(114), recently observed with helium atom scattering, is sustained by multivalley electron−phonon interaction with a pronounced 1D character.

In the case of topological materials, the researchers show that the analysis of previous helium atom scattering data on Bi_{2}Te_{3}(111) and Bi_{2}Se_{3}(111) as well as new experimental data on Bi_{2}Te_{2}Se(111) indicates the overwhelming contribution to the electron−phonon mass-enhancement factor from the surface quantum well states as compared to that of the Dirac states.

This extension from metal surfaces and thin metal films to topological semimetal surfaces qualifies helium atom scattering as a universal tool for the measurement of electron−phonon coupling in conducting low-dimensional systems.

*Author: César Tomé López is a science writer and the editor of Mapping Ignorance*

*Disclaimer: Parts of this article may be copied verbatim or almost verbatim from the referenced research paper.*

## References

- Giorgio Benedek, Salvador Miret-Artés, J. R. Manson, Adrian Ruckhofer, Wolfgang E. Ernst, Anton Tamtögl (2020) Origin of the Electron–Phonon Interaction of Topological Semimetal Surfaces Measured with Helium Atom Scattering
*J. Phys. Chem. Lett.*doi: 10.1021/acs.jpclett.9b03829 ↩