A team led by Zhi-Xun Shen at Stanford University has developed an experimental technique that precisely measures electron-phonon coupling in iron selenide (FeSe), a superconductor. This work, published recently in Science, will help researchers understand the interactions that influence properties especially of quantum materials.

Quantum materials, such as superconductors, defy conventional understanding of matter. For many materials, researchers use density functional theory (DFT) to calculate the energy levels and properties of a substance from its chemical structure and bonding. Computational methods struggle to accurately calculate the properties of unconventional quantum materials, where interactions between different electrons (electron-electron coupling) or electrons and the lattice of the solid (electron-phonon coupling) play a role. “It’s a question that’s been around for a long time, and there’s no real answer to [it],” Shen says, “because it’s too complicated of a problem.” The magnitude of the electron-electron or electron-phonon coupling in a material can be deduced from the size of the corrections included in DFT calculations to match the bulk properties. A direct experimental measurement of the electron-electron or electron-phonon coupling would provide a benchmark for these corrections.

To measure the electron-phonon coupling, Shen’s team combined two extremely difficult techniques: time-resolved x-ray diffraction (trXRD) and time-resolved angle-resolved photoemission spectroscopy (trARPES). These experimental methods allowed the researchers to track both the displacement of the selenium atoms, δz_Se, using trXRD, and the electronic energy levels, using trARPES, immediately after excitation of a coherent lattice oscillation, or phonon. Shuolong Yang, a graduate student during the project who is currently working as a Kavli postdoctoral fellow at Cornell University, led the trARPES studies. They also collaborated with Robert Moore, assistant director of SIMES, to make the superconducting samples. By comparing the amplitude of the oscillations in the trXRD and trARPES data, Shen calculated the electron-phonon coupling.

“The virtue of [this] experiment is that it is the most direct and most unambiguous measurement of the electron-phonon coupling,” says Dung-Hai Lee of the University of California, Berkeley. Lee was not connected with this work.

“In this work, we measured the electron-phonon coupling in a complex material very precisely,” says Patrick Kirchmann, a staff scientist at the Stanford Institute for Materials and Energy Sciences (SIMES) at the Stanford Linear Accelerator Center (SLAC) National Laboratory and a member of Shen’s experimental team. Kirchmann and Shen used the lock-in method, where a small signal is stabilized to a reference wave to filter out noise. This method allowed the team to measure the atomic displacement with a precision of 0.001 Å (10^-10 m) and an energy level shift of 1 meV, Shen says.

Shen’s team then compared their experimentally determined electron-phonon coupling strengths to those used in theory for FeSe. The electron-phonon coupling strength calculated by standard DFT methods mentioned previously was off by a factor of ten—demonstrating that the strength of the electron-phonon coupling had been greatly underestimated. Shen’s results were in agreement with previous theoretical work published in Physical Review B that included both the electron-phonon and electron-electron coupling. Shen sees this as confirmation that both quantities play an interconnected role in the superconductivity of FeSe.

In the future, Shen and Kirchmann want to apply this technique to study fundamental properties of novel exotic materials. Some interesting materials could be superconductors that have similar coherent lattice motion, such as materials in the cuprate family, Kirchmann says. “We are hoping to develop this as a tool to calibrate the development and advancement of a more sophisticated many-body theory for quantum materials,” Shen says. Their efforts will be used to form a more complete theoretical framework to predict properties of materials before they are observed in the laboratory. 

Read the abstract in Science.