Solve a superconductivity puzzle with more precise calculations

High-temperature superconducting materials based on copper or cuprates have been known to researchers since the 1980s. Below a certain temperature (approx. -130 degrees Celsius) the electrical resistance of these materials disappears and magnetic flux fields are repelled. However, the basis for this superconductivity continues to be discussed and researched.

“It is widely accepted that conventional superconductors result from the interaction of electrons with phonons, where the phonons pair two electrons as a unit and the latter can travel in a material without resistance,” said Yao Wang, assistant professor of physics and astronomy at Clemson University .

However, strong repulsions between electrons, known as the Coulomb force, have been found in cuprates and are believed to be the cause of this particular high-temperature superconductivity.

Phonons are the vibrational energy produced by oscillating atoms in a crystal. The behavior and dynamics of phonons are very different from those of electrons, and putting these two interacting pieces of the puzzle together has been a challenge.

Writing in the journal in November 2021 Physical Verification LettersWang, along with Stanford University researchers, presented compelling evidence that phonons do indeed contribute to a key feature observed in cuprates, which could point to their indispensable contribution to superconductivity.

The study innovatively considered the forces of electrons and phonons together. They showed that phonons act not only on electrons in their immediate vicinity, but also on electrons that are several neighbors away.

“A key discovery in this work is that electron-phonon coupling creates non-local attractive interactions between neighboring electrons in space,” Wang said. When they used only local coupling, they calculated an attractive force that was an order of magnitude smaller than the experimental results. “That tells us that the longer-range part is dominant, extending up to four unit cells,” or neighboring electrons.

Wang, who led the computational side of the project, used the National Science Foundation (NSF)-funded Frontera supercomputer at the Texas Advanced Computing Center (TACC) — the world’s fastest academic system — to replicate experiments performed at the Stanford synchrotron were carried out radiation light source and presented in science in Sept. 2021 in a simulation.

The results drew not only on Frontera’s super-fast parallel computing capabilities, but also on a new mathematical and algorithmic method that enabled far greater accuracy than ever before.

The method, called variational non-Gaussian exact diagonalization, can perform matrix multiplications on billions of elements. “It’s a hybrid method,” Wang explained. “It treats the electron and the phonon with two different approaches that can adjust to each other. This method works well and can describe strong coupling with high precision.” Method development was also supported by a grant from the NSF.

Evidence of phonon-mediated attraction also has significant implications beyond the realm of superconductors. “In practical terms, the results mean that we found a way to manipulate Coulomb interactions,” Wang said, referring to the attraction or repulsion of particles or objects due to their electrical charge.

“If the superconductivity comes only from Coulomb forces, then we can’t just manipulate this parameter,” he said. “But if part of the reason comes from the phonon, then we can do something, for example by placing the sample on a substrate that changes the electron-phonon interaction. This gives us a direction to develop a better superconductor.”

“This research provides new insight into the mystery of cuprate superconductivity, which can lead to higher-temperature superconducting materials and devices,” said Daryl Hess, program director in NSF’s Materials Science Division. “They could find their way into future mobile phones and quantum computers. A journey started by human creativity, clever algorithms and Frontera.”

Wang and his collaborator Cheng-Chien Chen from the University of Alabama, Birmingham, also applied this new approach and powerful TACC supercomputers to study laser-induced superconductivity. They reported these results in Physical Check X in November 2021. And in collaboration with a team from Harvard, Wang used TACC supercomputers to study the formation of Wigner crystals in a paper published in nature in June 2021.

As in many areas of science, supercomputers are the only tool that can study quantum behavior and explain the underlying phenomena.

“In physics we have very nice frames to describe an electron or an atom, but when we talk about real materials with 10²³ Atoms, we don’t know how to use these beautiful frameworks,” Wang said.

Especially with quantum or correlated materials, physicists have had a hard time applying “beautiful” theories. “Instead, we use ugly theories – numerical simulations of the materials. Although we do not yet have an established quantum computer, we can use classic high-performance computers to push the problem forward. Ultimately, this will guide the experiment.”

Wang is currently working with IBM and IonQ to develop quantum algorithms for testing on current and future quantum computers. “Supercomputing is our first step.”

When it comes to major future developments in technology, Wang believes that computational studies combined with experiments, observations and theories will help unravel mysteries and achieve practical goals such as tunable superconducting materials.

“A new algorithm can make a difference. More numerical precision can make a difference,” he said. “Sometimes we don’t understand the nature of a phenomenon because we haven’t looked closely enough at the details. Only when you press the simulation and zoom in to the nth place does an important aspect of nature become visible.”