Energy, Physics
July 2015

When electrons cooperate

University of Illinois physicists apply supercomputing to explore unconventional, high-temperature superconductivity.

The spin density of iron selenide, an unconventional superconductor, as calculated with quantum Monte Carlo. The yellow signifies regions in which electron spins are pointing up; the blue regions have electron spins pointing down. Gray is the cutoff of periodic boundary conditions. It is likely that the behavior of these spins aid in creating a superconducting state. Image courtesy of Brian Busemeyer, University of Illinois.

Remaining uncertainties in the century-plus effort to explain superconductivity and advance its applications has a University of Illinois team of physicists using advanced computing to grease the skids for its high-temperature variant.

It’s been a research target since 1911, when a Dutch physicist discovered that electricity could flow with no resistance in metallic mercury while also elevating magnetic fields above the metal’s surface. Dreams of levitating trains and super-efficient power delivery arose – and then evaporated because of one big hitch: The effect could only occur, at least back then, at the temperature of liquid helium – negative 268.8 Celsius.

It wasn’t until 1957 that three scientists finally posited an acceptable explanation for how a growing list of such very-low-temperature superconductors functioned. The trio won a Nobel Prize for their research.

“Somewhat magical quantum mechanics happens,” says Lucas Wagner, an assistant research professor of physics at Illinois’ Urbana-Champaign campus and leader of an investigation on Mira, Argonne National Laboratory’s IBM Blue Gene/Q supercomputer.

In 1986, two IBM researchers in Switzerland joined the Nobel-for-superconductivity club. They’d identified a barium-doped ceramic of lanthanum and copper oxide that could superconduct at a comparatively balmy -238 C. It was deemed the first of several high-temperature, or high-Tc, superconductors.

Some high-Tc materials can superconduct at temperatures warmer than the boiling point of liquid nitrogen – negative 196 C. Although that’s still frigid, liquid nitrogen would be far less expensive than the liquid helium used to chill standard superconductors in devices like high-energy particle accelerators and magnetic resonance imaging (MRI) magnets. “Liquid nitrogen’s costs are like Coca Cola’s, and liquid helium is at least 10 times more – one reason why your MRI is so expensive,” Wagner says.

Researchers began fabricating a second group of unconventional superconductors that contained iron rather than copper.

Older kinds of superconductors have indeed entered the marketplace, but high-Tc substitutes are proving difficult to fabricate, unable to handle high currents, and – most important from Wagner’s perspective – much harder to understand than the low-temperature versions.

The scientifically accepted BCS theory (named for initials of the Nobel laureates’ last names) only applies to conventional low-temperature superconductivity, says Wagner, an expert at simulating the effects of quantum mechanics using petaflops supercomputers such as Mira.

BCS explains how electrons, when sufficiently chilled, can coordinate with each other even though their mutual negative charges would normally repel. Guided by the strange rules of quantum mechanics, some of these electrons interact with their own crystal lattices to generate phonons, a kind of vibrational energy.

Each phonon-electron team-up then attracts one additional electron to form a so-called Cooper Pair. The resulting swarms of two-electron Cooper pairings enables current to flow without resistance and magnetic fields to levitate, even while all electrons in the superconducting material remain free to move.

But Wagner and other researchers consider high-Tcs unconventional because they “don’t fit into the conventional understanding of how superconductors work,” he says. Whereas Cooper Pairs can explain conventional superconductivity, “in the unconventional ones we don’t really know.” He suspects, however, electron cooperation is still involved.

His interest was piqued only after 2008, when researchers began fabricating a second group of unconventional superconductors that contained iron rather than copper “to make a fairly high-temperature superconductor, “ Wagner recalls. “Not quite as high as copper but pretty high.”

After structurally analyzing the two groups, he concluded at the time that they looked like they had little in common. Still, he thought there had to be some common thread. In fact, both share what he calls “strongly correlated” electrons. That “doesn’t necessarily have anything to do with superconductivity,” he adds, but “it’s when one lone electron cares about what the others are doing.”

As a graduate student at North Carolina State University from 2002 to 2006, Wagner helped beef up an older quantum mechanics computer modeling program his group renamed QWalk. The open-source code uses Monte Carlo algorithms, which take repeated random samplings of the unfolding data, and “is specifically written to run on the leadership-class Blue Gene machines available at Argonne and other DOE facilities,” he says.

QWalk’s initial focus was correlated electrons, which Wagner calls one of two big challenges in condensed matter physics. The other is the explanation for high Tc. “We have two big problems, and maybe they are coming together” in these iron- and copper-based unconventional superconductors, he says.

As principal investigator of a project using 166 million processor hours on Mira at Argonne’s Leadership Computing Facility, Wagner has proposed using QWalk to simulate the behavior of “correlated electrons for superconducting materials.” Working with about seven students and postdoctoral researchers under the DOE Office of Science Innovative and Novel Computational Impact on Theory and Experiment (INCITE) program, he aims “to completely characterize, for the first time, the electronic structure of unconventional superconductors.”

At the time he received his Ph.D., “computers were not as strong as they are now,” Wagner says. “Now our programs have also gotten better, so suddenly we’re able to apply much more accurate and powerful techniques to this problem.”

As part of this work, he’ll “use the computing power of Mira to solve the Schrödinger equation with unprecedented accuracy for high-temperature superconductors.” Schrödinger is the master equation for quantum mechanics, but “the trick is that it is difficult to solve,” Wagner says. “If I want to describe a bunch of electrons that get together and behave quantum mechanically, that’s a very difficult problem.”

Wagner says his group is also a “small part” of a Brookhaven National Laboratory-based Energy Frontier Research Center – the Center for Emergent Superconductivity. That larger collaboration’s stated mission is “to advance the frontier of understanding and control of the materials, mechanisms and critical currents of superconductors, including existing and new materials.”