May 19, 2021 — Scientists have long been trying to understand the behavior of superconductors, materials that have zero electrical resistance when they reach sufficiently low temperatures. Superconductors might be useful for technologies such as magnets for MRIs, fusion devices, and particle accelerators. To understand superconductors, one concept is pivotal: phonons, which are quantum waves of vibrational motions of atoms in a material.
Just as photons are the smallest units of light, phonons are the smallest units of energy from vibrational motion. As negatively charged electron particles flow through metals, they may bump into phonons, leading to electrical resistance. On the other hand, phonons can also glue pairs of electrons together, leading to superconductivity—known as the phonon mechanism for conventional superconductors.
In the last 35 years, a family of copper-based—or cuprate—unconventional superconductors has puzzled scientists and spurred considerable research interest because the temperature at which these materials become superconductive is much higher than that of conventional superconductors. Their rich, elusive properties also make them unique.
A team led by principal investigator Steven Louie, a computational condensed-matter physicist and senior faculty scientist at Lawrence Berkeley National Laboratory (Berkeley Lab), and Zhenglu Li, a postdoctoral researcher at Berkeley Lab, is studying cuprate superconductors to understand the interactions between electrons and the other particles in these materials. The team performed simulations on the Summit supercomputer at the Oak Ridge Leadership Computing Facility (OLCF) and found that electrons in cuprates interact with phonons much more strongly than was previously thought, leading to experimentally observed “kinks,” or sudden changes, in the relationship between an electron’s energy and the momentum it carries. The team’s study was published in Physical Review Letters.
“People have tried to explain what couples with the electron to give us these kinks,” Li, first author on the paper, said. “This has been a two-decade-old puzzle that has now been clarified with the help of Summit.”
The team determined how to calculate from first principles—or from the basic laws of nature, without fitting parameters to experiments—the correct interaction strength between the electrons and phonons in a material to explain the kink phenomena in photoemission spectroscopy experiments on cuprates. These experiments, which eject electrons from a material using photons, measure the relationships between electrons’ energies and momenta.
“Imagine you’re an experimentalist, and one day you see this new feature that’s a kink,” Louie said. “You want to learn the properties and significance of these kinks, but without knowing their physical origins, you can’t just calculate them. What we’ve done is proposed a mechanism and computational method that explains them.”
Signature ignites a mystery
For the last 20 years, scientists recognized this signature kink in the behavior of cuprate superconductors, signaling that something interacts strongly with electrons in these materials. But just what that something is has been unknown.
To solve the 20-year-old mystery, the Berkeley Lab team performed simulations on Summit and captured the complicated electron interactions and the interactions between the electrons and phonons, performing one of the team’s largest calculations to date. These simulations involved millions of electron states and millions of phonon states, with each state comprising distinct characteristics such as momentum, energy, and velocity.
“We used a crystal array of atoms and computed these interactions at a highly accurate theoretical level,” Li said. “This computation is one of the biggest calculations I have ever done—and likely in this field.”
In some materials, electrons and phonons might interact strongly, whereas in others, their interactions might be weaker.
“As an analogy, if you think of the interaction between two people in a crowded room, the interaction can be diminished or enhanced depending on the situation,” Louie said. “We wanted to know: how does the interaction between phonons and electrons change when these are in a crowded space with lots of other electrons interacting with one another?”
Complex enough for the cuprates
The method allowed the team to determine how one electron interacts with phonons while being affected by all the other electrons, giving the researchers a framework to study the so-called “self-energy” of electrons.
“In previous methods, the electron-phonon interactions were computed with effective interactions corresponding to some averaging,” Louie said. “Our method, based on a quantum many-body theory called the GW approximation, deals with the correlated motion of a specific electron with all others and determines how such a correlated electron bumps into the phonons. The theory is thus more complex mathematically and computationally, but Summit allowed us to make predictions from this method so that we can compare with experiment.”
The team hopes the results will help them better understand the cuprate materials, a fascinating class of high-transition temperature superconductors.
“Just because the kink is there doesn’t mean it is related to or will reveal the mechanism for superconductivity,” Louie said. “But at least we understand the kink, and that might give us some insight into this class of superconducting materials.”
The OLCF is a DOE Office of Science user facility located at DOE’s Oak Ridge National Laboratory.
Related Publication: Zhenglu Li, Meng Wu, Yang-Hao Chan, and Steven G. Louie, “Unmasking the Origin of Kinks in the Photoemission Spectra of Cuprate Superconductors,” Physical Review Letters 126 (2021): 146401, doi:10.1103/PhysRevLett.126.146401.
The work was supported by DOE’s Office of Science through the Theory of Materials Program at Berkeley Lab and by the National Science Foundation. Advanced codes were provided by the Center for Computational Study of Excited-State Phenomena in Energy Materials (C2SEPEM). The Texas Advanced Computing Center (TACC) and National Energy Research Scientific Computing Center (NERSC) provided additional computational resources in this study.
