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Winter 2019

Crunching Numbers

How supercomputers are driving superconductor research

James Furness

The Cori supercomputer at the National Energy Research Scientific Computing Center (NERSC) uses almost 700,000 processors to perform around 30 quadrillion (30,000,000,000,000,000) operations a second and is the size of a small warehouse! Credit: NERSC

If you walked the halls of the Energy Frontier Research Centers (EFRCs), you might hear a common tone: the whirring of supercomputers tirelessly running complex simulations. Supercomputers are used across the centers to study a wide variety of problems. They model spin-forbidden reactions, visualize lithium battery processes, analyze plant cell wall components, and predict the effects of radiation on materials, as well as many other things. In this article, we will dive into how researchers at one center—the Center for Complex Materials from First Principles (CCM)—are using supercomputers to help discover the electrical materials of tomorrow.

The anatomy of a supercomputer

What is a supercomputer and what makes it different from the computer you are reading this article on? A supercomputer is a collection of thousands of smaller computers working in parallel. Your computer can do about four billion mathematical operations per second, one after another. A supercomputer performs many more operations simultaneously by giving small pieces of calculations to thousands of smaller computers. In this way, supercomputers carry out trillions (or quadrillions!) of operations per second. So it’s not that a supercomputer can do things your common computer can’t, it just does a lot of things at the same time for a massive speed up. In this way, much like a shoal of hungry piranha, a lot of small mouths quickly devour an unlucky explorer.

Researchers use supercomputers to run simulations of physical problems and examine the results to help them understand traditional experiments. To see how simulations help, imagine playing a game of pool after a long day in the lab. Think about the core problem you face: each turn you must select the best shot from the many you could take. How could a supercomputer help? Well, one strategy is to write equations to describe how the balls interact on the table. Then you could write a computer program to solve those equations and simulate every possible shot. Now that you know all the possibilities, you can choose the best one.

A single computer would run the simulation of each shot one after another. However, this might take so long that your opponent becomes bored and wanders off. This is where the power of a supercomputer comes in. On a supercomputer, the program is split into small parts that are distributed to the many processors to be solved all at the same time. Now you only have to wait for the slowest of the small parts to get your answer.

Using simulations to quickly identify candidates from a big set of possibilities has produced astounding breakthroughs. However, that is only one way computer simulations help to solve research problems.

New materials often have exciting properties, but scientists are unable to explain why the material has these properties. This makes designing new materials with the desired property difficult. In many cases, even the best experimental instruments cannot measure the subtle interactions responsible for the property. Scientists can use simulations on supercomputers to better examine these hidden interactions.

Simulating superconductors


The superconductor was discovered in 1911 when solid mercury was cooled down to 4 Kelvin, that’s a frosty -452 degrees Fahrenheit. The cause of superconductivity was a mystery until the 1950s, when the Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity brought about two conclusions. First, superconductivity is the result of unbreakable attractions between pairs of electrons. Second, superconductivity was predicted to be impossible at temperatures warmer than ~30 Kelvin (-405 degrees Fahrenheit).

The BCS theory confined superconductor technologies to science fiction. So it was until a chain of discoveries smashed through the 30 Kelvin limit. These discoveries blew the doors to superconductor technologies back open and a frenzy of excitement followed, including the now infamous “Woodstock of Physics” session at the American Physical Society Meeting in 1987 where a number of researchers presented work on the new class of superconducting materials that function at temperatures upwards of 90 Kelvin.

Was BCS theory wrong? Well … no. It correctly explained the materials that were known at the time (now called “conventional” superconductors). Despite intense research, scientists still don’t know what allows modern “high-temperature” superconductors to break this limit and that’s hugely exciting! The new upper limit on temperature (if any) is waiting to be found! Credit: James Furness, CCM EFRC

The power of supercomputer simulations has been proving essential for the CCM’s work in understanding high-temperature superconductivity. A superconductor is a material through which electricity can flow without any electrical resistance. This means no matter how much electrical current is pushed through it, no energy is lost as heat. Such materials present many exciting possibilities! The copper wires in power lines could be replaced with superconductors; then, electricity could be transported across great distances with ease. Superconductors also come with exotic magnetic properties vital to high-speed levitating trains, medical scanners, super-efficient electric motors, and many other high-tech wonders.

An explanation for high-temperature superconductivity has remained elusive. This is in part because measuring the microscopic behavior of electrons in superconductors is extremely difficult. It’s here that computer simulations, and the ability to perfectly examine every component of them, are proving essential. Creating and applying such simulations is an important focus at the CCM.

The complete behavior of electrons in any material, including high-temperature superconductors, is (almost) perfectly described by the laws of quantum mechanics. Unfortunately, the exact equations of quantum mechanics are simple on paper but impractical to solve for more than a few electrons. The computer time needed to exactly simulate a collection of electrons grows much faster than the number of electrons being simulated. For example, a computer that takes one second to simulate a single electron, takes 42 days to simulate ten electrons. Simulating a hundred electrons would take many, many times longer than the lifetime of the sun! Exactly modeling the 1987 breakthrough high-temperature superconductor requires simulating at least 180 electrons. This would need a program so complex that if the Cori supercomputer at National Energy Research Scientific Computing Center was left running until the sun burns out, it would barely have made a start.

An exact simulation is obviously impossible. Instead it comes down to physicists to carefully work out short-cuts and approximations. Some parts of the quantum mechanics can be safely ignored, while others are important to simulate. In this way, researchers at the CCM are building approximate simulations that are fast to compute while remaining accurate to the real physics.

The new model: Accuracy at low cost

One of the key outcomes of the Center for Computational Design of Functional Layered Materials, a previous incarnation of the CCM, was the SCAN density functional. It is a new simulation technique that can be run efficiently on supercomputers whilst keeping useful accuracy. Researchers at the center extensively tested this technique, which was developed with National Science Foundation support in 2015.

Recently, researchers at the CCM applied this technique to simulate the electrons in copper-oxide high-temperature superconductors. Very large changes in the electron behavior of these superconductors are caused by very small changes in material, presenting a significant challenge to most approximate simulations. Particularly important is the change in copper oxides from electrical insulators, when pure, to regular conductive metals with enough impurities. Previous approximate simulations have either failed to reproduce this transition or remained too slow to be useful. When researchers at the CCM ran simulations using the SCAN density functional, however, it reproduced this transition, proving SCAN a truly useful breakthrough method.

Following this exciting result, they used SCAN simulations to perform an in-depth study of the microscopic magnetic behaviors of copper-oxide superconductors and help understand the pure material’s electrical insulator properties. They are also investigating other high-temperature superconductors built from a diverse range of elements. The success of these simulations gives researchers a powerful new tool in the quest towards unravelling the mystery of high-temperature superconductivity.

Whether identifying and designing new technologies or unravelling long-standing mysteries, the information revolution has changed the way basic energy research is done. The huge computing power has rendered previously unthinkable simulations routine and helped push the rate of materials innovation ever faster. Problems like high-temperature superconductivity that previously seemed impossible are rapidly being brought to heel.

More Information

Furness JW, Y Zhang, C Lane, IG Buda, B Barbiellini, RS Markiewicz, A Bansil, and J Sun. 2018. “An Accurate First-Principles Treatment of Doping-Dependent Electronic Structure of High-Temperature Cuprate Superconductors.” Communications Physics 1(11):1. DOI: 10.1038/s42005-018-0009-4

Lane C, JW Furness, IG Buda, Y Zhang, RS Markiewicz, B Barbiellini, J Sun, and A Bansil. 2018. “Antiferromagnetic Ground State of La2CuO4: A Parameter-Free Ab Initio Description.” Physical Review B 98(12):125140. DOI: 10.1103/PhysRevB.98.125140

Acknowledgments

Furness et al. The work at Tulane University was supported by the start-up funding from Tulane University and by the U.S. Department of Energy (DOE), Office of Science, Energy Frontier Research Centers (development and applications of density functional theory): Center for the Computational Design of Functional Layered Materials. The work at Northeastern University was supported by the DOE, Office of Science, Basic Energy Sciences (core research) and benefited from Northeastern University’s Advanced Scientific Computation Center, the DOE National Energy Research Scientific Computing Center and support (testing the efficacy of new functionals in diversely bonded materials) from the DOE Energy Frontier Research Centers: Center for the Computational Design of Functional Layered Materials.

Lane et al. This work was supported (testing efficacy of new functionals in complex materials) by the U.S. Department of Energy (DOE), Office of Science, Energy Frontier Research Centers: Center for the Computational Design of Functional Layered Materials. The work at Northeastern University was also supported by the DOE, Office of Science, Basic Energy Sciences (core research) and benefited from Northeastern University's Advanced Scientific Computation Center, DOE’s National Energy Research Scientific Computing Center. The work at Tulane University was also supported by the startup funding from Tulane University. B.B. acknowledges support from the COST Action.

About the author(s):

  • James Furness is a postdoctoral research fellow in the Department of Physics at Tulane University, New Orleans. He works in collaboration with researchers at Northeastern University in Boston and Temple University in Philadelphia as part of the Center for Complex Materials from First Principles (CCM), an Energy Frontier Research Center, to design new density functionals for use in modeling materials with applications in energy science (and quantum chemistry more generally).

More Information

Furness JW, Y Zhang, C Lane, IG Buda, B Barbiellini, RS Markiewicz, A Bansil, and J Sun. 2018. “An Accurate First-Principles Treatment of Doping-Dependent Electronic Structure of High-Temperature Cuprate Superconductors.” Communications Physics 1(11):1. DOI: 10.1038/s42005-018-0009-4

Lane C, JW Furness, IG Buda, Y Zhang, RS Markiewicz, B Barbiellini, J Sun, and A Bansil. 2018. “Antiferromagnetic Ground State of La2CuO4: A Parameter-Free Ab Initio Description.” Physical Review B 98(12):125140. DOI: 10.1103/PhysRevB.98.125140

Disclaimer: The opinions in this newsletter are those of the individual authors and do not represent the views or position of the Department of Energy.